{"id":178,"date":"2008-06-26T11:37:34","date_gmt":"2008-06-26T09:37:34","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/le-paquet-pro-tablor-sty\/"},"modified":"2023-10-14T20:12:20","modified_gmt":"2023-10-14T18:12:20","slug":"le-paquet-pro-tablor-sty","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-tablor-sty\/","title":{"rendered":"Le paquet pro-tablor.sty"},"content":{"rendered":"

Tablor.sty<\/strong> est un paquet con\u00e7u par Guillaume CONNAN pour g\u00e9n\u00e9rer automatiquement le tableau de signes ou le tableau de variations d’une fonction donn\u00e9e.<\/p>\n

Le paquet pro-tablor<\/strong> n’est qu’une adaptation pour \u00eatre utiliser dans professor.sty<\/strong>.<\/p>\n

Dans le pr\u00e9ambule<\/h2>\n
\n

On rajoute ceci :<\/p>\n

\\usepackage[xcas]{pro-tablor}<\/code><\/p>\n

\n

LES TABLEAUX DE VARIATIONS<\/h2>\n
\n

<\/h2>\n

TV<\/h2>\n
\n

Fonction simple :<\/p>\n

\\begin{TV}\nTV([-5,7],[],\"f\",\"x\",x^2,0,n,\\tv);\n\\end{TV}<\/pre>\n
\n
On obtient :<\/p>\n
\"tv.jpg\"<\/p>\n
TV<\/h2>\n
\n
En couleur :<\/p>\n
\\coultab{blue}\n\\begin{TV}\nTV([0,2],[],\"f\",\"x\",x^2,1,n,\\tv);\n\\end{TV}<\/pre>\n
On obtient :<\/p>\n
\"tvblue.jpg\"<\/p>\n
TV<\/h2>\n
\n
Fonction trigo :<\/p>\n
\\begin{TV}\n   TV([0,2*pi],[],\"g\",\"t\",sin(2*x)+x\/2,1,t,\\tv)\n \\end{TV}<\/pre>\n
On obtient :<\/p>\n
\"tablor1.jpg\"<\/p>\n
TVS<\/h2>\n
\n
Tableau de variation \u00e0 partir d’une liste d’abscisses et d’une liste d’images :<\/p>\n
\\begin{TVS}\nTVS([1,2,3,4],[-1,5,2,9],[],\"f\",\"x\",\\tv)\n\\end{TVS}<\/pre>\n
On obtient :<\/p>\n
\"tvs1.jpg\"<\/p>\n
ou encore :<\/p>\n
\\begin{TVS}\nTVS([1,2,3,4],[-1,-infinity,+infinity,2,9],[2],\"f\",\"x\",\\tv)\n\\end{TVS}<\/pre>\n
On obtient :<\/p>\n
\"tvs2.jpg\"<\/p>\n
TVPC<\/h2>\n
\n
Fonction prolongeable par continuit\u00e9. (Nouveaut\u00e9 20\/10\/2008)<\/p>\n
Par exemple pour $x\\mapsto e^-1\/x^2<\/em>$, on entre trois listes :<\/p>\n
– l’intervalle d’\u00e9tude ;
\n– les valeurs o\u00f9 la fonction est prolongeable par continuit\u00e9 ;
\n– les valeurs o\u00f9 la d\u00e9riv\u00e9e n’est pas d\u00e9finie.<\/p>\n
Le reste est comme dans TV.<\/p>\n
\\begin{TVPC}\nTVPC([-infinity,+infinity],[0],[0],\"g\",\"t\",e^(-1\/x^2),1,n,\\tv); \n\\end{TVPC}<\/pre>\n
On obtient :<\/p>\n
\"tvpc.jpg\"<\/p>\n
TVZ<\/h2>\n
\n
Fonction avec une zone interdite :<\/p>\n
\\begin{TVZ}\n  TVZ([-infinity,+infinity],[],[[-1,1]],\"f\",\"x\",sqrt(x^2-1),1,n,\\tv)\n\\end{TVZ}<\/pre>\n
On obtient :<\/p>\n
\"tvz.jpg\"<\/p>\n
TVI<\/h2>\n
\n
Tableau de fonction avec le th\u00e9or\u00e8me des valeurs interm\u00e9diaires :<\/p>\n
\\begin{TVI}\nTVI([-10,+infinity],[-1,1],\"f\",\"x\",x^2\/(x^2-1),1,10,n,\\tv)\n\\end{TVI}<\/pre>\n
On obtient :<\/p>\n
\"tvi.jpg\"<\/p>\n
Tableau de fonction trigo avec le th\u00e9or\u00e8me des valeurs interm\u00e9diaires :<\/p>\n
\\begin{TVI}\n   TVI([0,2*pi],[],\"f\",\"x\",sin(x),1,1\/2,t,\\tv)\n \\end{TVI}<\/pre>\n
On obtient :<\/p>\n
\"tablor7.jpg\"<\/p>\n
TVIex<\/h2>\n
\n
Tableau de fonction avec le th\u00e9or\u00e8me des valeurs interm\u00e9diaires avec racines exactes:<\/p>\n
\\begin{TVIex}\n  TVIex([0,2*pi],[],\"f\",\"x\",sin(x),1,1\/2,t,\\tv)\n\\end{TVIex}<\/pre>\n
On obtient :<\/p>\n
\"TVIex-2.jpg\"<\/p>\n
Tableau de variations avec valeurs approch\u00e9es.<\/p>\n
\\begin{TVapp}\nTVapp([0,+infinity],[0],\"g\",\"x\",ln(x)-x*exp(2-x),1,n,\\tv)\n\\end{TVapp}<\/pre>\n
On obtient :<\/p>\n
\"tvapp.jpg\"<\/p>\n
TVIapp<\/h2>\n
\n
