De invoegtoepassing MS Mathematics
Paul Verheyen, Generated with
chmProcessor
<div class="WordSection1"> <p style="TEXT-ALIGN: center; MARGIN-LEFT: -1cm" class="MsoNormal" align="center"><b><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 24pt">De invoegtoepassing Microsoft Mathematics in Word 2007 en 2010 (Engelstalig)</span></b></p> <h1><a name="collegealgebrasolve" id= "collegealgebrasolve"></a><a name="_Toc307065924">Gelijkheden in één variabele / Ontbinden in factoren</a></h1> <h2><a name="_Toc307065925">Oplossen van een eerstegraadsvergelijking</a></h2> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image001.png" width="75" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal">Rechtsklik op de vergelijking en kies <span style="FONT-FAMILY: 'Calibri','sans-serif'">Compute</span> > <span style="FONT-FAMILY: 'Calibri','sans-serif'">Solve for x</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image002.jpg" width="356" height="390" alt= "image"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Dit geeft</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image003.png" width="53" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Je kan ook in het <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Lint</span> kiezen voor het tabblad <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Mathematics</span> en <span style="FONT-FAMILY: 'Calibri','sans-serif'">Solve for x</span>:</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image004.jpg" width="367" height="203" alt= "image"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <h2><a name="_Toc307065926">Oplossen van een tweedegraadsvergelijking in</a> <span style= "FONT-FAMILY: 'Cambria Math','serif'">ℝ</span></h2> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image005.png" width="111" height="22" alt="image"></span></p> <p class="MsoNormal">kan je analoog oplossen:</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image006.png" width="113" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">of in de Nederlandstalige versie</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Afbeelding 100" alt="m01.jpg" src= "MSMath_files/image007.jpg" width="168" height="59" name= "Afbeelding 100"></p> <p class="MsoNormal"><span lang="NL-BE">Voor</span> <span style= "FONT-FAMILY: 'Cambria Math','serif'" lang="NL-BE"><br> </span><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image008.png" width="111" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">bekom je analoog</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image009.png" width="211" height="43" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">Wanneer je rechts klikt op de uitdrukking</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image010.png" width="68" height="43" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">en je selecteert</span> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "NL-BE">Compute > Calculate</span> <span lang="NL-BE">krijg je een numerieke benadering</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image011.png" width="139" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Door te werken met het</span> commando <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> solve</span></span><span lang="NL-BE">, syntax</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "NL-BE">solve(equation,variable)</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">bekom je na</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Compute > Calculate</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image012.png" width="177" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image006.png" width="113" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">Numeriek oplossen</span></span> <span lang="NL-BE">kan met</span> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> nsolve</span></span><span lang="NL-BE">, syntax</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "EN-US">nsolve({equation},{variable})</span></p> <p class="MsoNormal"><span lang="EN-US">of</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "EN-US">nsolve({equation},{variable,varminimum,varmaximum})</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "EN-US"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">Zo leidt</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image013.png" width="211" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">tot</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image014.png" width="349" height="22" alt="image"></span><span lang="NL-BE">.</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <h2><a name="_Toc307065927">Oplossen van een tweedegraadsvergelijking in</a> <span style= "FONT-FAMILY: 'Cambria Math','serif'">ℂ</span>  </h2> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Bij de voorkeuren dien je in te geven of je met reële of complexe getallen wil werken:</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image015.jpg" width="576" height="128" alt= "image"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Je kan hier ook bepalen hoeveel decimalen je wil tonen en hoe je hoeken meet.</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Met de optie</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Complex</span> <span lang="NL-BE">vind je voor</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image016.png" width="74" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image017.png" width="124" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">terwijl met de optie</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Real</span> <span lang="NL-BE">de boodschap</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image018.png" width="368" height="126" alt= "image"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">verschijnt.</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <h2 style="TEXT-ALIGN: left" align="left"><a name= "_Toc307065928"><span lang="NL-BE">Oplossen van een veeltermvergelijking met graad groter dan 2</span></a></h2> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image019.png" width="150" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">heeft als oplossingen</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image020.png" width="175" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Voor</span> <span style= "FONT-FAMILY: 'Cambria Math','serif'" lang="NL-BE"><br> </span><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image021.png" width="150" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">bekom je als reële oplossingen</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image022.png" width="175" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">en als complexe oplossingen</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image023.png" width="421" height="43" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <h2><a name="_Toc307065929"><span lang="NL-BE">Ontbinden in factoren</span></a></h2> <p class="MsoNormal"><span lang="NL-BE">Door rechts te klikken op een veeltermuitdrukking zoals</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image024.png" width="81" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US">kan je ontbinden in factoren</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image025.jpg" width="433" height="169" alt= "image"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">wat leidt tot</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image026.png" width="104" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US"> </span></p> <p class="MsoNormal">Deze ontbinding wordt enkel over <span style= "FONT-FAMILY: 'Cambria Math','serif'">ℝ</span> uitgevoerd: voor</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image027.png" width="121" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">bekom je als ontbinding</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image028.png" width="201" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US">De ontbinding in factoren van</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image029.png" width="142" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">is</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image030.png" width="158" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h2><a name="_Toc307065930"><span lang="EN-US">Uitwerken van een product</span></a></h2> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image028.png" width="201" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image031.jpg" width="413" height="158" alt= "image"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <h2><a name="_Toc307065931"><span lang="EN-US">Uitwerken van een uitdrukking</span></a></h2> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image032.png" width="228" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">geeft</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image033.png" width="121" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">via</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 19" src="MSMath_files/image034.jpg" width="365" height="140" alt="image" name="Picture 19"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">De invoegtoepssing kan als het ware gebruikt worden als een “rekenmachine” via</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Compute</span> <span lang="NL-BE">></span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Calculate (in feite</span> <span lang="NL-BE"> </span><span style= "FONT-FAMILY: 'Calibri','sans-serif'">Lint > Mathematics > Mathematics ></span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'"><span lang= "NL-BE">Compute</span></span> <span lang="NL-BE">></span> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "NL-BE">Calculate</span><span lang="NL-BE">)</span><span lang= "NL-BE">:</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image035.png" width="19" height="24" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image036.png" width="127" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Het aantal getoonde cijfers na het decimaalteken wordt bepaald via</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang="EN-US">Lint > Mathematics > Mathematics > Decimal places</span><span lang="EN-US">.</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "Z-INDEX: 7; POSITION: absolute; MARGIN-TOP: 64px; WIDTH: 127px; HEIGHT: 33px; MARGIN-LEFT: 200px; LEFT: 0px"> <img src="MSMath_files/image037.png" width="127" height="33" alt= "image"></span><img src="MSMath_files/image038.jpg" width="215" height="118" alt="image"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="NL-BE">Je moet wel als decimale teken een punt gebruiken en geen komma!</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image039.png" width="28" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image040.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <h2><a name="_Toc307065932">Oplossen van rationale vergelijkingen</a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image041.png" width="165" height="41" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">heeft als oplossing</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image042.png" width="51" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h2><a name="_Toc307065933">Ontbinden in factoren van rationale uitdrukkingen</a></h2> <p class="MsoNormal">Voor</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image043.png" width="135" height="41" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">bekom je</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image044.png" width="161" height="41" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">Om ook de noemer te ontbinden, moet je deze apart plaatsen en ontbinden in factoren:</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image045.png" width="65" height="22" alt="image"></span></p> <p class="MsoNormal">om tot <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image046.png" width="70" height="22" alt="image"></span><span lang="EN-US"> </span>te komen.</p> <p class="MsoNormal"> </p> <h2><a name="_Toc307065934">Symbolische berekeningen</a></h2> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image047.png" width="119" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 22" src="MSMath_files/image048.jpg" width="422" height="122" alt="image" name="Picture 22"></p> <p class="MsoNormal"><u><span lang="EN-US"><span style= "TEXT-DECORATION: none"> </span></span></u></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt" lang="EN-US">Solve for x</span></span> <span lang= "EN-US">geeft:</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image049.png" width="533" height="137" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">en bv. </span> <span class= "Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt" lang="EN-US">Solve for a</span></span> <span lang= "EN-US">geeft</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image050.png" width="237" height="77" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p class="MsoNormal"><u><span lang="EN-US"><span style= "TEXT-DECORATION: none"> </span></span></u></p> <h2><a name="_Toc307065935">Goniometrische vergelijkingen</a></h2> <p class="MsoNormal">Enkel wanneeer je radialen gebruikt om hoeken te meten, kan je bv.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image051.png" width="72" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">oplossen:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image052.png" width="245" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">wat in feite betekent</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image053.png" width="224" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h2><a name="_Toc307065936">Logaritmische en exponentiële vergelijkingen</a></h2> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image054.png" width="93" height="22" alt="image"></span>   geeft  x<span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image055.png" width="60" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image056.png" width="47" height="22" alt="image"></span>   leidt tot  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image057.png" width="65" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image058.png" width="55" height="22" alt="image"></span>     <span style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image059.png" width="60" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image060.png" width="55" height="22" alt= "image"></span><i>      </i> geeft<i>  </i> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image061.png" width="232" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <i> </i></p> <h2><a name="_Toc307065937">Waarschuwing</a></h2> <table style= "BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" class="MsoTableGrid" border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 104.65pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm" valign="top" width="140"> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style="FONT-SIZE: 11pt"><img id= "Picture 104" alt= "Thumbnail of file:///C:/Users/Paul/Pictures/0/Steren_Warning.png" src="MSMath_files/image062.png" width="97" height="89" name= "Picture 104"></span></p> </td> <td style= "PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 306.2pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm" valign="top" width="408"> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "FONT-SIZE: 11pt">De vergelijking</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image063.png" width="96" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-SIZE: 11pt" lang="EN-US">geeft na</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt" lang= "EN-US">Solve for x</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image064.png" width="101" height="22" alt="image"></span></p> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "FONT-SIZE: 11pt"> </span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">De lineaire voorstelling toont dat er staat</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image065.png" width="137" height="22" alt="image"></span>’ x^2</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">d.w.z. (onzichtbare) haken rond <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image066.png" width="18" height="22" alt="image"></span>, waardoor deze vergelijking dezelfde is als</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image067.png" width="103" height="22" alt="image"></span>.</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Je merkt ook op dat er geen spatie staat tussen de <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image068.png" width="9" height= "22" alt="image"></span> en <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image069.png" width="17" height="22" alt="image"></span><span lang="EN-US"> </span>in <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image063.png" width="96" height="22" alt="image"></span>.</p> <p class="MsoNormal">Manueel wijzigen door deze spatie achteraf in te voeren wijzigt hier niets aan: je moet bij de eerste invoer duidelijk deze spatie gebruiken (zie ook de lineaire formuleopbouw in de vergelijkingseditor). Zelfs een * of \cdot  (d.w.z. een vermenigvuldigingsteken <span style= "FONT-FAMILY: 'Cambria Math','serif'">⋅</span> ) achteraf invoeren levert hetzelfde. Dit is te wijten aan het feit dat de oorspronkelijke vergelijking werd ingevoerd door via het <span style="FONT-FAMILY: 'Calibri','sans-serif'">Lint</span> en <span style="FONT-FAMILY: 'Calibri','sans-serif'">Insert Equation</span> te werken met een visueel kiezen van <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Superscript</span>.</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Een nieuwe formule invoeren</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image070.png" width="99" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> (lineair: <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image071.png" width="109" height="22" alt="image"></span>)</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">leidt to</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image072.png" width="101" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <h2><a name="_Toc307065938">Irrationale gelijkheden</a></h2> <p class="MsoNormal">Er wordt blijkbaar correct omgegaan met kwadrateringsvoorwaarden:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image073.png" width="77" height="23" alt="image"></span>   heeft als enige oplossing   <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image074.png" width="39" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image075.png" width="105" height="24" alt="image"></span>   geeft  <span style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image076.png" width="39" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image077.png" width="163" height="24" alt="image"></span>  is echter te complex om opgelost te worden via de add-in</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <h2><a name="_Toc307065939"><span lang="NL-BE">Formulegebieden samenvoegen</span></a></h2> <p class="MsoNormal"><span lang="NL-BE">Je kan twee formulegebieden die op twee verschillende lijnen staan samenvoegen en tot bv.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image078.png" width="88" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">komen als volgt vanaf de beginsituatie</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image039.png" width="28" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image040.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left; TEXT-INDENT: -18pt" class= "MsoListParagraphCxSpFirst" align="left"><span lang= "NL-BE">1.<span style= "FONT: 7pt 'Times New Roman'">     </span></span> <span lang="NL-BE">Typ = in het formulegebied achteraan de uitdrukking</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image039.png" width="28" height="22" alt="image"></span><span lang="NL-BE"><br> Je bekomt<br>                                                   </span> <img id="Afbeelding 134" alt="1.jpg" src= "MSMath_files/image079.jpg" width="69" height="50" name= "Afbeelding 134"></p> <p style="TEXT-ALIGN: left; TEXT-INDENT: -18pt" class= "MsoListParagraphCxSpLast" align="left"><span lang= "NL-BE">2.