<!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"><head> <!--[ GuppY v5.0.9 CeCILL Copyright (C) 2004-2014 by Laurent Duveau - http://www.freeguppy.org/ ]--> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <meta name="application-name" content="Casyopée - Créer fonction par formule, Calculer, Grapher, Tabuler, Résolution Approchée"> <title>Casyopée - Créer fonction par formule, Calculer, Grapher, Tabuler, Résolution Approchée</title> <meta name="description" content="Casyopée: a learning environment dedicated to functions"> <meta name="generator" content="GuppY CMS"> <meta name="author" content="lagrange"> <meta name="keywords" content="casyopée, functions, mathematics, geodynamic geometry, cas, symbolic computation,"> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <meta name="apple-mobile-web-app-capable" content="yes"> <meta name="apple-mobile-web-app-status-bar-style" content="black"> <link rel="shortcut icon" href="https://casyopee.math.univ-paris-diderot.fr/guppy.ico"> <link rel="alternate" type="application/rss+xml" title="Casyopée : Actualité" hreflang="fr" href="https://casyopee.math.univ-paris-diderot.fr/data/fr-news.xml"> <link type="text/css" rel="stylesheet" href="skins/casyop/style.css"> <link type="text/css" rel="stylesheet" href="skins/casyop/jqstyle.css"> <style type="text/css" media="screen"> @import url(inc/auto.css); </style> <style type="text/css" media="print"> @import url(inc/print.css); </style> <link type="text/css" rel="stylesheet" href="inc/csshead/fotorama.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/menubox.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/slidesjs.css"> <script type="text/javascript"> //<![CDATA[ <!-- var charset = "UTF-8"; var site0 = "Casyopée"; var site3 = "https://casyopee.math.univ-paris-diderot.fr/"; var sValue = screen.width + "||" + screen.height + "||" + screen.availWidth + "||" + screen.availHeight; var today = new Date(), expires = new Date(); expires.setTime(today.getTime() + (365*24*60*60*1000)); document.cookie = "GuppYScreen" + "=" + encodeURIComponent(sValue) + ";expires=" + expires.toGMTString(); //--> //]]> </script> <script type="text/javascript" src="inc/hpage.js"></script> <script type="text/javascript" src="inc/jquery-min.js"></script> <script type="text/javascript" src="inc/jquery-migrate-min.js"></script> <script type="text/javascript" src="inc/jqscript.js"></script> <script type="text/javascript" src="inc/jshead/boxmenu_toggle.js"></script> <script type="text/javascript" src="inc/jshead/fotorama.js"></script> <script type="text/javascript" src="inc/jshead/jquery.imagecube.min.js"></script> <script type="text/javascript" src="inc/jshead/sidephoto.js"></script> <script type="text/javascript" src="inc/jshead/slides.min.jquery.js"></script> <script type="text/javascript" src="inc/jshead/slidesjs.js"></script> </head><body> <h1>Créer fonction par formule, Calculer, Grapher, Tabuler, Résolution Approchée</h1> <h3><span style=""><span style="">On souhaite définir la fonction de répartition de la loi normale gaussienne centrée et connaître la valeur critique pour le seuil de 0,95 </span></span></h3> <p class="MsoNormal"><span style=""><span style="">Nous allons utiliser le premier item </span></span><span style=""><span style=""><b style=""><span style="line-height: 115%;">par</span></b> </span></span><span><span style=""><b style=""><span style="">formule</span></b></span></span><span style=""><span><span style="line-height: 115%;">&nbsp;</span> de l entrée </span></span><span style=""><span style=""><b style=""><span style="line-height: 115%;">Créer fonction</span></b> du menu de l onglet d Algèbre. A la différence de la <span style="">Figure <span style="">3</span> : Boite de création des expressions<!