\\begin{TVIapp}\n TVIapp([0,+infinity],[0],\"g'\",\"x\",diff(ln(x)-x*exp(2-x),x),1,n,\\tv)\n\\end{TVIapp}<\/pre>\n
On obtient :<\/p>\n
\"tviapp.jpg\"<\/p>\n
\n
\n
LES COURBES PARAM\u00c9TR\u00c9ES<\/h2>\n
\n
\n
TVP (premier exemple)<\/h2>\n
\n
Fonction param\u00e9tr\u00e9e :<\/p>\n
\\begin{TVP}\n TVP([0,pi\/2],[[],[]],[\"x\",\"y\"],\"t\",[cos(3*t),sin(4*t)],1,t,\\tv)\n \\end{TVP}<\/pre>\n
On obtient :<\/p>\n
\"tvp1.jpg\"<\/p>\n
TVP (deuxi\u00e8me exemple)<\/h2>\n
\n
Fonction param\u00e9tr\u00e9e :<\/p>\n
\\begin{TVP}\nTVP([-infinity,+infinity],[[-1,2],[-1]],[\"x\",\"y\"],\"t\",[t^2\/((t+1)*(t-2)),t^2*(t+2)\/(t+1)],1,0,\\tv)\n\\end{TVP}<\/pre>\n
On obtient :<\/p>\n
\"tvp2.jpg\"<\/p>\n
\n
\n
LES TABLEAUX DE SIGNES<\/h2>\n
\n
\n
TSa<\/h2>\n
\n
Cas du produit de deux facteurs affines :<\/p>\n
\\begin{TSa}\nTSa(-2,3,-1,5,\\tv);\n\\end{TSa}<\/pre>\n
On obtient :<\/p>\n
\"tsa.jpg\"<\/p>\n
TS<\/h2>\n
\n
Autres produits :<\/p>\n
\\begin{TS}\nTS(\"P\",[-2*x+3,x^2-1,x^2+1,x-1,x^2-2],[-infinity,+infinity],n,\\tv);\n\\end{TS}<\/pre>\n
\n
On obtient :<\/p>\n
\"tabS.jpg\"<\/p>\n
Avec des fonctions trigo :<\/p>\n
\\begin{TS}             \nTS(\"P\",[sin(x)+1\/2,cos(x)-1\/2],[0,2*pi],t,\\tv)\n\\end{TS}<\/pre>\n
\n
On obtient :<\/p>\n
\"tablor6.jpg\"<\/p>\n
TSq<\/h2>\n
\n
Quotient :<\/p>\n
\\begin{TSq}\nTSq(\"Q\",[-2*x+3,-4*x+5],[x^2-16,x-2],[-infinity,+infinity],n,\\tv)\n\\end{TSq}<\/pre>\n
On obtient :<\/p>\n
\"tsq.jpg\"<\/p>\n
Quotient trigo :<\/p>\n
\\begin{TSq}\n   TSq(\"q\",[sin(x)],[cos(x)],[0,3*pi],t,\\tv)\n\\end{TSq}<\/pre>\n
On obtient :<\/p>\n
\"tablor4.jpg\"<\/p>\n
TSc<\/h2>\n
\n
Pour un tableau de signe \u00e0 une seule ligne :<\/p>\n
\\begin{TSc}\nTSc(tan(x),[0,2*pi],[pi\/2,3*pi\/2],t,\\tv)\n\\end{TSc}<\/pre>\n
On obtient :<\/p>\n
\"TSc-2.jpg\"<\/p>\n
R\u00e9duction d’\u00e9chelle<\/h2>\n
\n
Pour r\u00e9duire la taille d’un tableau, on utilise la commande \\ech sans oublier de remettre \u00e0 l’\u00e9chelle 1 ensuite :<\/em><\/em><\/p>\n
\\ech{0.8}\n\\begin{TS}              \nTS(\"P\",[sin(x)+1\/2,cos(x)-1\/2,cos(x)-sqrt(3)\/2],[0,3*pi\/2],t,\\tv)\n\\end{TS}\n\\ech{1}<\/pre>\n
\n
On obtient :<\/p>\n
\"tablor4.jpg\"<\/p>\n","protected":false},"excerpt":{"rendered":"
Tablor.sty est un paquet con\u00e7u par Guillaume CONNAN pour g\u00e9n\u00e9rer automatiquement le tableau de signes ou le tableau de variations d’une fonction donn\u00e9e. Le paquet pro-tablor n’est qu’une adaptation pour…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2247,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-178","page","type-page","status-publish","hentry"],"yoast_head":"\nLe paquet pro-tablor.sty - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-tablor-sty\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le paquet pro-tablor.sty - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Tablor.sty est un paquet con\u00e7u par Guillaume CONNAN pour g\u00e9n\u00e9rer automatiquement le tableau de signes ou le tableau de variations d’une fonction donn\u00e9e. Le paquet pro-tablor n’est qu’une adaptation pour…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-tablor-sty\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:12:20+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/06\/jpg_tv.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-tablor-sty\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-tablor-sty\/\",\"name\":\"Le paquet pro-tablor.sty - 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