<span style= "FONT: 7pt 'Times New Roman'">     </span></span> <span lang="NL-BE">Plaats de invoegpositie net achter dit gelijkheidsteken en druk op</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang= "NL-BE">Delete</span><span lang="NL-BE">, waardoor de formulegebieden samensmelten tot één gebied:<br>                                                 </span><img id="Afbeelding 135" alt="1.jpg" src="MSMath_files/image080.jpg" width="136" height="40" name="Afbeelding 135"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="NL-BE"> </span></p> <h1><a name="_Toc307065940"><span lang="EN-US">Ongelijkheden in één variable</span></a></h1> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image081.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image082.png" width="53" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image083.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image084.png" width="53" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image085.png" width="111" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image086.png" width="124" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image087.png" width="111" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image088.png" width="222" height="43" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image089.png" width="74" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image090.png" width="40" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image091.png" width="150" height="22" alt="image"></span><span lang="NL-BE"> is te complex voor de add-in, net zoals</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image092.png" width="70" height="30" alt="image"></span><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <h1><a name="_Toc307065941">Stelsels vergelijkingen</a></h1> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style="LINE-HEIGHT: 115%">Als je twee verschillende gelijkheden invoert zoals</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image093.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image094.png" width="67" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style="LINE-HEIGHT: 115%">en deze selecteert, waarna je rechts klikt en kiest voor</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%"> </span></p> <p style="TEXT-ALIGN: center; MARGIN-BOTTOM: 10pt" class= "MsoNormal" align="center"><img src="MSMath_files/image095.jpg" width="406" height="70" alt="image"></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left">bekom je</p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image096.png" width="109" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">Let op:  als structuur optie (case) <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 12pt" lang="EN-US"><img src="MSMath_files/image097.png" width="82" height="39" alt="image"></span> vind je <span style= "LINE-HEIGHT: 115%">via</span> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'">Calculate</span> <span style="LINE-HEIGHT: 115%"> </span><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image098.png" width="165" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="EN-US"> </span><span style="LINE-HEIGHT: 115%">en bij een</span> vergelijkingsarray (“eqarray”, “stack”) <span style= "LINE-HEIGHT: 115%">  </span><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 10pt" lang="EN-US"><img src="MSMath_files/image099.png" width="52" height="33" alt="image"></span> krijg je een foutmelding. De invoegtoepassing werkt dus enkel bij verschillende formulegebieden.</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"></p> <table cellspacing="0" cellpadding="0"> <tbody> <tr> <td style= "BORDER-BOTTOM: black 0.75pt solid; BORDER-LEFT: black 0.75pt solid; BACKGROUND: white; VERTICAL-ALIGN: top; BORDER-TOP: black 0.75pt solid; BORDER-RIGHT: black 0.75pt solid" bgcolor="white" height="39" width="133"> <table cellspacing="0" cellpadding="0" width="100%"> <tbody> <tr> <td> <div style= "PADDING-BOTTOM: 4.35pt; PADDING-LEFT: 7.95pt; PADDING-RIGHT: 7.95pt; PADDING-TOP: 4.35pt"> <p class="MsoNormal"><span lang="EN-US">optie  (“case”)</span></p> </div> </td> </tr> </tbody> </table>  </td> </tr> </tbody> </table> <table cellspacing="0" cellpadding="0"> <tbody> <tr> <td style= "BORDER-BOTTOM: black 0.75pt solid; BORDER-LEFT: black 0.75pt solid; BACKGROUND: white; VERTICAL-ALIGN: top; BORDER-TOP: black 0.75pt solid; BORDER-RIGHT: black 0.75pt solid" bgcolor="white" height="60" width="166"> <table cellspacing="0" cellpadding="0" width="100%"> <tbody> <tr> <td> <div style= "PADDING-BOTTOM: 4.35pt; PADDING-LEFT: 7.95pt; PADDING-RIGHT: 7.95pt; PADDING-TOP: 4.35pt"> <p class="MsoNormal">vergelijkingsarray (“eqarray”, “stack”)</p> </div> </td> </tr> </tbody> </table>  </td> </tr> </tbody> </table> <span style= "Z-INDEX: 14; POSITION: absolute; MARGIN-TOP: 241px; WIDTH: 50px; HEIGHT: 30px; MARGIN-LEFT: 118px; LEFT: 0px"><img src="MSMath_files/image100.png" width="50" height="30" alt="image"></span><span style= "Z-INDEX: 15; POSITION: absolute; MARGIN-TOP: 204px; WIDTH: 119px; HEIGHT: 67px; MARGIN-LEFT: 369px; LEFT: 0px"><img src="MSMath_files/image101.png" width="119" height="67" alt="image"></span><span style= "Z-INDEX: 1; POSITION: absolute; MARGIN-TOP: 266px; WIDTH: 135px; HEIGHT: 90px; MARGIN-LEFT: 162px; LEFT: 0px"><img src="MSMath_files/image102.png" width="135" height="90" alt="image"></span><span style= "Z-INDEX: 2; POSITION: absolute; MARGIN-TOP: 266px; WIDTH: 71px; HEIGHT: 90px; MARGIN-LEFT: 304px; LEFT: 0px"><img src="MSMath_files/image103.png" width="71" height="90" alt="image"></span><img src= "MSMath_files/image104.jpg" width="308" height="361" alt="image"> <p class="MsoNormal"> </p> <p class="MsoNormal">Soms zijn er <span class= "Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">oneindig veel oplossingen</span></span> en kiest de add-in de hoofd- en nevenonbekenden</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image105.png" width="112" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image106.png" width="133" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image107.png" width="133" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image108.png" width="267" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p class="MsoNormal"> </p> <p class="MsoNormal">Indien er initieel al duidelijk <span class= "Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">meer onbekenden dan vergelijkingen</span></span> zijn, dien je zelf te bepalen welke variabelen je wil berekenen:</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image105.png" width="112" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image106.png" width="133" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 16" src="MSMath_files/image109.jpg" width="326" height="131" alt="image" name="Picture 16"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">Solve for x, y geeft</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image110.png" width="219" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image105.png" width="112" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image111.png" width="130" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US">Solve for x, y geeft</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image112.png" width="178" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal">Bij <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">meer vergelijkingen dan onbekenden</span></span>, krijg je een foutmelding.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image093.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image094.png" width="67" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image113.png" width="76" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image114.jpg" width="412" height="44" alt= "image"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">Stelsels met parameters</span></span> worden niet correct opgelost. Zo leidt <span style="FONT-FAMILY: 'Calibri','sans-serif'">Solve for x,y</span> bij</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image115.png" width="85" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image116.png" width="67" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">tot</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image117.png" width="295" height="40" alt="image"></span></p> <p class="MsoNormal">De voorwaarde <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image118.png" width="39" height="22" alt="image"></span> is in feite overbodig want</p> <p class="MsoNormal"> </p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%">voor</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image119.png" width="39" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="NL-BE"> is er één oplossing,</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%">voor</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image120.png" width="39" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="NL-BE"> en</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image121.png" width="39" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="NL-BE"> is er geen oplossing,</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%">voor</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image120.png" width="39" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="NL-BE"> en</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image122.png" width="39" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="NL-BE"> zijn er oneindig veel oplossingen met 1 vrijheidsgraad.</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%" lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Indien je de volgorde van de opgegeven variabelen wijzigt, verdwijnt de overbodige</span> voorwaarde <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image118.png" width="39" height="22" alt="image"></span> , maar niet alle gevallen worden besproken.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <p class="MsoNormal">Het stelsel</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image123.png" width="95" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image124.png" width="119" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">geeft als oplossing</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image125.png" width="229" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Het stelsel</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image126.png" width="91" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image127.png" width="186" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">heeft als oplossingen</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image128.png" width="49" height="22" alt="image"></span><span lang="NL-BE"> en</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image129.png" width="37" height="22" alt="image"></span><span lang="NL-BE">, maar</span> <span lang="NL-BE">de invoegtoepassing geeft</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image130.png" width="96" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Via het commando</span> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> solve</span></span> <span lang="NL-BE">kan je stelsels oplossen</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <pre> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image131.png" width="370" height="19" alt="image"></span> </pre> <pre> <span style="FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 12pt" lang="EN-US"> </span> </pre> <pre> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image132.png" width="146" height="36" alt="image"></span> </pre> <pre> <span style="FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 12pt" lang="EN-US"> </span> </pre> <p class="MsoNormal"><span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> nsolve</span></span> <span lang="NL-BE">geeft numerieke oplossingen.</span></p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="NL-BE"><br style="PAGE-BREAK-BEFORE: always" clear= "all"></span> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><b><span style= "LINE-HEIGHT: 115%; COLOR: blue; FONT-SIZE: 18pt" lang= "NL-BE"> </span></b></p> <h1><a name="_Toc307065942"><span lang="NL-BE">Grafische voorstellingen</span></a></h1> <h2><a name="_Toc307065943"><span lang="NL-BE">Tweedimensionele figuren / Functies in één variabele</span></a></h2> <p class="MsoNormal"><span lang="NL-BE">Via de rechtermuisknop kan je bv.</span> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">grafieken van functies</span></span> <span lang="NL-BE">tekenen:</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image024.png" width="81" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 1" src="MSMath_files/image133.jpg" width="466" height="190" alt="image" name="Picture 1"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"></p> <table cellspacing="0" cellpadding="0"> <tbody> <tr> <td style="VERTICAL-ALIGN: top" height="101" width="120"> <table cellspacing="0" cellpadding="0" width="100%"> <tbody> <tr> <td> <div style= "PADDING-BOTTOM: 3.6pt; PADDING-LEFT: 7.2pt; PADDING-RIGHT: 7.2pt; PADDING-TOP: 3.6pt"> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="NL-BE">Proportional Display /</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="NL-BE">Maximize Graph</span></p> </div> </td> </tr> </tbody> </table>  </td> </tr> </tbody> </table> <span style= "Z-INDEX: 4; POSITION: absolute; MARGIN-TOP: 84px; WIDTH: 115px; HEIGHT: 41px; MARGIN-LEFT: 63px; LEFT: 0px"><img src="MSMath_files/image134.png" width="115" height="41" alt="image"></span><span style= "Z-INDEX: 3; POSITION: absolute; MARGIN-TOP: 119px; WIDTH: 20px; HEIGHT: 24px; MARGIN-LEFT: 176px; LEFT: 0px"><img src="MSMath_files/image135.png" width="20" height="24" alt="image"></span><img src= "MSMath_files/image136.jpg" width="456" height="348" alt="image"> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "Z-INDEX: 6; POSITION: absolute; MARGIN-TOP: 331px; WIDTH: 58px; HEIGHT: 28px; MARGIN-LEFT: 430px; LEFT: 0px"> <img src="MSMath_files/image137.png" width="58" height="28" alt= "image"></span><img src="MSMath_files/image138.jpg" width="473" height="361" alt="image"></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 13" src="MSMath_files/image139.png" width="450" height="450" alt="image" name="Picture 13"></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image140.png" width="47" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 99" src="MSMath_files/image141.png" width="318" height="312" alt="image" name="Picture 99"></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image142.png" width="69" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 102" src="MSMath_files/image143.png" width="328" height="328" alt="image" name="Picture 102"></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Om de</span> <span class= "Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">grafieken</span></span> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">van meerdere functies of van vlakke figuren</span></span> <span lang="NL-BE">te tonen, geef je de betrokken functievoorschriften of vergelijkingen weer in aparte formulegebieden, waarna je deze selecteert en ze vervolgens tekent via</span> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang= "NL-BE">Plot in 2D</span><span lang="NL-BE">:</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image144.png" width="75" height="41" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image145.png" width="51" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image042.png" width="51" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image146.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 125" src="MSMath_files/image147.png" width="543" height="523" alt="image" name="Picture 125"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal">Eventueel zoom je in of uit om een goed beeld te bekomen.</p> <p class="MsoNormal">Je kan zoals getoond op bovenstaande figuur de markeringen op de assen tonen en niet aan de buitenrand via <span style="FONT-FAMILY: 'Calibri','sans-serif'">Show/Hide Outer Frame</span>.</p> <p class="MsoNormal"> </p> <p class="MsoNormal">Kegelsneden zoals ellipsen en hyperbolen kan je eenvoudig plotten:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <sub><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: always" clear="all"></span></sub> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><sub> </sub></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image148.png" width="84" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: center; MARGIN-BOTTOM: 10pt" class= "MsoNormal" align="center"><sub><img src= "MSMath_files/image149.png" width="360" height="360" alt= "image"></sub></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image150.png" width="84" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: center; MARGIN-BOTTOM: 10pt" class= "MsoNormal" align="center"><img src="MSMath_files/image151.png" width="360" height="360" alt="image"></p> <p class="MsoNormal">Snijpunten kan je visueel voorstellen, bv.:</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image093.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image094.png" width="67" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img src="MSMath_files/image152.png" width="298" height="298" alt= "image"></p> <p class="MsoNormal"> </p> <p class="MsoNormal">Analoog voor</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image123.png" width="95" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image124.png" width="119" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 9" src="MSMath_files/image153.png" width="324" height="324" alt="image" name="Picture 9"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US">en voor</span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image126.png" width="91" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image127.png" width="186" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 11" src="MSMath_files/image154.png" width="450" height="450" alt="image" name="Picture 11"></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><b>Opmerking</b>: via Display kan je plotdesiderata aangeven</p> <p class="MsoNormal"></p> <table cellspacing="0" cellpadding="0" align="left"> <tbody> <tr> <td height="6" width="12"></td> <td width="290"></td> <td width="43"></td> <td width="272"></td> </tr> <tr> <td height="6"></td> <td colspan="2"></td> <td valign="top" rowspan="3" align="left"><img src= "MSMath_files/image155.png" width="272" height="150" alt= "image"></td> </tr> <tr> <td height="128"></td> <td valign="top" align="left"><img src="MSMath_files/image156.png" width="290" height="128" alt="image"></td> </tr> <tr> <td height="16"></td> </tr> </tbody> </table>   <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <br clear="all"> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 7" src="MSMath_files/image157.jpg" width="406" height="78" alt="image" name="Picture 7"></p> <p class="MsoNormal"><span style= "Z-INDEX: 13; POSITION: relative"><span style= "POSITION: absolute; WIDTH: 236px; HEIGHT: 107px; TOP: -9px; LEFT: 392px"> <img alt= "Line Callout 2: Proportionele voorstelling (dezelfde eenheden op beide assen)?" src="MSMath_files/image158.png" width="236" height= "107"></span></span><span lang="EN-US"> </span></p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="NL-BE"><br style="PAGE-BREAK-BEFORE: always" clear= "all"></span> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><b><i><span style= "LINE-HEIGHT: 115%; COLOR: red; FONT-SIZE: 16pt" lang= "NL-BE"> </span></i></b></p> <br clear="all"> <h2><a name="_Toc307065944"><span lang="NL-BE">Driedimensionele figuren / Functies in twee variabelen</span></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image159.png" width="81" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 114" src="MSMath_files/image160.png" width="449" height="449" alt="image" name="Picture 114"></p> <p class="MsoNormal"><span lang="NL-BE">Via het grafiekvenster kan je bv. deze grafiek laten roteren rond een as:</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "Z-INDEX: 8; POSITION: absolute; MARGIN-TOP: 105px; WIDTH: 267px; HEIGHT: 57px; MARGIN-LEFT: 167px; LEFT: 0px"> <img src="MSMath_files/image161.png" width="267" height="57" alt= "image"></span><img id="Picture 18" src="MSMath_files/image162.jpg" width="324" height="211" alt="image" name="Picture 18"></p> <p style="MARGIN-BOTTOM: 10pt" class="MsoNormal"><span lang= "NL-BE">Deze grafiek kan ook als “wireframe” worden voorgesteld.