--[if gte mso 9]><xml> <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F00520065006 6003300360034003100380036003000350036000000</w:data> </xml><![endif]--></span>, la boîte de dialogue comporte un bouton permettant d entrer un identificateur de variable. Notez que plusieurs identificateurs sont possibles, <i style="">x </i>étant proposé par défaut. Notez aussi que comme pour les pour les expressions, il est possible de demander à Casyopée de vérifier si la fonction ainsi créée est bien définie pour tous les réels (case à cocher <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Vérification Existence</span>).</span></span></p> <table class="MsoTableGrid" style="border: medium none currentcolor; border-collapse: collapse;" border="1" cellpadding="0" cellspacing="0"> <tbody> <tr style="height: 127.85pt;"> <td style="border: medium none currentcolor; padding: 0cm 5.4pt; width: 153.05pt; height: 127.85pt;" valign="top" width="204"> <p class="MsoNormal"><!--[if gte vml 1]><v:oval id="_x0000_s1182" style='position:absolute; left:0;text-align:left;margin-left:27.5pt;margin-top:25.95pt;width:66pt; height:18pt;z-index:4' filled="f" strokecolor="green" strokeweight="2.25pt"/><![endif]--><!--[if !vml]--><!-- [endif]--><span style=""><span><!--[if gte vml 1]><v:shape id="_x0000_i1082" type="#_x0000_t75" style='width:140.25pt;height:78.75pt' o:bordertopcolor="blue" o:borderleftcolor="blue" o:borderbottomcolor="blue" o:borderrightcolor="blue"> <v:imagedata src="/help/imgFrHelp/image099.png" o:title=""/> <w:bordertop type="single" width="8"/> <w:borderleft type="single" width="8"/> <w:borderbottom type="single" width="8"/> <w:borderright type="single" width="8"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image100.jpg" v:shapes="_x0000_i1082" height="107" width="189"><!-- [endif]--></span></span></p> <p class="MsoNormal"><span style=""><span style=""><o:p>&nbsp;</o:p></span></span></p> </td> <td style="border: medium none currentcolor; padding: 0cm 5.4pt; width: 379.25pt; height: 127.85pt;" valign="top" width="506"> <p class="MsoNormal"><!--[if gte vml 1]><v:oval id="_x0000_s1184" style='position:absolute; left:0;text-align:left;margin-left:154.95pt;margin-top:79.95pt;width:88pt; height:27pt;z-index:6;mso-position-horizontal-relative:text; mso-position-vertical-relative:text' filled="f" strokecolor="green" strokeweight="2.25pt"/><![endif]--><!--[if !vml]--><!-- [endif]--><!--[if gte vml 1]><v:oval id="_x0000_s1183" style='position:absolute;left:0;text-align:left; margin-left:226.95pt;margin-top:53.55pt;width:66pt;height:18pt;z-index:5; mso-position-horizontal-relative:text;mso-position-vertical-relative:text' filled="f" strokecolor="green" strokeweight="2.25pt"/><![endif]--><!--[if ! vml]--><!-- [endif]--><span style=""><span><!--[if gte vml 1]><v:shape id="_x0000_i1083" type="#_x0000_t75" style='width:290.25pt;height:112.5pt' o:ole="" o:bordertopcolor="blue" o:borderleftcolor="blue" o:borderbottomcolor="blue" o:borderrightcolor="blue"> <v:imagedata src="/help/imgFrHelp/image103.png" o:title=""/> <w:bordertop type="single" width="8"/> <w:borderleft type="single" width="8"/> <w:borderbottom type="single" width="8"/> <w:borderright type="single" width="8"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image104.jpg" v:shapes="_x0000_i1083" height="152" width="389"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1083" DrawAspect="Content" ObjectID="_1473694189"> </o:OLEObject> </xml><![endif]--></span></span></p> </td> </tr> <tr style="height: 22.8pt;"> <td colspan="2" style="border: medium none currentcolor; padding: 0cm 5.4pt; width: 532.3pt; height: 22.8pt;" valign="top" width="710"> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span><a name="_Toc364193793">Figure </a></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193793'></span></span></span><span style='mso-element:field-begin'></span><span style='mso- bookmark:_Ref275337160'><span style='mso-bookmark:_Ref275337357'><span style='mso- bookmark:_Toc364193793'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso- element: field-separator'></span></span></span></span><![endif]--><span style=""><span><span