</span></p> <p style="MARGIN-BOTTOM: 10pt" class="MsoNormal"><span lang= "NL-BE"> </span></p> <p class="MsoNormal"><span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 13pt">Meerdere 3D figuren</span></span> <span lang="NL-BE">kunnen getoond worden op dezelfde wijze als waarop dat voor 2D supra gebeurde:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image105.png" width="112" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image106.png" width="133" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image107.png" width="133" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 123" src="MSMath_files/image163.png" width="449" height="449" alt="image" name="Picture 123"></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">De optie</span> <span style="FONT-FAMILY: 'Calibri','sans-serif'" lang="NL-BE">Plot in 3D</span> <span lang="NL-BE">wordt niet getoond bij</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image164.png" width="66" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image165.png" width="66" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image166.png" width="67" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">maar wel als je dit herschrijft als</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image167.png" width="103" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image168.png" width="103" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image169.png" width="103" height="22" alt="image"></span></p> <p class="MsoNormal"><u><span lang="EN-US"><span style= "TEXT-DECORATION: none"> </span></span></u></p> <p class="MsoNormal"><u><span lang="EN-US"><span style= "TEXT-DECORATION: none"> </span></span></u></p> <p class="MsoNormal"><u><span lang="EN-US"><span style= "TEXT-DECORATION: none"> </span></span></u></p> <h2><a name="_Toc307065945">Ongelijkheden</a></h2> <p class="MsoNormal">Je kan ook ongelijkheden plotten via <span style="FONT-FAMILY: 'Calibri','sans-serif'">Graph</span> > <span style="FONT-FAMILY: 'Calibri','sans-serif'">Plot Inequality</span>:</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image170.png" width="76" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 20" src="MSMath_files/image171.png" width="450" height="450" alt="image" name="Picture 20"></p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <p class="MsoNormal">Om bv.</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image172.png" width="129" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image173.png" width="129" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image174.png" width="56" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image175.png" width="48" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image176.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image177.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">te schetsen moet je <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Graph > Plot in 2D</span> gebruiken, maar de figuur is onoverzichtelijk:</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 100" src="MSMath_files/image178.png" width="450" height="450" alt="image" name="Picture 100"></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left">Wanneer je telkens het “complementaire gebied” tekent, d.w.z.</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image179.png" width="129" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image180.png" width="129" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image181.png" width="56" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image182.png" width="48" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image183.png" width="39" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image184.png" width="39" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left">wordt dit duidelijker omdat het niet-gearceerde gebied nu het oorspronkelijk gezochte is:</p> <p style="TEXT-ALIGN: center; MARGIN-BOTTOM: 10pt" class= "MsoNormal" align="center"><img id="Picture 105" src= "MSMath_files/image185.png" width="450" height="450" alt="image" name="Picture 105"></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <h2><a name="_Toc307065946">Animaties</a></h2> <p class="MsoNormal">Het is mogelijk om animaties te tonen bij figuren. Zo kan je bv. een parameter a introduceren bij</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image186.png" width="75" height="22" alt="image"></span></p> <p class="MsoNormal">wat leidt tot een optie</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 4" src="MSMath_files/image187.jpg" width="457" height="100" alt="image" name="Picture 4"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">waarbij de animatie gestart wordt met de pijl.</p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: always" clear="all"></span> <p class="MsoNormal"><b><span style= "LINE-HEIGHT: 115%; COLOR: blue; FONT-SIZE: 18pt"> </span></b></p> <h1><a name="_Toc307065947">Sommaties</a></h1> <p class="MsoNormal">Een som zoals</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image188.png" width="34" height="57" alt="image"></span></p> <p class="MsoNormal">kan via <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute</span> > <span style="FONT-FAMILY: 'Calibri','sans-serif'">Calculate</span> berekend worden. Als je alles op één lijn plaatst (‘inline’), worden de sub- en superscripten bij het sommatieteken naast dit teken geplaatst, tenzij het om één formulegebied gaat:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image189.png" width="45" height="23" alt="image"></span>   = <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image190.png" width="18" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal"><b>Waarschuwing 1</b>: je mag geen indices zoals i gebruiken omdat dit symbool voorbehouden is voor complexe getallen. Hetzelfde geldt voor bv. het getal <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image191.png" width="8" height= "22" alt="image"></span>.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image192.png" width="84" height="57" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image193.png" width="294" height="55" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <p class="MsoNormal"><b>Waarschuwing 2</b>: sommige bewerkingen kan je niet uitvoeren, zoals bv.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image194.png" width="50" height="57" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">waarbij <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 10.5pt" lang="EN-US"><img src="MSMath_files/image195.png" width="89" height="32" alt="image"></span> een binomiaalgetal voorstelt. Nochtans vind je in de lijst met voorgedefinieerde formules</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image196.png" width="182" height="55" alt="image"></span></p> <p class="MsoNormal">terug.</p> <p class="MsoNormal"> </p> <p class="MsoNormal">Zelfs <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> oneindige sommen</span></span> kan je laten uitrekenen</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image197.png" width="96" height="55" alt="image"></span></p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: always" clear="all"></span> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <h1><a name="_Toc307065948">Limieten</a></h1> <p class="MsoNormal">Gebruik na rechtsklikken de optie <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute</span> > <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Calculate</span>:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image198.png" width="90" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image191.png" width="8" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image199.png" width="60" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image200.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image201.png" width="42" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image200.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image202.png" width="35" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image203.png" width="105" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p class="MsoNormal">Het lijkt alsof linker- en rechterlimieten niet ingebouwd werden.</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image204.png" width="42" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image205.png" width="14" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image206.png" width="47" height="39" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image207.png" width="26" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal"> </p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: always" clear="all"></span> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><b><span style= "LINE-HEIGHT: 115%; COLOR: blue; FONT-SIZE: 18pt"> </span></b></p> <h1><a name="_Toc307065949">Afgeleiden</a></h1> <p class="MsoNormal">Afgeleiden zijn symbolisch berekenbaar:</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image208.png" width="76" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 8" src="MSMath_files/image209.jpg" width="416" height="202" alt="image" name="Picture 8"></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">wat leidt tot</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image210.png" width="37" height="54" alt="image"></span></p> <p class="MsoNormal">Analoog:</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image211.png" width="36" height="28" alt="image"></span> heeft als afgeleide  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 13pt" lang="EN-US"><img src="MSMath_files/image212.png" width="45" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image213.png" width="51" height="22" alt="image"></span>  heeft als afgeleide  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image214.png" width="72" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Je kan ook een afgeleide berekenen via het gebruik van de functie <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> deriv</span></span>, met syntax</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'">deriv(function, variable)</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <i> </i>en dan berekenen via rechtsklikken<i>,</i> bv.</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image215.png" width="84" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <i> </i></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <i><img id="Picture 14" src="MSMath_files/image216.jpg" width="502" height="76" alt="image" name="Picture 14"></i></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <i> </i></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image217.png" width="29" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Via <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> derivn</span></span> bekom je hogere orde afgeleiden, syntax</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="FONT-FAMILY: 'Calibri','sans-serif'">derivn(function, variable,</span> <i>n</i><span style= "FONT-FAMILY: 'Calibri','sans-serif'">)</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">met <i> </i><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image218.png" width="39" height="22" alt="image"></span><i> :</i></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <i> </i></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image219.png" width="108" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image220.png" width="21" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image221.png" width="108" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image222.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <h1><a name="_Toc307065950">Integralen</a></h1> <h2><a name="_Toc307065951">Onbepaalde integralen</a></h2> <p class="MsoNormal">Zoals je hierboven reeds kon zien, kan je ook integreren naar een variabele en primitieve functies berekenen:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image208.png" width="76" height="22" alt="image"></span> heeft integraal  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image223.png" width="214" height="32" alt="image"></span></p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image213.png" width="51" height="22" alt="image"></span>   heeft als integraal   <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image224.png" width="86" height="31" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">Zo kan je</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image225.png" width="355" height="43" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">bekomen door rechts te klikken op</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image226.png" width="165" height="40" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE">en</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate</span> te gebruiken:</p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Analoog:</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 10pt" lang="EN-US"><img src="MSMath_files/image227.png" width="72" height="35" alt="image"></span><span lang="NL-BE"> =</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image228.png" width="88" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Let hierbij goed op: deze inverse functie</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image229.png" width="68" height="22" alt="image"></span><span lang="NL-BE"> moet je soms ook zelf hanteren bij een invoer voor cyclometrische functies (i.p.v. atan).</span></p> <p class="MsoNormal"><span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="NL-BE"> </span></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span lang="NL-BE">Soms verkrijg je ongebruikelijke (maar correcte) resultaten: zo levert het integreren van </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 10.5pt" lang="EN-US"><img src="MSMath_files/image230.png" width="42" height="36" alt="image"></span><span style= "LINE-HEIGHT: 115%; FONT-SIZE: 14pt" lang="NL-BE"> </span> <span lang="NL-BE">naar x  het antwoord  </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image231.png" width="115" height="32" alt="image"></span><span lang= "NL-BE"> op.</span></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span lang="NL-BE"> </span></p> <p class="MsoNormal"><span lang="NL-BE">Onbepaalde integralen kan je op drie manieren berekenen:</span></p> <p style="TEXT-INDENT: -18pt" class="MsoListParagraphCxSpFirst"> <span style="FONT-FAMILY: Symbol">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> Typ een uitdrukking, selecteer <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Integrate on x</span> na rechts te klikken.</p> <p style="TEXT-INDENT: -18pt" class="MsoListParagraphCxSpMiddle"> <span style="FONT-FAMILY: Symbol">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> Voer symbolisch de integraal in via het Lint en gebruik  <span style="FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate</span>.</p> <p style="TEXT-ALIGN: left; TEXT-INDENT: -18pt" class= "MsoListParagraphCxSpLast" align="left"><span style= "FONT-FAMILY: Symbol">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> Via het invoeren van het commando <span style= "FONT-FAMILY: 'Calibri','sans-serif'">integral</span>, syntax<br> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt">                                                     integral(input, variable)<br></span></span> waarna je <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate</span> gebruikt.</p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left">Zo leidt</p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image232.png" width="105" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left">tot</p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image233.png" width="45" height="41" alt="image"></span></p> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"> </p> <h2><a name="_Toc307065952">Bepaalde integralen</a></h2> <p class="MsoNormal">Bepaalde integralen zoals</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image234.png" width="58" height="60" alt="image"></span></p> <p class="MsoNormal">bereken je analoog via <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate,</span> met resultaat  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image235.png" width="9" height= "22" alt="image"></span>.</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span lang="NL-BE">Een dergelijke bepaalde integraal kan je op twee manieren berekenen:</span></p> <p style="TEXT-INDENT: -18pt" class="MsoListParagraphCxSpFirst"> <span style="FONT-FAMILY: Symbol">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> Voer symbolisch de bepaalde integraal in via het Lint en gebruik  <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate</span> zoals in bovenstaand voorbeeld.</p> <p style="TEXT-ALIGN: left; TEXT-INDENT: -18pt" class= "MsoListParagraphCxSpLast" align="left"><span style= "FONT-FAMILY: Symbol">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> Via het invoeren van het commando <span style= "FONT-FAMILY: 'Calibri','sans-serif'">integral</span>, met syntax<br> <span style= "FONT-FAMILY: 'Calibri','sans-serif'">                                    </span> <span class="Heading4Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 13pt"> integral(input, variable, lowervalue, uppervalue)</span></span><br> waarna je <span style="FONT-FAMILY: 'Calibri','sans-serif'">Compute > Calculate</span> gebruikt.</p> <p class="MsoNormal"> </p> <p class="MsoNormal">Zo leidt</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image236.png" width="144" height="22" alt="image"></span></p> <p class="MsoNormal">tot</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image235.png" width="9" height= "22" alt="image"></span></p> <p class="MsoNormal"> </p> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: always" clear="all"></span> <p style="TEXT-ALIGN: left; MARGIN-BOTTOM: 10pt" class="MsoNormal" align="left"><b><i><span style= "LINE-HEIGHT: 115%; COLOR: red; FONT-SIZE: 16pt"> </span></i></b></p> <h2><a name="_Toc307065953">Meervoudige integratie</a></h2> <p class="MsoNormal">Zelfs meervoudige integralen zoals bv.</p> <pre> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image237.png" width="93" height="43" alt="image"></span> </pre> <pre> <span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"> </span> </pre> <pre> <span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt">kan je uitwerken, met als resultaat</span> </pre> <pre> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image238.png" width="9" height= "36" alt="image"></span> </pre> <pre> <span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"> </span> </pre> <pre> <span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt">Lineair weergegeven is dit</span><span style="FONT-FAMILY: 'Cambria Math','serif'; FONT-SIZE: 12pt"><br></span><span style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image239.png" width="202" height="20" alt="image"></span> </pre> <pre> <span style= "FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 12pt"> </span> </pre> <p class="MsoNormal"> </p> <h1><a name="_Toc307065954">Differentiaalvergelijkingen</a></h1> <p class="MsoNormal">Eenvoudige differentiaalvergelijkingen zoals</p> <p class="MsoNormal"> </p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image240.png" width="45" height="22" alt="image"></span></p> <p class="MsoNormal"> </p> <p class="MsoNormal">kan je oplossen door scheiding van variabelen:</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image241.png" width="59" height="43" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image242.png" width="101" height="42" alt="image"></span></p> <p class="MsoNormal">waarbij <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Solve for x</span> leidt tot</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image243.png" width="150" height="22" alt="image"></span></p> <p class="MsoNormal">en <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Solve for y</span> tot</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image244.png" width="129" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal">wat slechts particuliere oplossingen geeft.</p> <p class="MsoNormal">Als je apart de beide integralen uitrekent, kan je komen tot de algemene oplossing</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 10.5pt" lang="EN-US"><img src="MSMath_files/image245.png" width="48" height="32" alt= "image"></span>   =    <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image246.png" width="34" height="23" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image247.png" width="73" height="22" alt="image"></span>  =     <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image248.png" width="37" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image249.png" width="130" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image250.png" width="159" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image251.png" width="153" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <h1><a name="_Toc307065955">Matrices</a></h1> <p class="MsoNormal">De add-in kan bewerkingen met matrices aan:</p> <p class="MsoNormal"> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image252.png" width="129" height="54" alt="image"></span>    =   <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image253.png" width="105" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image254.png" width="129" height="54" alt="image"></span>    =  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image255.png" width="40" height="22" alt="image"></span> </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image256.png" width="102" height="54" alt="image"></span>  heeft als inverse matrix   <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 25.5pt" lang="EN-US"><img src="MSMath_files/image257.png" width="82" height="76" alt="image"></span>  en als determinant  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image235.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> Eigenwaarden voor <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image256.png" width="102" height="54" alt="image"></span> kan je vinden door</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image258.png" width="271" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">te vormen en via <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Calculate</span> te komen tot</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image259.png" width="161" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Deze laatste matrix heeft determinant</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image260.png" width="166" height="22" alt="image"></span> ,</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">wat ontbonden kan worden in factoren als  <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image261.png" width="122" height="22" alt="image"></span>  , d.w.z. dat er twee eigenwaarden zijn voor de matrix <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image256.png" width="102" height="54" alt="image"></span>, nl. 3 (met multipliciteit 1) en 1 (met multipliciteit 2).</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> Eigenvectoren van <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image256.png" width="102" height="54" alt="image"></span> zijn niet-nul oplossingen van</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image262.png" width="240" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Voor de eigenwaarde 3 wordt dit</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image263.png" width="192" height="54" alt="image"></span> = <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 17.5pt" lang="EN-US"><img src="MSMath_files/image264.png" width="116" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">waarbij oplossingen van</span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image265.png" width="78" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image266.png" width="60" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image265.png" width="78" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">gegeven worden door</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image267.png" width="153" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Voor de eigenwaarde 1 wordt dit</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image268.png" width="192" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image269.png" width="104" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span lang="EN-US">waarbij oplossingen van</span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image270.png" width="103" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">gegeven worden door</p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image271.png" width="38" height="22" alt="image"></span>  met <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image272.png" width="9" height= "22" alt="image"></span> een willekeurig reëel getal.</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <h1><a name="_Toc307065956">Logische voorwaarden</a></h1> <p class="MsoNormal">De logische commando’s <span style= "FONT-FAMILY: 'Calibri','sans-serif'">not</span><i>,</i> <span style= "FONT-FAMILY: 'Calibri','sans-serif'">and</span><i>,</i> <span style="FONT-FAMILY: 'Calibri','sans-serif'">or</span><i>,</i> en <span style="FONT-FAMILY: 'Calibri','sans-serif'">xor</span> kunnen gebruikt worden (“or” is de standaard inclusieve of, terwijl “xor” een exclusieve of betreft).  Om te testen of een uitdrukking waar is, gebruik je “<span style= "FONT-FAMILY: 'Calibri','sans-serif'">isTrue</span><i>”</i> gevolgd door de voorwaarde binnen haken<i>.</i></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> </div> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria Math','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: auto" clear="all"></span> <div class="WordSection2"> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image273.png" width="113" height="24" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image274.png" width="31" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image275.png" width="113" height="24" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image276.png" width="38" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image277.png" width="186" height="24" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image274.png" width="31" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image278.png" width="197" height="24" alt="image"></span></p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image276.png" width="38" height="22" alt="image"></span></p> </div> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: auto" clear="all"></span> <div class="WordSection3"> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left"> Opmerking: commando’s zijn <b>niet hoofdlettergevoelig</b>, namen van sommige variabelen zoals x, y en z wel.</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">  </p> <h1><a name="_Toc307065957">Lijst met automatisch herkende functies en commando’s</a></h1> <h2><a name="_Toc307065958">Opmerkingen</a></h2> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Voor functies die complexe argumenten hebben, moet je er voor zorgen dat bij de opties <span style= "FONT-FAMILY: 'Calibri','sans-serif'">Complex</span> aangegeven is.</p> <p style="TEXT-ALIGN: left" class="MsoNormal" align="left">Verder zijn commando’s zijn niet hoofdlettergevoelig<b>.</b></p> <h2><a name="_Toc307065959"><span lang="EN-US">Data sets and lists</span></a></h2> <p class="MsoNormal"><span lang="EN-US">A <i>data set</i> is any collection of observations or measurements, from a set of course grades to a set of temperature readings to a set of high tide times. Data sets can be more complicated, for example, observations of age, height, weight, and blood pressure for patients in a medical study. Data sets are most frequently collected for the purpose of calculating statistics on the data.</span></p> <p class="MsoNormal"><span lang="EN-US">A <i>list</i>, in Microsoft Mathematics, is a collection of elements, separated by commas and surrounded by braces {}. The elements can be numbers, <span class= "glossary">variables</span><span class="glossarydef"><span style= "DISPLAY: none">A symbol that represents an unspecified or unknown quantity, such as "a," "b," or "x"</span></span>, <span class= "glossary">expressions</span><span class="glossarydef"><span style= "DISPLAY: none">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span>, or other lists.</span></p> <p class="MsoNormal"><span lang="EN-US">In Microsoft Mathematics, you represent a data set as a list. A set of course grades can be represented as a list of numbers, while the data set for the medical study can be represented as a list of lists.</span></p> <p class="MsoNormal"><span lang="EN-US">You can use a list as an <span class="glossary">argument</span><span class= "glossarydef"><span style="DISPLAY: none">An independent variable whose value determines the value of a mathematical expression</span></span> to most <span class= "glossary">functions</span><span class="glossarydef"><span style= "DISPLAY: none">A mathematical relationship between variables in which the value of one variable determines a unique value for another variable</span></span> that take a single argument; in general, such functions return a list that contains the value of the function for each element of the input list.</span></p> <p class="MsoNormal"><span lang="EN-US">One particular use of lists in Microsoft Mathematics is to store <span class= "glossary">vectors</span><span class="glossarydef"><span style= "DISPLAY: none">A quantity that has both magnitude and direction. Examples of vectors include force and velocity</span></span>. Math textbooks typically present vectors as comma-separated pairs or triples surrounded by parentheses. In Microsoft Mathematics, you enter them as two, three, or more elements surrounded by braces.</span></p> <h2><a name="_Toc307065960"><span lang= "EN-US">Operators</span></a></h2> <p class="MsoNormal"><span lang="EN-US">The := and -> operators store a value as a variable. The := operator is placed after the variable name and before the value while the -> operator is placed after the value and before the variable name.</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 106.2pt" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Courier New'; FONT-SIZE: 10pt" lang="EN-US">x := value</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 106.2pt" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Courier New'; FONT-SIZE: 10pt" lang="EN-US">value -> x</span></p> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">!</span> <a name="NODO0" id="NODO0"></a></h2> <p class="MsoNormal"><span lang="EN-US">The ! operator returns the</span> <span class="glossary"><span lang= "EN-US">factorial</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">The number that results from multiplying a whole number by every whole number between itself and 1 inclusive. The factorial is symbolized by the exclamation point (!). 5 factorial, or 5!, is 5 x 4 x 3 x 2 x 1 = 120</span></span> <span lang="EN-US">of a non-negative integer n.</span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">‼</span><a name="NODO1" id="NODO1"></a></h2> <p class="MsoNormal"><span lang="EN-US">The !! operator returns the double factorial of an integer n. If n is even, the double factorial is the product of the even factors of the factorial, that is, n*(n-2)*(n-4)*...*6*4*2. If n is odd, the double factorial is the product of the odd factors of the factorial, that is, n*(n-2)*(n-4)*...*5*3*1.</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">^</span><a name= "NODO2" id="NODO2"></a></h2> <p class="MsoNormal"><span lang="EN-US">The ^ operator returns a number or</span> <span class="glossary"><span lang= "EN-US">expression</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span> <span lang="EN-US">raised to a power.</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">%</span> <a name= "NODO3" id="NODO3"></a></h2> <p class="MsoNormal"><span lang="EN-US">The % operator (called the "modulo operator") returns the remainder that is left after you divide one number by another.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image279.png" width="32" height="22" alt="image"></span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image280.png" width="101" height="22" alt="image"></span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image281.png" width="169" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">abs</span> <a name="NODO4" id="NODO4"></a></h2> <p class="MsoNormal"><span lang="EN-US">The abs function returns the</span> <span class="glossary"><span lang="EN-US">absolute value</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">The distance between 0 and any real or complex number. For example, 8 would be the absolute value of -8. Absolute value is symbolized by placing the number within vertical bars</span></span> <span lang="EN-US">of a real or</span> <span class="glossary"><span lang="EN-US">complex number</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span></span><span lang="EN-US">, also known as the modulus of a complex number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">and</span><a name="NODO5" id="NODO5"></a></h2> <p class="MsoNormal"><span lang="EN-US">The logical operators <i>and</i>, <i>not</i>, <i>or</i>, and <i>xor</i> are used to construct logical statements. Together with the comparison operators (=,<>,<,>,≤,≥) and the isTrue function, you can use the logical operators to create and verify a variety of logical statements.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arccos</span><a name="NODO6" id="NODO6"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arccot</span><a name="NODO7" id="NODO7"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arccsc</span><a name="NODO8" id="NODO8"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arcsec</span><a name="NODO9" id="NODO9"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arcsin</span><a name="NODO10" id="NODO10"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arctan</span><a name="NODO11" id="NODO11"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">arg</span><a name="NODO12" id="NODO12"></a></h2> <p class="MsoNormal"><span lang="EN-US">The arg function returns the argument, or angle, of a complex number<span style= "DISPLAY: none">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span>. The argument is sometimes called the <i>phase</i> of a complex number.</span></p> <p class="MsoNormal"><span lang="EN-US">Warning</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">Make sure you have enabled the option</span> <span style= "FONT-FAMILY: 'Calibri','sans-serif'" lang= "EN-US">Complex</span><span lang="EN-US">!</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 106.2pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 10pt" lang="EN-US">arg(z)</span></p> <p style="MARGIN-LEFT: 106.2pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 10pt" lang="EN-US">arg({z1,z2,...})</span></p> <p class="MsoNormal"><span lang="EN-US">Domain: all complex numbers.</span></p> <p class="MsoNormal"><span lang="EN-US">Range: the interval ]-</span>π<span lang="EN-US">,</span>π<span lang= "EN-US">]</span></p> <p class="MsoNormal"><span lang="EN-US">Examples</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image282.png" width="45" height="22" alt="image"></span><span lang="EN-US">   geeft </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image283.png" width="8" height= "28" alt="image"></span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image284.png" width="89" height="22" alt="image"></span>  geeft <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 9pt" lang="EN-US"><img src="MSMath_files/image285.png" width="63" height="32" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">cbrt</span><a name="NODO13" id="NODO13"></a></h2> <p class="MsoNormal"><span lang="EN-US">The cbrt function returns the</span> <span class="glossary"><span lang="EN-US">cube root</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A number or quantity that, when multiplied by itself twice, equals a given number or quantity</span></span> <span lang="EN-US">of a number or</span> <span class="glossary"><span lang= "EN-US">expression</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">ceiling</span><a name="NODO14" id="NODO14"></a></h2> <p class="MsoNormal"><span lang="EN-US">The ceiling function returns the smallest integer that is greater than or equal to a number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">column</span><a name="NODO15" id="NODO15"></a></h2> <p class="MsoNormal"><span lang="EN-US">The column function returns the specified column in a matrixA rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems as a list.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left">column(matrix,n)</p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image286.png" width="173" height="65" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image287.png" width="51" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">combination</span><a name="NODO16" id="NODO16"></a></h2> <p class="MsoNormal"><span lang="EN-US">The combination function returns the number of <span class= "glossary">combinations</span><span class= "glossarydef"><span style="DISPLAY: none">A subset that contains a specified number of the elements of a given set, selected without regard to the order in which they were chosen</span></span> of size <i>k</i> that can be chosen from a set of <i>n</i> elements</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">concatenate</span><a name="NODO17" id="NODO17"></a></h2> <p class="MsoNormal"><span lang="EN-US">The concatenate function combines two or more inputs into a single list.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">conjugate</span><a name="NODO18" id="NODO18"></a></h2> <p class="MsoNormal"><span lang="EN-US">The conjugate function returns the</span> <span class="glossary"><span lang= "EN-US">complex conjugate</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Either of a pair of complex numbers that are symmetrically located on either side of an x-axis, differing only in the sign of the imaginary component. For the complex number a+bi, the complex conjugate number is a-bi</span></span> <span lang="EN-US">of a</span> <span class="glossary"><span lang="EN-US">complex number</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">correlation</span><a name="NODO19" id="NODO19"></a></h2> <p class="MsoNormal"><span lang="EN-US">The correlation function returns the <span class="glossary">correlation</span><span class= "glossarydef"><span style="DISPLAY: none">The degree to which two or more variables are related and change together</span></span> of two data sets. Both data sets must contain the same number of observations.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">cos</span><a name="NODO20" id="NODO20"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">cosh</span><a name="NODO21" id="NODO21"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">cot</span><a name="NODO22" id="NODO22"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">coth</span><a name="NODO23" id="NODO23"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">covariance</span><a name="NODO24" id="NODO24"></a></h2> <p class="MsoNormal"><span lang="EN-US">The covariance and unbiasedCovariance functions return the <span class= "glossary">covariance</span><span class="glossarydef"><span style= "DISPLAY: none">A statistical measure of the tendency of two variables to change in conjunction with each other. It is equal to the product of their standard deviations and correlation coefficients</span></span> of two data sets. Both data sets must contain the same number of observations. The covariance function returns a biased estimate of the covariance and the unbiasedCovariance function returns an unbiased estimate. The biased estimate is (n-1)/n times the unbiased estimate.