style=""><span>33</span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193793'></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span style=""> : Créer fonction par formule</span></span></span><span style=""><span><span style="color: rgb(51, 153, 102); font-weight: normal;"><o:p></o:p></span></span></span></p> </td> </tr> </tbody> </table> <p class="MsoNormal"><span style=""><span style="">La fonction étant définie, le bouton <b style="">Calculer</b> donne accès à trois calculs supplémentaires,<span style="">&nbsp; </span>spécifiques des fonctions. Nous essayons ici le calcul «&nbsp;primitive&nbsp;» qui donne à une constante près la fonction de répartition de la loi normale gaussienne centrée. Comme la primitive obtenue s annule en zéro, nous définissons une fonction g en ajoutant ½ <span style="">&nbsp;</span>(<b>Créer<span style="">&nbsp; </span>fonction, par formule</b>, puis entrer la formule </span></span><span><span style=""><span>1/2+If(t)</span>).</span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span><!--[if gte vml 1]><v:shape id="_x0000_i1084" type="#_x0000_t75" style='width:469.5pt;height:154.5pt' o:bordertopcolor="#36f" o:borderleftcolor="#36f" o:borderbottomcolor="#36f" o:borderrightcolor="#36f"> <v:imagedata src="/help/imgFrHelp/image105.png" o:title=""/> <w:bordertop type="single" width="12"/> <w:borderleft type="single" width="12"/> <w:borderbottom type="single" width="12"/> <w:borderright type="single" width="12"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image106.jpg" v:shapes="_x0000_i1084" height="210" width="630"><!-- [endif]--></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><a name="_Toc364193794">Figure </a></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193794'></span></span></span><span style='mso- element: field-begin'></span><span style='mso-bookmark:_Ref275337160'><span style='mso-bookmark:_Ref275337357'><span style='mso- bookmark:_Toc364193794'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element: field-separator'></span></span></span></span><![endif]--><span style=""><span><span style=""><span>34</span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193794'></span></span></span><span style='mso- element: field-end'></span><![endif]--><span style=""><span style=""><span style="">: calculer et grapher</span></span></span></p> <p class="MsoNormal"><span style=""><span style="">Notez les boutons en bas de la<span style="">&nbsp; </span>fenêtre graphique qui permettent de grapher les fonctions et d obtenir les limites aux bornes. Dans la barre d outils en haut, plusieurs types de zoom sont accessibles par un seul bouton. Ici pour cadrer correctement la fonction il a<span style="">&nbsp; </span>été nécessaire d opérer plusieurs zoom in en y et un zoom in en x. On a aussi déplacé les axes en tirant simplement le graphique à la souris. Il aurait été aussi possible aussi de cadrer en entrant des données numériques par le bouton W. On tabule les fonctions à l aide du bouton <sub><!--[if gte vml 1]><v:shape id="_x0000_i1085" type="#_x0000_t75" style='width:21.75pt;height:19.5pt'> <v:imagedata src="/help/imgFrHelp/image107.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image107.gif" v:shapes="_x0000_i1085" height="26" width="29"><!--[endif]--></sub>. Le bouton<!--[if gte vml 1]><v:shape id="_x0000_i1086" type="#_x0000_t75" style='width:32.25pt;height:17.25pt'> <v:imagedata src="/help/imgFrHelp/image108.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--> <img src="/help/imgFrHelp/image108.gif" v:shapes="_x0000_i1086" height="23" width="43"><!--[endif]--><span style="">&nbsp;</span>permet de copier la table dans le presse- papier (séparateurs&nbsp;: tabulation et saut de ligne). Il est alors possible de coller les valeurs dans un traitement de texte ou un tableur.</span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span><!--[if gte vml 1]><v:shape id="_x0000_i1087" type="#_x0000_t75" style='width:225pt;height:245.25pt'> <v:imagedata src="/help/imgFrHelp/image109.