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">cross</span><a name="NODO25" id="NODO25"></a></h2> <p class="MsoNormal"><span lang="EN-US">The cross function returns the cross product of two 3D vectors (a quantity that has both magnitude and direction). Examples of vectors include force and velocity.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image288.png" width="149" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image289.png" width="51" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">csc</span><a name="NODO26" id="NODO26"></a></h2> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">csch</span><a name="NODO27" id="NODO27"></a></h2> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">deriv</span><a name="NODO28" id="NODO28"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span lang="EN-US">The deriv function returns the derivative of a mathematical function. For functions of more than one variable, the deriv function returns the partial derivative with respect to the specified variable of differentiation.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image290.png" width="77" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">f</span></i> <span lang="EN-US">is a function of the variable<span style="DISPLAY: none">A symbol that represents an unspecified or unknown quantity, such as "a," "b," or "x"</span> of differentiation.</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">x</span></i> <span lang="EN-US">is the variable of differentiation, that is, the variable with respect to which the derivative is taken.</span></p> <p class="MsoNormal"><span lang="EN-US">Radian measure is automatically selected whenever you integrate or differentiate a trigonometric function.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">derivn</span><a name="NODO29" id="NODO29"></a></h2> <p class="MsoNormal"><span lang="EN-US">The derivn function returns the second and higher derivatives of a mathematical function. For functions of more than one variable, the derivn function returns the higher-order partial derivative with respect to the specified variable of differentiation.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image291.png" width="101" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">det</span><a name="NODO30" id="NODO30"></a></h2> <p class="MsoNormal"><span lang="EN-US">The det function returns the</span> <span class="glossary"><span lang= "EN-US">determinant</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">The value computed from a square matrix that determines whether the matrix is singular (has 0 determinant) or invertible (has non-zero determinant)</span></span> <span lang="EN-US">of a</span> <span class="glossary"><span lang= "EN-US">matrix</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">diagonalMatrix</span><a name="NODO31" id="NODO31"></a></h2> <p class="MsoNormal"><span lang="EN-US">The diagonalMatrix function returns a square <span class="glossary">matrix</span><span class= "glossarydef"><span style="DISPLAY: none">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span></span> that has the specified elements on the diagonal and zeros everywhere else</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">e</span><a name= "NODO32" id="NODO32"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">expand</span><a name="NODO33" id="NODO33"></a></h2> <p class="MsoNormal"><span lang="EN-US">The expand function returns the expanded form of the product of two or more</span> <span class= "glossary"><span lang="EN-US">expressions</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span><span lang="EN-US">. Microsoft Mathematics does not expand expressions by default as part of its normal simplification; to obtain the expanded form you must use the expand function explicitly.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">factor</span><a name="NODO34" id="NODO34"></a></h2> <p class="MsoNormal"><span lang="EN-US">The factor function returns the prime</span> <span class="glossary"><span lang= "EN-US">factors</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">One of two or more numbers or quantities that can be multiplied together to give a specified number or quantity. For example, 3 and 5 are factors of 15</span></span> <span lang="EN-US">of an integer or simple expression.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">floor</span><a name="NODO35" id="NODO35"></a></h2> <p class="MsoNormal"><span lang="EN-US">The floor function returns the largest integer less than or equal to a number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">frequency</span><a name="NODO36" id="NODO36"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The frequency function returns the number of times an item you specify appears in a list<span style="DISPLAY: none">An ordered set of elements enclosed in braces</span>.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax:</span> <span style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image292.png" width="152" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: center; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class="MsoNormal" align="center"><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image293.png" width="244" height="22" alt="image"></span><span style= "FONT-FAMILY: 'Times New Roman','serif'"> geeft </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image294.png" width="9" height= "22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">gcf</span><a name="NODO37" id="NODO37"></a></h2> <p class="MsoNormal"><span lang="EN-US">The gcf function returns the <span class="glossary">greatest common factor</span><span class="glossarydef"><span style= "DISPLAY: none">The largest number that can be exactly divided into each element of a set of numbers. The greatest common factor of 12, 60, and 84 is 12. Also called greatest common divisor</span></span> of one or more numbers</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">geometricMean</span><a name="NODO38" id="NODO38"></a></h2> <p class="MsoNormal"><span lang="EN-US">The geometricMean function returns the</span> <span class="glossary"><span lang= "EN-US">geometric mean</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">The nth root of the product of a set of n numbers</span></span> <span lang= "EN-US">of a data set. The geometric mean is computed by multiplying all numbers in the set and then taking the <i>n</i>th root, where <i>n</i> is the size of the set.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">harmonicMean</span><a name="NODO39" id="NODO39"></a></h2> <p class="MsoNormal"><span lang="EN-US">The harmonicMean function returns the</span> <span class="glossary"><span lang= "EN-US">harmonic mean</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A value found by adding the reciprocals of all the numbers in the data set, taking the reciprocal of the resulting sum, and multiplying by the size of the set</span></span> <span lang="EN-US">of a data set. The harmonic mean is computed by adding the reciprocals of all the numbers in the data set, taking the reciprocal of the resulting sum, and multiplying by the size of the set.</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">i</span><a name= "NODO40" id="NODO40"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">identityMatrix</span><a name="NODO41" id="NODO41"></a></h2> <p class="MsoNormal"><span lang="EN-US">The identityMatrix function returns the <i>n</i> × <i>n</i> identity matrix (a square matrix that has the numeral 1 in each position on the principal diagonal and 0 in all other positions).</span></p> <p class="MsoNormal">Syntax</p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image295.png" width="131" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">imaginaryPart</span><a name="NODO42" id="NODO42"></a></h2> <p class="MsoNormal"><span lang="EN-US">The realPart function returns the real part of a complex number<span style= "DISPLAY: none">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span> and the imaginaryPart function returns the imaginary part of a complex number.</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image296.png" width="125" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image235.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image297.png" width="173" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image068.png" width="9" height= "22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image298.png" width="233" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image299.png" width="51" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">inner</span><a name="NODO43" id="NODO43"></a></h2> <p class="MsoNormal"><span lang="EN-US">The inner function returns the inner product (or dot or scalar product) of two vectors</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image300.png" width="176" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image301.png" width="27" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">integral</span><a name="NODO44" id="NODO44"></a></h2> <p class="MsoNormal"><span lang="EN-US">The integral function returns the definite integral or indefinite integral of a mathematical function.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%" lang="EN-US">For the indefinite integral: </span> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'" lang= "EN-US">integral(f,x)</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%" lang="EN-US">For the definite integral:    </span> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'" lang= "EN-US">integral(f,x,lower, upper)</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">intersect</span><a name="NODO45" id="NODO45"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The intersect function returns the intersection of two or more sets.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image302.png" width="176" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">{3}</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Cambria Math','serif'" lang= "EN-US"> </span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image303.png" width="234" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">{d}</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">inverse</span><a name="NODO46" id="NODO46"></a></h2> <p class="MsoNormal"><span lang="EN-US">The inverse function returns the inverse of a non-singular</span> <span class= "glossary"><span lang="EN-US">matrix</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span></span><span lang="EN-US">. The inverse is that matrix which, when multiplied by the original matrix, yields the</span> <span class="glossary"><span lang="EN-US">identity matrix</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A square matrix that has the numeral 1 in each position on the principal diagonal and 0 in all other positions</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">isPrime</span><a name="NODO47" id="NODO47"></a></h2> <p class="MsoNormal"><span lang="EN-US">The isPrime function tells whether a number is prime. The nextPrime and prevPrime functions return, respectively, the first prime greater than a given number and the first prime less than a given number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">isTrue</span><a name="NODO48" id="NODO48"></a></h2> <p class="MsoNormal"><span lang="EN-US">The isTrue function evaluates a logical comparison and returns true or false. The isTrue function is generally used in conjunction with the comparison operators (=,<,>,≥,≤, and ≠) and the logical operators <i>and</i>, <i>or</i>, <i>xor</i>, and <i>not</i>.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">lcm</span><a name="NODO49" id="NODO49"></a></h2> <p class="MsoNormal"><span lang="EN-US">The lcm function returns the</span> <span class="glossary"><span lang="EN-US">least common multiple</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">The lowest whole number that is divisible without a remainder by all of the elements of a set of numbers</span></span> <span lang="EN-US">of one or more numbers.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">limit</span><a name="NODO50" id="NODO50"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The limit function returns the limit of a mathematical function at a particular point, which may be infinity.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image304.png" width="88" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">linearSolve</span><a name="NODO51" id="NODO51"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The linearSolve function returns the solution to the linear system Mx = v, where M is a matrix of coefficients, x is a column vector of unknown variables, and v is a column vector.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image305.png" width="162" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">matrix</span></i> <span lang="EN-US">is an arbitrary matrix.</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">v</span></i> <span lang="EN-US">is a vector with as many elements as the number of rows of <i>matrix</i>.</span></p> <p class="MsoNormal"><span lang="EN-US">Return Value</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">If the input matrix <i>M</i> is square and invertible, then the solution is equivalent to the matrix product of the inverse of <i>M</i> and the column vector <i>v</i>. If the number of rows of <i>M</i> is greater than the number of columns, then in general the system is overdetermined and there is no solution. If the number of rows of <i>M</i> is less than the number of columns, the system is generally underdetermined and it is possible to find solutions for the first <i>n-k</i> terms (where <i>n-k</i> is the number of columns minus the number of rows) expressed as linear combinations of the last <i>k</i> terms.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Example</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image306.png" width="371" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Courier New'">{−87/5, 47/5, 4/5}</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">listIndex</span><a name="NODO52" id="NODO52"></a></h2> <p class="MsoNormal"><span lang="EN-US">The listIndex function returns a list containing the position of an item that you specify in a list<span style="DISPLAY: none">An ordered set of elements enclosed in braces</span>.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">listItem</span><a name="NODO53" id="NODO53"></a></h2> <p class="MsoNormal"><span lang="EN-US">The listItem function returns the item at the position that you specify in a list<span style="DISPLAY: none">An ordered set of elements enclosed in braces</span>.</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">ln</span><a name= "NODO54" id="NODO54"></a></h2> <p class="MsoNormal"><span lang="EN-US">The ln function returns the</span> <span class="glossary"><span lang="EN-US">natural logarithm</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A logarithm with the irrational number e as a base</span></span> <span lang="EN-US">of a number or</span> <span class="glossary"><span lang= "EN-US">expression</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">log</span><a name="NODO55" id="NODO55"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The log function returns the base 10 logarithm of a number or expression, or the logarithm to an arbitrary base b.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image307.png" width="46" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image308.png" width="114" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image309.png" width="61" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image310.png" width="129" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">magnitude</span><a name="NODO56" id="NODO56"></a></h2> <p class="MsoNormal"><span lang="EN-US">The magnitude function returns the magnitude of a vector</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">matrixToColumnList</span><a name="NODO57" id= "NODO57"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">matrixToRowList</span><a name="NODO58" id= "NODO58"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The matrixToColumnList and matrixToRowList functions take a matrix and convert it to a list that contains one or more component lists.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US">matrixToColumnList(matrix)</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US">matrixToRowList(matrix)</span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">matrix</span></i> <span lang="EN-US">is a matrix that contains one or more columns (for matrixToColumnList) or rows (for matrixToRowList). Each column or row becomes a component list of the resulting list.</span></p> <p class="MsoNormal"><span lang="EN-US">Return Value</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">A list</span> <span lang="EN-US">containing as component lists the columns (for matrixToColumnList) or rows (for matrixToRowLis</span><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">t) of the matrix.</span></p> <p class="MsoNormal"><span lang="EN-US">Examples</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image311.png" width="375" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US">{{2, 3, 4}, {3, 5, 7}, {7, 9, 6} }</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Cambria Math','serif'" lang= "EN-US"> </span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image312.png" width="351" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US">{{2, 3, 7}, {3, 5, 9}, {4, 7, 6} }</span></p> <p class="MsoNormal"><b><span lang="EN-US">Related</span></b></p> <p class="MsoNormal"><span lang="EN-US">The</span> <span class= "Heading2Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-SIZE: 16pt" lang= "EN-US">columnListToMatrix</span></span> <span lang= "EN-US">and</span> <span class="Heading2Char"><span style= "LINE-HEIGHT: 115%; FONT-STYLE: normal; FONT-SIZE: 16pt" lang= "EN-US">rowListToMatrix</span></span> <span lang="EN-US">functions take a list that contains one or more component lists and convert it to a matrix<span style="DISPLAY: none">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span>.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'" lang= "EN-US">columnListToMatrix(list)</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style="FONT-FAMILY: 'Courier New'" lang="EN-US">rowListToMatrix(list)</span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">list</span></i> <span lang="EN-US">is a list that contains one or more lists of equal length. Each of the component lists becomes a column (for columnListToMatrix) or row (for rowListToMatrix) of the resulting matrix.</span></p> <p class="MsoNormal"><span lang="EN-US">Return Value</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">A matrix that has columns (for columnListToMatrix) or rows (for rowListToMatrix) that are the same as the component lists of the input.</span></p> <p class="MsoNormal"><span lang="EN-US">Example</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image313.png" width="323" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image314.png" width="78" height="54" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Cambria Math','serif'" lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image315.png" width="298" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image316.png" width="78" height="54" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">max</span><a name="NODO59" id="NODO59"></a></h2> <p class="MsoNormal"><span lang="EN-US">The max function returns the largest element of a data set.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'" lang= "EN-US">max(x1,x2,...)</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'" lang= "EN-US">max({x1,x2,...})</span></p> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">mean</span><a name="NODO60" id="NODO60"></a></h2> <p class="MsoNormal"><span lang="EN-US">The mean function returns the</span> <span class="glossary"><span lang= "EN-US">mean</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">The sum of all the elements of a set divided by the number of elements in the set. Also called arithmetic mean or average.</span></span> <span lang="EN-US">of a data set. The mean is computed by adding all numbers in the set, and then dividing by the size of the set.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">median</span><a name="NODO61" id="NODO61"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The median function returns the median of a data set. The median is often used in place of the mean as a measure of the center of a data set because it is not influenced by large disparities in extreme values. For example, data on incomes and housing prices are often reported as median values, rather than means.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">min</span><a name="NODO62" id="NODO62"></a></h2> <p class="MsoNormal"><span lang="EN-US">The min function returns the minimum of a data set.</span></p> <h2><a name="_Toc307066024"><span style="FONT-STYLE: normal" lang= "EN-US">mode</span></a></h2> <p class="MsoNormal"><span lang="EN-US">The mode function returns the mode of a data set. The mode is frequently introduced in discussions of average values as a companion to the mean and median. Unlike those two statistics, the mode does not represent a measure of central tendency. Depending on the particular distribution and the particular observations, the mode can be found near the extremes of a distribution.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">nextPrime</span><a name="NODO63" id="NODO63"></a></h2> <p class="MsoNormal"><span lang="EN-US">The nextPrime function returns the first prime greater than a given number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">not</span><a name="NODO64" id="NODO64"></a></h2> <p class="MsoNormal"><span lang="EN-US">The logical operators <i>and</i>, <i>not</i>, <i>or</i>, and <i>xor</i> are used to construct logical statements. Together with the comparison operators (=,<>,<,>,≤,≥) and the isTrue function, you can use the logical operators to create and verify a variety of logical statements.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">nsolve</span><a name="NODO65" id="NODO65"></a></h2> <p class="MsoNormal"><span lang="EN-US">The nsolve function returns a numerical solution to one or more equations. The nsolve function solves equations simultaneously, meaning that for a solution to exist, it must hold for all equations at the same time. There must be as many unknown variables as there are equations.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="TEXT-INDENT: -14.2pt; MARGIN-LEFT: 14.2pt" class= "MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 11pt" lang= "EN-US">nsolve({eq1,eq2,...,eqn},{{var1},{var2},...,{varn}})</span></p> <p style="TEXT-INDENT: -14.2pt; MARGIN-LEFT: 14.2pt" class= "MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 11pt" lang= "EN-US">nsolve({eq1,eq2,...,eqn},{{var1,init1},{var2,init2},...,{varn,initn}})</span></p> <p style="TEXT-INDENT: -14.2pt; MARGIN-LEFT: 14.2pt" class= "MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 11pt" lang= "EN-US">nsolve({eq1,eq2,...,eqn},{{var1,min1,max1},{var2,min2,max2},...,{varn,minn,maxn}})</span></p> <p style="TEXT-INDENT: -14.2pt; MARGIN-LEFT: 14.2pt" class= "MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Courier New'; FONT-SIZE: 11pt" lang= "EN-US">nsolve({eq1,eq2,...,eqn},{{var1,min1,init1,max1},{var2,min2,init2,max2},...,{varn,minn,initn,maxn}})</span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">{eq1,eq2,...,eqn}</span></i> <span lang="EN-US">is a braced set of <i>n</i> equations in <i>n</i> unknown variables. (Although the syntax is identical to that of a list, the input is <i>not</i> a list of equations. Microsoft Mathematics does not permit equations in lists.)</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">{{var1,min1,init1,max1},{var2,min2,init2,max2},...,{varn,minn,initn,maxn}}</span></i> <span lang="EN-US">is a list of variable, initial value, and range specifications for each unknown variable. The range specification tells Microsoft Mathematics to look in a particular range for the solution for that variable. The range specification is optional for each variable. If omitted, Microsoft Mathematics looks for solutions anywhere on the real number line. The initial value provides a starting point for the calculation. <i>The unknown variables must be unassigned, that is, they must not currently be listed among your Stored Variables.</i></span></p> <p class="MsoNormal"><span lang="EN-US">Result</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">All real solutions for the equation or set of equations.</span></p> <p class="MsoNormal"><span lang="EN-US">Example</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image317.png" width="214" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="center"><span style="LINE-HEIGHT: 115%" lang= "EN-US">x≈0.1502825229612</span></p> <p style="TEXT-ALIGN: center; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="center"><span lang="EN-US"> </span></p> <p style="TEXT-ALIGN: center; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="center"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image318.png" width="338" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="center"><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image319.png" width="327" height="22" alt="image"></span><span style="LINE-HEIGHT: 115%" lang="EN-US">)</span></p> <h2><span style="FONT-STYLE: normal" lang="EN-US">or</span><a name= "NODO66" id="NODO66"></a></h2> <p class="MsoNormal"><span lang="EN-US">Or is a logical operator (inclusive or)</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">permutation</span><a name="NODO67" id="NODO67"></a></h2> <p class="MsoNormal"><span lang="EN-US">The permutation function returns the number of</span> <span class="glossary"><span lang= "EN-US">perm</span></span><span lang="EN-US">u</span><span class= "glossary"><span lang="EN-US">tations</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">An ordered arrangement of elements from a set</span></span> <span lang= "EN-US">of size <i>k</i> from a set of <i>n</i> elements.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">plot2d</span><a name="NODO68" id="NODO68"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The plot2D function plots y as a function of x.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image320.png" width="94" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">f(x)</span></i> <span lang="EN-US">is a function of the variable<span style="DISPLAY: none">A symbol that represents an unspecified or unknown quantity, such as "a," "b," or "x"</span> <i>x</i>.</span></p> <h4><b><span lang="EN-US">Additional Arguments for the stand-alone program</span></b><a name="NODO69" id="NODO69"></a></h4> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span lang= "EN-US">Plotting options may be supplied as arguments to this function.</span></p> <h4 style="MARGIN-LEFT: 14.2pt"><span style="FONT-STYLE: normal" lang="EN-US"> </span><span style="FONT-STYLE: normal" lang= "EN-US">Plotting options</span><a name="NODO70" id= "NODO70"></a></h4> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">There are several plotting options available for use with the various plot and show functions in Microsoft Mathematics. Each option is specified as an argument to the plot and show functions and is specified in list format (inside braces {}). The option must be included after all required arguments in the function. You can specify multiple options in the same command. Not all options can be used with all plot and show functions.</span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Data Range and Display Range Options</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">A range can be specified for each plotted variable. If the range is specified within a plot command, it is used as the data range—the interval over which the data for plotting is calculated. If the range is specified within a show command, it is used as the display range.</span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <pre style="MARGIN-LEFT: 14.2pt"> <span style="FONT-SIZE: 12pt" lang= "EN-US">Option Syntax Example</span> </pre> <pre style="TEXT-INDENT: -21.3pt; MARGIN-LEFT: 21.3pt"> <span style="FONT-SIZE: 12pt" lang= "EN-US">{x,min,max} plot2D(sin(x),{x,0,90})</span> </pre> <pre> <span style="FONT-SIZE: 12pt" lang= "EN-US">{y,min,max} plotY2D(cos(y),{y,-2,2})</span> </pre> <pre> <span style="FONT-SIZE: 12pt" lang= "EN-US">{z,min,max} plot3D(x^2+y^2,{z,0,4})</span> </pre> <pre> <span style="FONT-SIZE: 12pt" lang= "EN-US">{r,min,max} plotPolar2D(1/theta,{r,1,4})</span> </pre> <pre> <span style="FONT-SIZE: 12pt" lang= "EN-US">{theta,min,max} plotPolar2D(theta*sin(theta),{theta,0,3})</span> </pre> <pre> <span style="FONT-SIZE: 12pt" lang= "EN-US">{phi,min,max} plotPolar3D(cos(3theta)sin(2phi),{phi,-1/2,1/2})</span> </pre> <pre style="TEXT-INDENT: -140.35pt; MARGIN-LEFT: 5cm"> <span style="FONT-SIZE: 12pt" lang= "EN-US">{t,min,max} plotParam3D(cos(t)(3 + cos(s))/2,sin(t)(3 + cos(s))/2,sin(s)/2,{t,0,3})</span> </pre> <pre style="TEXT-INDENT: -140.35pt; MARGIN-LEFT: 5cm"> <span style="FONT-SIZE: 12pt" lang= "EN-US">{s,min,max} plotParam3D(cos(t)(3 + cos(s))/2,sin(t)(3 + cos(s))/2,sin(s)/2,{s,0,3})</span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Axis Label Options</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">Microsoft Mathematics plots all graphs on a limited set of axes—2D Cartesian, 2D Polar, 3D Cartesian, 3D Cylindrical, and 3D Spherical. These graphs use a select set of plot variables, which are listed under Data Range and Display Range Options but there may be times when you want to see graphs of other variables. For example, you might want to plot a force vs. acceleration graph. You can create such a graph by first plotting your data using the variables x and y, then "aliasing" or renaming the axis labels to acceleration and force. The following axis label options are available only for the show2D and show3D functions.</span></p> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{AliasX,"alias"} show2D(plot2DY(sin(y)),{AliasX,"sin(y)"})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{AliasY,"alias"} show2D(plot2D(cos(x)),{AliasY,"cos(x)"}</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{AliasZ,"alias"} how3D(plot3D(cos(x)+sin(y)),{AliasZ,"height"})</span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Graph Control Options</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">The graph control options, which are available only with the show2D and show3D functions, are keyboard equivalents to the options available in the Graph Controls area of the Graphing tab:</span></p> <p style="TEXT-INDENT: -18pt; MARGIN-LEFT: 106.8pt" class= "MsoListParagraphCxSpFirst"><span style="FONT-FAMILY: Symbol" lang= "EN-US">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> <span lang="EN-US">Show or hide axes</span></p> <p style="TEXT-INDENT: -18pt; MARGIN-LEFT: 106.8pt" class= "MsoListParagraphCxSpMiddle"><span style="FONT-FAMILY: Symbol" lang="EN-US">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> <span lang="EN-US">Show or hide the outer frame</span></p> <p style="TEXT-INDENT: -18pt; MARGIN-LEFT: 106.8pt" class= "MsoListParagraphCxSpMiddle"><span style="FONT-FAMILY: Symbol" lang="EN-US">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> <span lang="EN-US">Show or hide gridlines</span></p> <p style="TEXT-INDENT: -18pt; MARGIN-LEFT: 106.8pt" class= "MsoListParagraphCxSpMiddle"><span style="FONT-FAMILY: Symbol" lang="EN-US">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> <span lang="EN-US">Show wireframe or 3D surface plot</span></p> <p style="TEXT-INDENT: -18pt; MARGIN-LEFT: 106.8pt" class= "MsoListParagraphCxSpLast"><span style="FONT-FAMILY: Symbol" lang= "EN-US">·<span style= "FONT: 7pt 'Times New Roman'">        </span></span> <span lang="EN-US">Use a proportional display or maximize graph size</span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">In order, these options take the following keyboard equivalent:</span></p> <pre style="MARGIN-LEFT: 5.65pt"> <span lang= "EN-US">{ShowAxis,true/false} show2D(plot2D(sin(x)),{ShowAxis,false})</span> </pre> <pre style="MARGIN-LEFT: 5.65pt"> <span lang= "EN-US">{ShowBox,true/false} show2D(plot2D(sin(x)),{ShowBox,false})</span> </pre> <pre style="MARGIN-LEFT: 5.65pt"> <span lang= "EN-US">{ShowGrid,true/false} show2D(plot2D(sin(x)),{ShowGrid,true})</span> </pre> <pre style="MARGIN-LEFT: 5.65pt"> <span lang= "EN-US">{ShowWireframe,true/false} show3D(plot3D(sin(x)+cos(y)),{ShowWireframe,true})</span> </pre> <pre style="MARGIN-LEFT: 5.65pt"> <span lang= "EN-US">{Proportional,true/false} show2D(plot2D(sin(x)),{Proportional,true})</span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Color Option</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">When you create multiple graphs on the Graphing tab, or by using the show2D or show3D functions, Microsoft Mathematics automatically plots each graph in a different color. You can use the color option to specify a particular color for a particular graph. You can specify the color in two formats:</span></p> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{Color,"rrggbb"} plot2D(sin(x),{Color,"00ff00"})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{Color,"aarrggbb"} plot2D(sin(x),{Color,"8800ff00"})</span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">The "rrggbb" format allows you to specify the red, green, and blue values in the range from 0 through 255 using hexadecimal notation (00=0, ff=255). The "aarrggbb" format allows you to specify an alpha value in addition to the standard RGB color. The alpha value specifies the transparency of the graph (00=transparent, ff=opaque).</span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Line Styles</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">Functions, equations, inequalities, and parametric equations are plotted as solid lines or curves by default. You can use the LineStyle option to specify that a graph be plotted using a particular line style:</span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{LineStyle,"Solid"} plot2D(sin(x),{LineStyle,"Solid"}) </span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{LineStyle,"Dot"} plot2D(sin(x),{LineStyle,"Dot"})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{LineStyle,"Dash"} plot2D(sin(x),{LineStyle,"Dash"})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{LineStyle,"DashDot"} plot2D(sin(x),{Linestyle,"DashDot"})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{LineStyle,"DashDotDot"} plot2D(sin(x),{LineStyle,"DashDotDot"})</span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US"> </span></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Sample Size</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">Use the SampleSize option to specify the number of sample points used to create the graph of a function, equation, parametric equation, or inequality. This option has no effect on data set plots.</span></p> <pre style="MARGIN-LEFT: 14.2pt"> <span lang= "EN-US">{SampleSize,integer} plot2D(sin(x),{SampleSize,15})</span> </pre> <pre style="MARGIN-LEFT: 14.2pt"> <span lang="EN-US"> </span> </pre> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><b><span lang= "EN-US">Note</span></b></p> <p style="MARGIN-LEFT: 14.2pt" class="MsoNormal"><span lang= "EN-US">Some options that can be used with a given function may have no effect.</span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h4><span lang="EN-US">Examples</span> <span lang= "EN-US">plot2D</span><a name="NODO71" id="NODO71"></a></h4> <p class="MsoNormal"><span lang="EN-US"> </span></p> <table style= "BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0"> <tbody> <tr> <td style= "BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext 1pt solid; PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 237.5pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid; PADDING-TOP: 0cm" valign="top" width="317"> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image321.png" width="107" height="22" alt="image"></span></p> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "FONT-SIZE: 11pt"><img id="Picture 3" src= "MSMath_files/image322.png" width="312" height="312" alt="image" name="Picture 3"></span></p> </td> <td style= "BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 237.5pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid; PADDING-TOP: 0cm" valign="top" width="317"> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image323.png" width="132" height="22" alt="image"></span></p> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "FONT-SIZE: 11pt"><img id="Picture 6" src= "MSMath_files/image324.png" width="312" height="312" alt="image" name="Picture 6"></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">plot3D</span><a name="NODO72" id="NODO72"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The plot3D function plots z as a function of x and y.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image325.png" width="122" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "FONT-FAMILY: 'Times New Roman','serif'"><img id="Picture 10" src= "MSMath_files/image326.png" width="373" height="357" alt="image" name="Picture 10"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">plotCylR3D</span><a name="NODO73" id="NODO73"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotCyl3D function plots <i>r</i> as a function<span style="DISPLAY: none">A mathematical relationship between variables in which the value of one variable determines a unique value for another variable</span> of <i>z</i> and</span> θ<span lang="EN-US">.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image327.png" width="174" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Cambria Math','serif'" lang="EN-US"> </span></p> <h2><span style="FONT-STYLE: normal; FONT-FAMILY: 'Courier New'" lang="EN-US">plotEq2d</span><a name="NODO74" id="NODO74"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotEq2D function plots equations<span style="DISPLAY: none">A mathematical statement that two expressions, usually separated by an equal sign, are of the same value</span> of the form</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image328.png" width="83" height="22" alt="image"></span><span lang="EN-US">. Any equation that includes the two variables <i>x</i> and <i>y</i> can be written in this form by subtracting the right side of the equation from both sides. For example,</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image329.png" width="93" height="22" alt="image"></span><span lang= "EN-US"> becomes</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image330.png" width="128" height="22" alt="image"></span><span lang="EN-US"> and</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image331.png" width="150" height="22" alt="image"></span><span lang="EN-US">becomes  </span><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image332.png" width="178" height="22" alt="image"></span><span lang="EN-US">.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Examples</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image333.png" width="186" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image334.png" width="190" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">plotEq3D</span><a name="NODO75" id="NODO75"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotEq3D function plots equations that can be written in the form f(x,y,z)=0.</span></p> <h2><span lang="EN-US">plotIneq2d</span><a name="NODO76" id= "NODO76"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotIneq2D function plots inequalities.