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image110.jpg" v:shapes="_x0000_i1087" height="327" width="300"><!-- [endif]--></span></span></p> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><a name="_Toc364193795">Figure </a></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193795'></span></span></span><span style='mso- element: field-begin'></span><span style='mso-bookmark:_Ref275337160'><span style='mso-bookmark:_Ref275337357'><span style='mso- bookmark:_Toc364193795'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element: field-separator'></span></span></span></span><![endif]--><span style=""><span><span style=""><span>35</span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193795'></span></span></span><span style='mso- element: field-end'></span><![endif]--><span style=""><span style=""><span style=""> : tabuler une fonction</span></span></span></p> <p class="MsoNormal"><span style=""><span style="">Approchons la valeur critique de la loi normale gaussienne centrée pour le seuil de 0,95. Pour une étude graphique, on peut entrer une fonction constante h et pointer sur l intersection<span style="">&nbsp; </span>des graphes pour faire apparaître un curseur et des valeurs approchées. Casyopée offre aussi la possibilité d entrer l équation en t, g(t)=h(t) et de résoudre en mode exact ou approché. Une nouvelle liste s ouvre en bas à gauche&nbsp;: c est la <i>liste des équations</i>. Le mode approché s impose ici. Casyopée applique la méthode de Newton avec comme point de départ la position du curseur.</span></span></p> <table class="MsoTableGrid" style="width: 100%; border-collapse: collapse;" border="0" cellpadding="0" cellspacing="0" width="100%"> <tbody> <tr style=""> <td style="padding: 0cm 5.4pt; width: 32.94%;" valign="top" width="32%"> <p class="MsoNormal"><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1088" type="#_x0000_t75" style='width:206.25pt;height:153.75pt'> <v:imagedata src="/help/imgFrHelp/image111.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image111.gif" v:shapes="_x0000_i1088" height="205" width="275"><!-- [endif]--></span></span></p> </td> <td style="padding: 0cm 5.4pt; width: 67.06%;" valign="top" width="67%"> <p class="MsoNormal" style="page-break-after: avoid;"><span style=""><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1089" type="#_x0000_t75" style='width:321pt;height:133.5pt' o:ole=""> <v:imagedata src="/help/imgFrHelp/image112.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image113.jpg" v:shapes="_x0000_i1089" height="178" width="428"><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="PBrush" ShapeID="_x0000_i1089" DrawAspect="Content" ObjectID="_1473694190"> </o:OLEObject> </xml><![endif]--></span></span></p> </td> </tr> </tbody> </table> <p class="MsoCaption" style="text-align: center;" align="center"><span style=""><span style=""><a name="_Toc364184527"></a><a name="_Toc364193796"><span style="">Figure </span></a></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193796'><span style='mso- bookmark:_Toc364184527'></span></span></span></span><span style='mso-element:field-begin'></span><span style='mso- bookmark:_Ref275337160'><span style='mso-bookmark:_Ref275337357'><span style='mso- bookmark:_Toc364193796'><span style='mso-bookmark:_Toc364184527'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field- separator'></span></span></span></span></span><![endif]--><span style=""><span><span style=""><span><span style="">36</span></span></span></span></span><!--[if supportFields]><span style='mso-bookmark:_Ref275337160'><span style='mso- bookmark:_Ref275337357'><span style='mso-bookmark:_Toc364193796'><span style='mso- bookmark:_Toc364184527'></span></span></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""><span><span style=""> : résolution graphique et résolution approchée</span></span></span></span></p> </body></html>