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Examples</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image335.png" width="179" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image336.png" width="204" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image337.png" width="338" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">plotParam2d</span><a name="NODO77" id="NODO77"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotParam2D function plots a parametric curve that consists of ordered pairs<br>  <i>(x = f(t),y = g(t))</i>.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Examples</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image338.png" width="218" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image339.png" width="316" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">plotParam3D</span><a name="NODO78" id="NODO78"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotParam3D function plots a surface that consists of ordered triples <i>(x = f(t,s),y = g(t,s),z = h(t,s))</i>.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">plotPolar2d</span><a name="NODO79" id="NODO79"></a></h2> <p class="MsoNormal"><span lang="EN-US">The plotPolar2D function plots r as a function of θ.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image340.png" width="156" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">plotPolar3D</span><a name="NODO80" id="NODO80"></a></h2> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">The plotPolar3D function plots r as a function of θ and φ.</span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">ploty2D</span><a name="NODO81" id="NODO81"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The plotY2D function plots the dependent variable x as a function of the independent variable y.</span> <span lang= "EN-US">Syntax</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image341.png" width="104" height="22" alt="image"></span></p> <p class="MsoNormal">Example</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image342.png" width="117" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <img id="Picture 126" src="MSMath_files/image343.png" width="376" height="376" alt="image" name="Picture 126"></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span lang="EN-US"> </span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">plotyz3D</span><a name="NODO82" id="NODO82"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The plotYZ3D function plots x as a function of y and z.</span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">plotzx3D</span><a name="NODO83" id="NODO83"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The plotzx3D function plots y as a function of x and z.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image344.png" width="124" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Example</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image345.png" width="137" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">PrevPrime</span><a name="NODO84" id="NODO84"></a></h2> <p class="MsoNormal"><span lang="EN-US">The prevPrime function returns the first prime less than a given number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">product</span><a name="NODO85" id="NODO85"></a></h2> <p class="MsoNormal"><span lang="EN-US">The product function returns the product of a data set.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">quadraticMean</span><a name="NODO86" id="NODO86"></a></h2> <p class="MsoNormal"><span lang="EN-US">The quadraticMean function returns the</span> <span class="glossary"><span lang= "EN-US">quadratic mean</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">The statistic found by adding the squares of all elements of the set, dividing by n (where n is the size of the set), and then taking the square root. Also called root mean square</span></span> <span lang="EN-US">of a data set. The quadratic mean is computed by adding the squares of all elements of the set, dividing by <i>n</i> (where <i>n</i> is the size of the set), and then taking the square root.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">random</span><a name="NODO87" id="NODO87"></a></h2> <p class="MsoNormal"><span lang="EN-US">The random function returns a random real number from the interval [<i>0,1</i>] or a random integer from the interval [<i>0,n</i>], where <i>n</i> is an integer specified as an argument to the function.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image346.png" width="70" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image347.png" width="80" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 70.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image348.png" width="149" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">realPart</span><a name="NODO88" id="NODO88"></a></h2> <p class="MsoNormal"><span lang="EN-US">The realPart function returns the real part of a complex number<span style= "DISPLAY: none">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span> and the imaginaryPart function returns the imaginary part of a complex number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">reduce</span><a name="NODO89" id="NODO89"></a></h2> <p class="MsoNormal"><span lang="EN-US">The reduce function returns the reduced echelon form of a matrix, which is an upper triangular form in which, in general, each row has a leading 1, and the column that contains each leading 1 has zeros in all other rows. The reduced echelon form is most useful in solving linear systems <i>Mx</i> = <i>v</i>, where <i>M</i> is a matrix<span style= "DISPLAY: none">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span> of coefficients, <i>x</i> is a column vector<span style="DISPLAY: none">A quantity that has both magnitude and direction. Examples of vectors include force and velocity</span> of unknown variables, and <i>v</i> is a column vector. If you add the column vector <i>v</i> as the last column of the matrix <i>M</i>, you obtain what is called the <i>augmented matrix</i>. The last column of the augmented matrix in reduced echelon form can be used to find the solution to the system of equations.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Example</span></p> <p style="TEXT-ALIGN: center; LINE-HEIGHT: normal" class= "MsoNormal" align="center"><span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 22pt" lang="EN-US"><img src="MSMath_files/image349.png" width="180" height="65" alt="image"></span><span style= "FONT-FAMILY: 'Times New Roman','serif'">   geeft   </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 32.5pt" lang="EN-US"><img src="MSMath_files/image350.png" width="127" height="94" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">reverse</span><a name="NODO90" id="NODO90"></a></h2> <p class="MsoNormal"><span lang="EN-US">The reverse function returns the input in reverse order.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image351.png" width="133" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">root</span><a name="NODO91" id="NODO91"></a></h2> <p class="MsoNormal"><span lang="EN-US">The root function returns the <i>x</i>th root of <i>y</i>.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image352.png" width="69" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image353.png" width="137" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image354.png" width="205" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">round</span><a name="NODO92" id="NODO92"></a></h2> <p class="MsoNormal"><span lang="EN-US">The round function returns the integer nearest the given number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">row</span><a name="NODO93" id="NODO93"></a></h2> <p class="MsoNormal"><span lang="EN-US">The row function returns the specified row in a matrixA rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems as a list.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "FONT-FAMILY: 'Times New Roman','serif'">Syntax</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image355.png" width="107" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">show2d</span><a name="NODO94" id="NODO94"></a></h2> <p class="MsoNormal"><span lang="EN-US">The show2D function plots multiple 2D graphs in a single command.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image356.png" width="175" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Example</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image357.png" width="551" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">show3D</span><a name="NODO95" id="NODO95"></a></h2> <p class="MsoNormal"><span lang="EN-US">The show3D function plots multiple 3D graphs in a single command.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image356.png" width="175" height="22" alt="image"></span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image358.png" width="175" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Example</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image359.png" width="467" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">sec</span><a name="NODO96" id="NODO96"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">sech</span><a name="NODO97" id="NODO97"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">seriesProduct</span><a name="NODO98" id="NODO98"></a></h2> <p class="MsoNormal"><span lang="EN-US">The seriesProduct function returns the product of a mathematical sequence.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image360.png" width="170" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><i><span lang= "EN-US">f</span></i> <span lang="EN-US">is a function of the product index.</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><i><span lang= "EN-US">n</span></i> <span lang="EN-US">is the product index.</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><i><span lang= "EN-US">a</span></i> <span lang="EN-US">is the lower limit of the index.</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><i><span lang= "EN-US">b</span></i> <span lang="EN-US">is the upper limit of the index.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">seriesSum</span><a name="NODO99" id="NODO99"></a></h2> <p class="MsoNormal"><span lang="EN-US">The seriesSum function returns the sum of a mathematical series.</span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image361.png" width="143" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Arguments</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">f</span></i> <span lang="EN-US">is a function of the index of summation. (Cannot be a reserved variable: <i>e</i>, <i>i</i>, <i>pi)</i></span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">n</span></i> <span lang="EN-US">is the index of summation.</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">a</span></i> <span lang="EN-US">is the lower limit of the index.</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><i><span lang= "EN-US">b</span></i> <span lang="EN-US">is the upper limit of the index.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">setDifference</span><a name="NODO100" id= "NODO100"></a></h2> <p class="MsoNormal"><span lang="EN-US">The setDifference function returns the set difference<span style="DISPLAY: none">Those elements of a set A which are not in a second set B</span> of two sets.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Syntax:   </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image362.png" width="278" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">sign</span><a name="NODO101" id="NODO101"></a></h2> <p class="MsoNormal"><span lang="EN-US">The sign function returns the sign of a real number or the value of a complex number divided by its absolute value. For real numbers, the sign function is defined as <i>+1</i> if <i>x</i> > <i>0</i>, <i>-1</i> if <i>x</i> < <i>0</i>, and <i>0</i> if <i>x = 0</i>. For complex numbers, the sign function is defined as <i>z/|z|</i>.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">simplify</span><a name="NODO102" id="NODO102"></a></h2> <p class="MsoNormal"><span lang="EN-US">The simplify function returns a simplified form of an expression, or the value of an expression at a particular point.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image363.png" width="102" height="22" alt="image"></span></p> <p style="MARGIN-LEFT: 70.8pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image364.png" width="269" height="22" alt="image"></span></p> <p class="MsoNormal">Examples</p> <pre style="TEXT-ALIGN: center"> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 3pt" lang="EN-US"><img src="MSMath_files/image365.png" width="268" height="19" alt="image"></span><span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"> geeft 7 x^2+5 x+5, wat na gebruik van</span><span style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 3pt" lang="EN-US"><img src="MSMath_files/image366.png" width="4" height= "19" alt="image"></span><span style= "FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt">Alt+= en lineaire formuleopbouw (spatie op de juiste plaats) leidt tot </span><span style="POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 3pt" lang="EN-US"><img src="MSMath_files/image367.png" width="97" height="19" alt="image"></span> </pre> <pre style="TEXT-ALIGN: center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image368.png" width="167" height="19" alt="image"></span> </pre> <pre style="TEXT-ALIGN: center"> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image369.png" width="221" height="19" alt="image"></span> </pre> <h2><span style="FONT-STYLE: normal" lang= "EN-US">sin</span><a name="NODO103" id="NODO103"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">sinh</span><a name="NODO104" id="NODO104"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">size</span><a name="NODO105" id="NODO105"></a></h2> <p class="MsoNormal"><span lang="EN-US">The size function returns different things depending on its input. For a single list, size returns a number that represents the length of the list. For a matrix<span style="DISPLAY: none">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span>, the size function returns a list that represents the size of a matrix as the number of rows and then the number of columns. For arbitrary input, size returns the number of inputs.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">slope</span><a name="NODO106" id="NODO106"></a></h2> <p class="MsoNormal"><span lang="EN-US">The slope function returns the slope of an equation involving <i>x</i> and <i>y</i>. For linear equations (that is, equations of lines), the slope is a constant. For higher-order equations, you must also specify a point at which you want the slope calculated.</span></p> <p class="MsoNormal">Syntax</p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image370.png" width="134" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Examples</span></p> <table style= "BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" class="MsoTableGrid" border="0" cellspacing="0" cellpadding="0"> <tbody> <tr> <td style= "PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 237.5pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm" valign="top" width="317"> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image371.png" width="136" height="22" alt="image"></span></p> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image372.png" width="23" height="39" alt="image"></span></p> </td> <td style= "PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; WIDTH: 237.5pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm" valign="top" width="317"> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image373.png" width="120" height="22" alt="image"></span></p> <p style="LINE-HEIGHT: normal" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image222.png" width="9" height= "22" alt="image"></span></p> </td> </tr> </tbody> </table> <h2><span style="FONT-STYLE: normal" lang= "EN-US">solve</span><a name="NODO107" id="NODO107"></a></h2> <p class="MsoNormal"><span lang="EN-US">The solve function returns the solution to one or more equations. The solve function solves equations simultaneously, meaning that for a solution to exist, it must hold for all equations at the same time. There must be as many unknown variables as there are equations.</span></p> <p class="MsoNormal"><span lang="EN-US">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image374.png" width="100" height="22" alt="image"></span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 45.8pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image375.png" width="333" height="22" alt="image"></span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">solveIneq</span><a name="NODO108" id="NODO108"></a></h2> <p class="MsoNormal"><span lang="EN-US">The solveIneq function returns the solution to a simple or compound inequality. A compound inequality is composed of multiple inequalities joined by the logical operators "and", "or", "not", and "xor". If the inequality involves more than one variable, it is solved for one variable in terms of the remaining variables.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Syntax:   </span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 5.5pt" lang="EN-US"><img src="MSMath_files/image376.png" width="146" height="22" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Examples</span></p> <p class="MsoNormal"><span lang="EN-US">Solve a simple inequality for the variable <i>x</i>:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image377.png" width="191" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="LINE-HEIGHT: 115%" lang="EN-US">x<5 and x>−5</span></p> <p class="MsoNormal"><span lang="EN-US">Solve a simple inequality for the variable <i>t</i>:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image378.png" width="234" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="LINE-HEIGHT: 115%" lang="EN-US">t≠1</span></p> <p class="MsoNormal"><span lang="EN-US">Solve a compound inequality for the variable <i>x</i>:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image379.png" width="220" height="22" alt="image"></span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image380.png" width="112" height="39" alt="image"></span></p> <p class="MsoNormal"><span lang="EN-US">Solve a compound inequality for the variable <i>x</i>:</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image381.png" width="258" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: center" class="MsoNormal" align="center"> <span style="LINE-HEIGHT: 115%" lang="EN-US">x≥2</span></p> <h2><a name="_Toc307066068"><span style="FONT-STYLE: normal" lang= "EN-US">sort</span></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The sort function returns its input sorted in ascending order.</span></p> <h2><a name="_Toc307066069"><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">sort(concatenate( ))</span></a></h2> <p class="MsoNormal"><span lang="EN-US">To sort two lists into a single sorted list, use the sort function with the concatenate function.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">sqrt</span><a name="NODO109" id="NODO109"></a></h2> <p class="MsoNormal"><span lang="EN-US">The sqrt function returns the</span> <span class="glossary"><span lang="EN-US">square root</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A number or quantity that when multiplied by itself gives the stated number or quantity.</span></span> <span lang="EN-US">of a number or</span> <span class="glossary"><span lang= "EN-US">expression</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">Any combination of constants, operators, and variables that represent numbers or quantities, for example, (5 + x)</span></span><span lang="EN-US">.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">stddev</span><a name="NODO110" id="NODO110"></a></h2> <p class="MsoNormal"><span lang="EN-US">The stddev and unbiasedStdDev functions return the</span> <span class= "glossary"><span lang="EN-US">standard deviation</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A statistical measure of the amount by which a set of values differs from the arithmetical mean, equal to the square root of the mean of the differences' squares</span></span> <span lang="EN-US">of a data set. You can calculate either a biased estimate (using stddev) or an unbiased estimate (using unbiasedStdDev) of the standard deviation, based on the biased or unbiased estimate of the</span> <span class= "glossary"><span lang="EN-US">variance</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A statistical measure of the spread or variation of a group of numbers in a sample, equal to the square of the standard deviation</span></span><span lang="EN-US">. At least two observations are required to calculate an unbiased estimate of the standard deviation.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">subBlockMatrix</span><a name="NODO111" id= "NODO111"></a></h2> <p class="MsoNormal"><span lang="EN-US">The subBlockMatrix function returns a submatrix that consists of a specified block of rows and columns. The specified rows and columns must be adjacent.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Syntax</span></p> <p style= "TEXT-ALIGN: left; LINE-HEIGHT: normal; MARGIN-LEFT: 35.4pt" class= "MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image382.png" width="542" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">subList</span><a name="NODO112" id="NODO112"></a></h2> <p class="MsoNormal"><span lang="EN-US">The subList function returns the specified sublist of a given list.</span></p> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">Syntax</span></p> <p style="MARGIN-LEFT: 35.4pt" class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image383.png" width="187" height="22" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">subMatrix</span><a name="NODO113" id="NODO113"></a></h2> <p class="MsoNormal"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">The subMatrix function returns a submatrix of specified rows and columns. The specified rows and columns need not be adjacent.</span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">sum</span><a name="NODO114" id="NODO114"></a></h2> <p class="MsoNormal"><span lang="EN-US">The sum function returns the sum of a data set.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">tan</span><a name="NODO115" id="NODO115"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">tanh</span><a name="NODO116" id="NODO116"></a></h2> <h2><span style="FONT-STYLE: normal" lang= "EN-US">toBase</span><a name="NODO117" id="NODO117"></a></h2> <p class="MsoNormal"><span lang="EN-US">The toBase function returns the base <i>b</i> equivalent of a number expressed in base 10. In particular, you can use the toBase function to obtain binary, octal, or hexadecimal equivalents for base 10 numbers.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">toFrac</span><a name="NODO118" id="NODO118"></a></h2> <p class="MsoNormal"><span lang="EN-US">The toFrac function returns the fractional form <i>d/c</i> of a decimal number.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">toPolar</span><a name="NODO119" id="NODO119"></a></h2> <p class="MsoNormal"><span lang="EN-US">The toPolar function returns the polar form <i>z</i> = <i>e</i>^(<i>i*</i></span>θ<span lang="EN-US">) of a complex numberA number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0.</span></p> <p class="MsoNormal"><span lang="EN-US">Domain: all complex numbers, particularly those in <i>rectangular form</i> <i>z</i> = <i>a + bi</i>.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Examples</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image384.png" width="121" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image385.png" width="114" height="30" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Cambria Math','serif'" lang="EN-US"> </span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image386.png" width="241" height="22" alt="image"></span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt" lang="EN-US"><img src="MSMath_files/image387.png" width="550" height="23" alt="image"></span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">toRect</span><a name="NODO120" id="NODO120"></a></h2> <p class="MsoNormal"><span lang="EN-US">The toRect function returns the rectangular form of a complex number<span style= "DISPLAY: none">A number in the form a + bi, where a and b are real numbers and i = sqrt(-1) , so that bi is imaginary unless b = 0</span>. You probably will not need to use this function much—when Microsoft Mathematics computes its numerical output, it always shows complex numbers in rectangular form.</span></p> <p style="TEXT-ALIGN: left; LINE-HEIGHT: normal" class="MsoNormal" align="left"><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">Domain : all complex numbers, particularly those in <i>polar form</i> <i>z</i> = <i>r*e^</i>(<i>i</i></span><span style="FONT-FAMILY: 'Times New Roman','serif'">θ</span><span style="FONT-FAMILY: 'Times New Roman','serif'" lang="EN-US">).</span></p> <h2><span style= "FONT-STYLE: normal; FONT-FAMILY: 'Times New Roman','serif'" lang= "EN-US">tr</span><a name="NODO121" id="NODO121"></a></h2> <p class="MsoNormal"><span lang="EN-US">The tr function returns the trace of a</span> <span class="glossary"><span lang= "EN-US">matrix</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span></span><span lang="EN-US">. The trace is the sum of the diagonal elements of a square matrix.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">transpose</span><a name="NODO122" id="NODO122"></a></h2> <p class="MsoNormal"><span lang="EN-US">The transpose function returns the</span> <span class="glossary"><span lang= "EN-US">transpose</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A matrix created by interchanging the rows and columns of a previously given matrix</span></span> <span lang="EN-US">of a</span> <span class= "glossary"><span lang="EN-US">matrix</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A rectangular array of mathematical elements. For example, the coefficients of linear equations, whose rows and columns can be combined with those of other arrays to solve problems</span></span><span lang="EN-US">. The transpose is computed by mapping each element</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 7pt" lang="EN-US"><img src="MSMath_files/image388.png" width="19" height="23" alt="image"></span><span lang="EN-US">  in a matrix A to the corresponding element</span> <span style= "POSITION: relative; LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt; TOP: 7pt" lang="EN-US"><img src="MSMath_files/image389.png" width="18" height="23" alt="image"></span><span lang="EN-US"> , where the first index indicates the row number and the second index represents the column number. In other words, the rows and columns of the matrix are transposed.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">unbiasedCoVariance</span><a name="NODO123" id= "NODO123"></a></h2> <p class="MsoNormal"><span lang="EN-US">The covariance and unbiasedCovariance functions return the <span class= "glossary">covariance</span><span class="glossarydef"><span style= "DISPLAY: none">A statistical measure of the tendency of two variables to change in conjunction with each other. It is equal to the product of their standard deviations and correlation coefficients</span></span> of two data sets. Both data sets must contain the same number of observations. The covariance function returns a biased estimate of the covariance and the unbiasedCovariance function returns an unbiased estimate. The biased estimate is (n-1)/n times the unbiased estimate.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">unbiasedStdDev</span><a name="NODO124" id= "NODO124"></a></h2> <p class="MsoNormal"><span lang="EN-US">The stddev and unbiasedStdDev functions return the</span> <span class= "glossary"><span lang="EN-US">standard deviation</span></span><span class="glossarydef"><span style= "DISPLAY: none" lang="EN-US">A statistical measure of the amount by which a set of values differs from the arithmetical mean, equal to the square root of the mean of the differences' squares</span></span> <span lang="EN-US">of a data set. You can calculate either a biased estimate (using stddev) or an unbiased estimate (using unbiasedStdDev) of the standard deviation, based on the biased or unbiased estimate of the</span> <span class= "glossary"><span lang="EN-US">variance</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A statistical measure of the spread or variation of a group of numbers in a sample, equal to the square of the standard deviation</span></span><span lang="EN-US">. At least two observations are required to calculate an unbiased estimate of the standard deviation.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">unbiasedVariance</span><a name="NODO125" id= "NODO125"></a></h2> <p class="MsoNormal"><span lang="EN-US">The variance and unbiasedVariance functions return the</span> <span class= "glossary"><span lang="EN-US">variance</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A statistical measure of the spread or variation of a group of numbers in a sample, equal to the square of the standard deviation</span></span> <span lang="EN-US">of a data set. You can calculate either the biased estimate of the variance or the unbiased estimate. Both the <b>variance</b> button on the calculator in MS Mathematics 4.0 and the variance function give the biased estimate. The two estimates use different denominators, <i>n</i> in the biased case, <i>n-1</i> in the unbiased case, where <i>n</i> is the number of observations. Because of the <i>n-1</i> used in the unbiased case, that case requires at least two observations to compute.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">union</span><a name="NODO126" id="NODO126"></a></h2> <p class="MsoNormal"><span lang="EN-US">The union function returns the set of all elements appearing in any of a specified collection of sets of two or more sets.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">variance</span><a name="NODO127" id="NODO127"></a></h2> <p class="MsoNormal"><span lang="EN-US">The variance and unbiasedVariance functions return the</span> <span class= "glossary"><span lang="EN-US">variance</span></span><span class= "glossarydef"><span style="DISPLAY: none" lang="EN-US">A statistical measure of the spread or variation of a group of numbers in a sample, equal to the square of the standard deviation</span></span> <span lang="EN-US">of a data set. You can calculate either the biased estimate of the variance or the unbiased estimate. Both the <b>variance</b> button on the calculator in MS Mathematics 4.0 and the variance function give the biased estimate. The two estimates use different denominators, <i>n</i> in the biased case, <i>n-1</i> in the unbiased case, where <i>n</i> is the number of observations. Because of the <i>n-1</i> used in the unbiased case, that case requires at least two observations to compute.</span></p> <h2><span style="FONT-STYLE: normal" lang= "EN-US">xor</span><a name="NODO128" id="NODO128"></a></h2> </div> <span style= "LINE-HEIGHT: 115%; FONT-FAMILY: 'Cambria','serif'; FONT-SIZE: 12pt"><br style="PAGE-BREAK-BEFORE: auto" clear="all"></span> <div class="WordSection4"> <p class="MsoNormal"><span lang="EN-US">xor is a logical operator (exclusive or)</span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> <p class="MsoNormal"><span lang="EN-US"> </span></p> </div> <!-- And the content tree: --> <ul id="contentsTree" class="contentTree"> <li><a href="1.htm#collegealgebrasolve">Gelijkheden in één variabele / Ontbinden in factoren</a> <ul> <li><a href="1.htm#_Toc307065925">Oplossen van een eerstegraadsvergelijking</a></li> <li><a href="1.htm#_Toc307065926">Oplossen van een tweedegraadsvergelijking in ℝ</a></li> <li><a href="1.htm#_Toc307065927">Oplossen van een tweedegraadsvergelijking in ℂ</a></li> <li><a href="1.htm#_Toc307065928">Oplossen van een veeltermvergelijking met graad groter dan 2</a></li> <li><a href="1.htm#_Toc307065929">Ontbinden in factoren</a></li> <li><a href="1.htm#_Toc307065930">Uitwerken van een product</a></li> <li><a href="1.htm#_Toc307065931">Uitwerken van een uitdrukking</a></li> <li><a href="1.htm#_Toc307065932">Oplossen van rationale vergelijkingen</a></li> <li><a href="1.htm#_Toc307065933">Ontbinden in factoren van rationale uitdrukkingen</a></li> <li><a href="1.htm#_Toc307065934">Symbolische berekeningen</a></li> <li><a href="1.htm#_Toc307065935">Goniometrische vergelijkingen</a></li> <li><a href="1.htm#_Toc307065936">Logaritmische en exponentiële vergelijkingen</a></li> <li><a href="1.htm#_Toc307065937">Waarschuwing</a></li> <li><a href="1.htm#_Toc307065938">Irrationale gelijkheden</a></li> <li><a href="1.htm#_Toc307065939">Formulegebieden samenvoegen</a></li> </ul> </li> <li><a href="1.htm#_Toc307065940">Ongelijkheden in één variable</a></li> <li><a href="1.htm#_Toc307065941">Stelsels vergelijkingen</a></li> <li><a href="1.htm#_Toc307065942">Grafische voorstellingen</a> <ul> <li><a href="1.htm#_Toc307065943">Tweedimensionele figuren / Functies in één variabele</a></li> <li><a href="1.htm#_Toc307065944">Driedimensionele figuren / Functies in twee variabelen</a></li> <li><a href="1.htm#_Toc307065945">Ongelijkheden</a></li> <li><a href="1.htm#_Toc307065946">Animaties</a></li> </ul> </li> <li><a href="1.htm#_Toc307065947">Sommaties</a></li> <li><a href="1.htm#_Toc307065948">Limieten</a></li> <li><a href="1.htm#_Toc307065949">Afgeleiden</a></li> <li><a href="1.htm#_Toc307065950">Integralen</a> <ul> <li><a href="1.htm#_Toc307065951">Onbepaalde integralen</a></li> <li><a href="1.htm#_Toc307065952">Bepaalde integralen</a></li> <li><a href="1.htm#_Toc307065953">Meervoudige integratie</a></li> </ul> </li> <li><a href= "1.htm#_Toc307065954">Differentiaalvergelijkingen</a></li> <li><a href="1.htm#_Toc307065955">Matrices</a></li> <li><a href="1.htm#_Toc307065956">Logische voorwaarden</a></li> <li><a href="1.htm#_Toc307065957">Lijst met automatisch herkende functies en commando’s</a> <ul> <li><a href="1.htm#_Toc307065958">Opmerkingen</a></li> <li><a href="1.htm#_Toc307065959">Data sets and lists</a></li> <li><a href="1.htm#_Toc307065960">Operators</a></li> <li><a href="1.htm#NODO0">!</a></li> <li><a href="1.htm#NODO1">‼</a></li> <li><a href="1.htm#NODO2">^</a></li> <li><a href="1.htm#NODO3">%</a></li> <li><a href="1.htm#NODO4">abs</a></li> <li><a href="1.htm#NODO5">and</a></li> <li><a href="1.htm#NODO6">arccos</a></li> <li><a href="1.htm#NODO7">arccot</a></li> <li><a href="1.htm#NODO8">arccsc</a></li> <li><a href="1.htm#NODO9">arcsec</a></li> <li><a href="1.htm#NODO10">arcsin</a></li> <li><a href="1.htm#NODO11">arctan</a></li> <li><a href="1.htm#NODO12">arg</a></li> <li><a href="1.htm#NODO13">cbrt</a></li> <li><a href="1.htm#NODO14">ceiling</a></li> <li><a href="1.htm#NODO15">column</a></li> <li><a href="1.htm#NODO16">combination</a></li> <li><a href="1.htm#NODO17">concatenate</a></li> <li><a href="1.htm#NODO18">conjugate</a></li> <li><a href="1.htm#NODO19">correlation</a></li> <li><a href="1.htm#NODO20">cos</a></li> <li><a href="1.htm#NODO21">cosh</a></li> <li><a href="1.htm#NODO22">cot</a></li> <li><a href="1.htm#NODO23">coth</a></li> <li><a href="1.htm#NODO24">covariance</a></li> <li><a href="1.htm#NODO25">cross</a></li> <li><a href="1.htm#NODO26">csc</a></li> <li><a href="1.htm#NODO27">csch</a></li> <li><a href="1.htm#NODO28">deriv</a></li> <li><a href="1.htm#NODO29">derivn</a></li> <li><a href="1.htm#NODO30">det</a></li> <li><a href="1.htm#NODO31">diagonalMatrix</a></li> <li><a href="1.htm#NODO32">e</a></li> <li><a href="1.htm#NODO33">expand</a></li> <li><a href="1.htm#NODO34">factor</a></li> <li><a href="1.htm#NODO35">floor</a></li> <li><a href="1.htm#NODO36">frequency</a></li> <li><a href="1.htm#NODO37">gcf</a></li> <li><a href="1.htm#NODO38">geometricMean</a></li> <li><a href="1.htm#NODO39">harmonicMean</a></li> <li><a href="1.htm#NODO40">i</a></li> <li><a href="1.htm#NODO41">identityMatrix</a></li> <li><a href="1.htm#NODO42">imaginaryPart</a></li> <li><a href="1.htm#NODO43">inner</a></li> <li><a href="1.htm#NODO44">integral</a></li> <li><a href="1.htm#NODO45">intersect</a></li> <li><a href="1.htm#NODO46">inverse</a></li> <li><a href="1.htm#NODO47">isPrime</a></li> <li><a href="1.htm#NODO48">isTrue</a></li> <li><a href="1.htm#NODO49">lcm</a></li> <li><a href="1.htm#NODO50">limit</a></li> <li><a href="1.htm#NODO51">linearSolve</a></li> <li><a href="1.htm#NODO52">listIndex</a></li> <li><a href="1.htm#NODO53">listItem</a></li> <li><a href="1.htm#NODO54">ln</a></li> <li><a href="1.htm#NODO55">log</a></li> <li><a href="1.htm#NODO56">magnitude</a></li> <li><a href="1.htm#NODO57">matrixToColumnList</a></li> <li><a href="1.htm#NODO58">matrixToRowList</a></li> <li><a href="1.htm#NODO59">max</a></li> <li><a href="1.htm#NODO60">mean</a></li> <li><a href="1.htm#NODO61">median</a></li> <li><a href="1.htm#NODO62">min</a></li> <li><a href="1.htm#_Toc307066024">mode</a></li> <li><a href="1.htm#NODO63">nextPrime</a></li> <li><a href="1.htm#NODO64">not</a></li> <li><a href="1.htm#NODO65">nsolve</a></li> <li><a href="1.htm#NODO66">or</a></li> <li><a href="1.htm#NODO67">permutation</a></li> <li><a href="1.htm#NODO68">plot2d</a> <ul> <li><a href="1.htm#NODO69">Additional Arguments for the stand-alone program</a></li> <li><a href="1.htm#NODO70">Plotting options</a></li> <li><a href="1.htm#NODO71">Examples plot2D</a></li> </ul> </li> <li><a href="1.htm#NODO72">plot3D</a></li> <li><a href="1.htm#NODO73">plotCylR3D</a></li> <li><a href="1.htm#NODO74">plotEq2d</a></li> <li><a href="1.htm#NODO75">plotEq3D</a></li> <li><a href="1.htm#NODO76">plotIneq2d</a></li> <li><a href="1.htm#NODO77">plotParam2d</a></li> <li><a href="1.htm#NODO78">plotParam3D</a></li> <li><a href="1.htm#NODO79">plotPolar2d</a></li> <li><a href="1.htm#NODO80">plotPolar3D</a></li> <li><a href="1.htm#NODO81">ploty2D</a></li> <li><a href="1.htm#NODO82">plotyz3D</a></li> <li><a href="1.htm#NODO83">plotzx3D</a></li> <li><a href="1.htm#NODO84">PrevPrime</a></li> <li><a href="1.htm#NODO85">product</a></li> <li><a href="1.htm#NODO86">quadraticMean</a></li> <li><a href="1.htm#NODO87">random</a></li> <li><a href="1.htm#NODO88">realPart</a></li> <li><a href="1.htm#NODO89">reduce</a></li> <li><a href="1.htm#NODO90">reverse</a></li> <li><a href="1.htm#NODO91">root</a></li> <li><a href="1.htm#NODO92">round</a></li> <li><a href="1.htm#NODO93">row</a></li> <li><a href="1.htm#NODO94">show2d</a></li> <li><a href="1.htm#NODO95">show3D</a></li> <li><a href="1.htm#NODO96">sec</a></li> <li><a href="1.htm#NODO97">sech</a></li> <li><a href="1.htm#NODO98">seriesProduct</a></li> <li><a href="1.htm#NODO99">seriesSum</a></li> <li><a href="1.htm#NODO100">setDifference</a></li> <li><a href="1.htm#NODO101">sign</a></li> <li><a href="1.htm#NODO102">simplify</a></li> <li><a href="1.htm#NODO103">sin</a></li> <li><a href="1.htm#NODO104">sinh</a></li> <li><a href="1.htm#NODO105">size</a></li> <li><a href="1.htm#NODO106">slope</a></li> <li><a href="1.htm#NODO107">solve</a></li> <li><a href="1.htm#NODO108">solveIneq</a></li> <li><a href="1.htm#_Toc307066068">sort</a></li> <li><a href="1.htm#_Toc307066069">sort(concatenate( ))</a></li> <li><a href="1.htm#NODO109">sqrt</a></li> <li><a href="1.htm#NODO110">stddev</a></li> <li><a href="1.htm#NODO111">subBlockMatrix</a></li> <li><a href="1.htm#NODO112">subList</a></li> <li><a href="1.htm#NODO113">subMatrix</a></li> <li><a href="1.htm#NODO114">sum</a></li> <li><a href="1.htm#NODO115">tan</a></li> <li><a href="1.htm#NODO116">tanh</a></li> <li><a href="1.htm#NODO117">toBase</a></li> <li><a href="1.htm#NODO118">toFrac</a></li> <li><a href="1.htm#NODO119">toPolar</a></li> <li><a href="1.htm#NODO120">toRect</a></li> <li><a href="1.htm#NODO121">tr</a></li> <li><a href="1.htm#NODO122">transpose</a></li> <li><a href="1.htm#NODO123">unbiasedCoVariance</a></li> <li><a href="1.htm#NODO124">unbiasedStdDev</a></li> <li><a href="1.htm#NODO125">unbiasedVariance</a></li> <li><a href="1.htm#NODO126">union</a></li> <li><a href="1.htm#NODO127">variance</a></li> <li><a href="1.htm#NODO128">xor</a></li> </ul> </li> </ul>
