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260 "" 0 "" {TEXT -1 35 "CHAPITRE 1:D\311COUVERTE DES PREMIERES" }{TEXT 324 0 "" }}{PARA 261 "" 0 "" {TEXT -1 33 "FONCTIONNALIT\311S DU LOGICIEL MAPLE" }}{PARA 19 "" 0 "" {TEXT -1 39 "\251 Apprendre Maple. Alain Le Stang. 2006" }}{PARA 19 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Tous les or dres pass\351s \340 l'ordinateur se font dans les zones pr\351c\351d \351es du signe " }{TEXT 256 1 ">" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 34 "Ces zones sont des zones d'entr\351e " }{TEXT 257 1 "(" } {TEXT 258 5 "input" }{TEXT 259 1 ")" }{TEXT -1 1 "." }}{PARA 0 "" 0 " " {TEXT -1 18 "Presser la touche " }{TEXT 260 6 "Entr\351e" }{TEXT -1 38 " pour transmettre l'ordre au logiciel." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Les lignes doivent imp \351rativement se terminer par un point-virgule " }{TEXT 262 2 "; " } {TEXT -1 19 "ou par deux points " }{TEXT 261 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 48 "Noter la diff\351rence entre ces deux possibilit\351s:" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "12+abs(4-3*sqrt(5)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\") \"\"\"*&\"\"$F%-%%sqrtG6#\"\"&F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "Si la ligne se termine par un po int-virgule, l'ordre est valid\351 et le logiciel fournit une r\351pon se \ndans une zone de sortie " }{TEXT 263 1 "(" }{TEXT 264 6 "output" }{TEXT 265 1 ")" }{TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "12+abs(4-3*sqrt(5)):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Si la ligne se termine par deux po ints, l'ordre est simplement valid\351 sans r\351ponse du logiciel." } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 " Des messages d'erreur peuvent appara\356tre en cas de mauvaise saisie \+ ou d'op\351rations illicites:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "12 +abs(4-3*sqrt(5);" }}{PARA 8 "" 1 "" {TEXT -1 22 "Error, `;` unexpecte d\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "1/cos(Pi/2);" }} {PARA 8 "" 1 "" {TEXT -1 43 "Error, numeric exception: division by zer o\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 266 48 "Obtenir de l'aide sur une fonction en utilisant " }{TEXT 267 1 "?" }{TEXT 268 1 " " }{TEXT 313 3 "ou " }{TEXT 269 4 "help" }}{PARA 0 "" 0 "" {TEXT -1 28 "Ici on cherche de l'aide sur" }{TEXT 311 13 " l a fonction " }{HYPERLNK 17 "solve" 2 "solve" "" }{TEXT 312 3 " . " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "??solve;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "help(solve);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Voir aussi plus en d\351tail pour les variantes " }{HYPERLNK 17 "? ?" 2 "??" "" }{TEXT -1 4 " et " }{HYPERLNK 17 "???" 2 "???" "" }{TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{EXCHG {PARA 0 "" 0 "" {TEXT 270 26 "Faire des calculs simples:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "15!; # ou factorial(15)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\".+!oVn28" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(1-1/7)*(1+2/3)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#]\"#@" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 271 48 "Affecter une valeur \340 une va riable en utilisant " }{TEXT 272 2 ":=" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "p:=2.14;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"$9#!\"#" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "expr:=p-ln(p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG$\"+rT>z8!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 273 55 "D\351velopper , factoriser , ou simplifier une expr ession:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f:=(a+b)^6;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*$),&%\"aG\"\"\"%\"bGF)\"\"'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(f);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,0*$)%\"aG\"\"'\"\"\"F(*(F'F()F&\"\"&F(%\"bGF(F( *(\"#:F()F&\"\"%F()F,\"\"#F(F(*(\"#?F()F&\"\"$F()F,F6F(F(*(F.F()F&F2F( )F,F0F(F(*(F'F(F&F()F,F+F(F(*$)F,F'F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&% \"aG\"\"\"%\"bGF'\"\"'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 " %%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*$)%\"aG\"\"'\"\"\"F(*(F'F()F &\"\"&F(%\"bGF(F(*(\"#:F()F&\"\"%F()F,\"\"#F(F(*(\"#?F()F&\"\"$F()F,F6 F(F(*(F.F()F&F2F()F,F0F(F(*(F'F(F&F()F,F+F(F(*$)F,F'F(F(" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "% permet de rappeler la derni\350re expression calcul\351e (% est le " } {HYPERLNK 17 "" 2 "ditto" "" }{HYPERLNK 17 "Ditto Operator" 2 "ditto" "" }{TEXT -1 1 ")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "%% permet de rappeler l'avant-derni\350re expression calcul\351e." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "%%% permet de rappeler l'avant-avant-dern i\350re expression calcul\351e." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "simplify(cos(x)^2+sin(x)^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 36 "Substituer en utilisan t la fonction " }{TEXT 274 38 "subs(variable=remplacement,expression) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(a=c,f);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#*$),&%\"cG\"\"\"%\"bGF'\"\"'F'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 275 33 "Calculer \340 une pr\351cision voulue: " }{TEXT 276 17 "evalf(expression)" }{TEXT 277 1 " " }{TEXT 314 32 "ou evalf(expression,nbd\351cimales)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalf(sqrt(3)); # sqrt d\351signe la racine \+ carr\351e" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+330K " 0 "" {MPLTEXT 1 0 20 "eva lf(sqrt(3),50); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"S/\"QD0G%pOse] TjWFNHx)ov!30K " 0 "" {MPLTEXT 1 0 20 "f:=a-3/a+1/(a* a+1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(%\"aG\"\"\"*&\"\"$F' F&!\"\"F**&F'F',&*$)F&\"\"#F'F'F'F'F*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\" \"\"*&\"\"$F%F$!\"\"F(*&F%F%,&*$)F$\"\"#F%F%F%F%F(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "lprint(f);" }}{PARA 6 "" 1 "" {TEXT -1 15 "a-3/a+1/(a^2+1)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction " } {HYPERLNK 17 "printf" 2 "printf" "" }{TEXT -1 76 " est celle du langag e C, permettant l'affichage de donn\351es selon des formats" }}{PARA 0 "" 0 "" {TEXT -1 56 " pr\351\351tablis et en utilisant des caract \350res de contr\364le.\n" }{TEXT 317 8 "Exemple:" }{TEXT -1 129 " %d \+ : nombre entier, %f : nombre en virgule flottante simple pr\351cision , \\n : passage \340 la ligne. \nVoir \351galement les fonctions: " } {HYPERLNK 17 "fprintf" 2 "fprintf" "" }{TEXT -1 3 ", " }{HYPERLNK 17 "sprintf" 2 "sprintf" "" }{TEXT -1 5 ", et " }{HYPERLNK 17 "nprintf" 2 "nprintf" "" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "printf(\"%d %f \\n\",123,1234/567);" }}{PARA 6 "" 1 "" {TEXT -1 13 "123 2.176367 " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 281 50 "D\351finir une fonction \340 une ou plusieurs \+ variables:" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=t->sin(t)-t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"tG 6\"6$%)operatorG%&arrowGF(,&-%$sinG6#9$\"\"\"F0!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f(3*x+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%$sinG6#,&%\"xG\"\"$\"\"#\"\"\"F+*&F)F+F(F+!\"\"F*F- " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "g:=(u,v,w)->1/u+exp(u+v )+(u-v+w)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6%%\"uG%\"vG% \"wG6\"6$%)operatorG%&arrowGF*,(*&\"\"\"F09$!\"\"F0-%$expG6#,&F1F09%F0 F0*$),(F1F0F7F29&F0\"\"#F0F0F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g(2*a,b,3*c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*& \"\"\"F%%\"aG!\"\"#F%\"\"#-%$expG6#,&F&F)%\"bGF%F%*$),(F&F)F.F'*&\"\"$ F%%\"cGF%F%F)F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " " 0 "" {TEXT 282 75 "D\351river une fonction \340 une ou plusieurs var iables en utilisant la fonction " }{TEXT 283 4 "diff" }{TEXT 284 1 " \+ " }{TEXT 318 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(t),t); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"tG\"\"\"F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(g(u,v,w),v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*-%$expG6#,&%\"uG\"\"\"%\"vGF)F)*&\"\"#F)F( F)!\"\"*&F,F)F*F)F)*&F,F)%\"wGF)F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "" 0 "" {TEXT 285 62 "Int\351grer une fonction \340 un e variable en utilisant la fonction " }{TEXT 286 3 "int" }{TEXT 287 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "int(f(t),t); # donne une primitive de f" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"tG!\"\"*&#\"\"\"\"\"#F+*$)F'F,F+F+F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Int(g(u,v,w),v)=int(g(u,v,w) ,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$,(*&\"\"\"F)%\"uG!\" \"F)-%$expG6#,&F*F)%\"vGF)F)*$),(F*F)F0F+%\"wGF)\"\"#F)F)F0,(*&F*F+F0F )F)F,F)*&#F)\"\"$F)*$)F3F:F)F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Int(f(t),t=0..Pi)=int(f(t),t=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$,&-%$sinG6#%\"tG\"\"\"F+!\"\"/F+;\"\"!%# PiG,&\"\"#F,*&#F,F3F,*$)F1F3F,F,F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Noter la forme inerte " }{HYPERLNK 17 "Int" 2 "Int" "" }{TEXT -1 37 " qui affiche l'int\351grale et la forme " }{HYPERLNK 17 "int" 2 "int" "" }{TEXT -1 25 " qui calcule l'int\351grale." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 288 42 "Calcul de li mites, de sommes, de produits:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "l imit((2*t-3)/(3*t+4),t=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6## \"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "limit((2*t-3) /(3*t+4),t=-4/3,right); #limite \340 droite" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%)infinityG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Sum(i^2,i=1..10)=sum(i^2,i=1..10);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%$SumG6$*$)%\"iG\"\"#\"\"\"/F);F+\"#5\"$&Q" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Product(1/i,i=1..10)=product (1/i,i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%(ProductG6$*&\"\" \"F(%\"iG!\"\"/F);F(\"#5#F(\"(+)GO" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Noter l\340 aussi les formes inertes " }{HYPERLNK 17 "Sum" 2 "S um" "" }{TEXT -1 4 " et " }{HYPERLNK 17 "Product" 2 "Product" "" } {TEXT -1 56 " qui affichent respectivement les symboles sigma et pi . " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 289 62 "R\351soudre une \351quation \340 une inconnue en utilisant la fonc tion " }{TEXT 290 5 "solve" }{TEXT 291 1 " " }{TEXT 319 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(2*t+3=-t+6*sqrt(2));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&!\"\"\"\"\"*&\"\"#F%-%%sqrtG6#F'F%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve(t-15/4*u=5/2*(u-t)+3,u );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"tG#\"#9\"#D#\"#7F'!\"\"" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 292 79 "R\351soudre un syst\350me d'\351 quations \340 plusieurs inconnues en utilisant la fonction " }{TEXT 293 5 "solve" }{TEXT 294 2 " :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "s olve(\{a-b=2,a+3*b=7\},\{a,b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$ /%\"aG#\"#8\"\"%/%\"bG#\"\"&F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 297 92 "Approcher les solutions d'une \351quation ou d'un syst\350me d' \351quations en utilisant la fonction " }{TEXT 295 6 "fsolve" }{TEXT 296 2 " :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "fsolve(cos(t)=t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+K8&3R(!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "fsolve(\{t^3+u=1,u-(t-1)^3=t\},\{t,u\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"tG$\"+0sXTp!#5/%\"uG$\"+\">S`l'F (" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 300 79 "Repr\351senter une fonction \340 une ou plusieurs variables en utilisant la fonction " }{TEXT 299 14 "plot ou plot3d" }{TEXT 298 2 " :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "plot(sin(t)/t,t=-20..20,title =\"fonction t ---> sin t / t\");" }}{PARA 13 "" 1 "" {GLPLOT2D 169 151 151 {PLOTDATA 2 "6&-%'CURVESG6$7ht7$$!#?\"\"!$\"3[Q\"QODEZc%!#>7$$ !3QLLL$Q6G\">!#;$\"3a3'H4j9vV\"F-7$$!3bmm;M!\\p$=F1$!3'G(3omV:9DF-7$$! 3u***\\7Y\"H%z\"F1$!3o&fQ9,t&)Q%F-7$$!3ILLL))Qj^:w<>bp&F-7$$!3BLL$3sj,t\"F1$!3))oH$pP(GydF-7$$!3? 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2A87C2775F57E3F54D2E49A665EF33F45FC2104102798-%&COLORG6^bm%$HUEG$F)F)F 4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4F4$\"3_ommmmmmT!#>F5F5F5F 5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5F5$\"3/PLLLLLL$)F7F8F8F8F8F8F8F 8F8F8F8F8F8F8F8F8F8F8F8F8F8F8F8F8F8$\"3c++++++]7!#=F:F:F:F:F:F:F:F:F:F :F:F:F:F:F:F:F:F:F:F:F:F:F:F:$\"3Snmmmmmm;F2*exp(-x^2)-x/2" "6#f*6#%\"xG7\"6$%)operatorG%&arrow G6\",&*&\"\"#\"\"\"-%$expG6#,$*$F%F-!\"\"F.F.*&F%F.F-F4F4F*F*F*" } {TEXT -1 3 " ." }}{PARA 0 "" 0 "" {TEXT -1 40 "2. Calculer les 3 prem i\350res d\351riv\351es de " }{TEXT 303 1 "f" }{TEXT -1 41 " , en les \+ donnant sous forme factoris\351e ." }}{PARA 0 "" 0 "" {TEXT -1 50 "3. \+ Calculer la valeur num\351rique de l'int\351grale de " }{TEXT 304 1 "f " }{TEXT -1 5 " sur " }{XPPEDIT 18 0 "[-1,2]" "6#7$,$\"\"\"!\"\"\"\"# " }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 35 "4. Repr\351senter da ns un m\352me rep\350re " }{TEXT 305 1 "f" }{TEXT -1 16 " et la foncti on " }{XPPEDIT 18 0 "x -> x" "6#f*6#%\"xG7\"6$%)operatorG%&arrowG6\"F% F*F*F*" }{TEXT -1 6 " sur " }{XPPEDIT 18 0 "[-1,2]" "6#7$,$\"\"\"!\" \"\"\"#" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 90 "5. Les deux c ourbes ont un point commun : calculer une valeur approch\351e de son a bscisse . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "f:=x->2*exp(-x^2)-x/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&-%$expG6#,$* $)9$\"\"#\"\"\"!\"\"F4*&#F5F4F5F3F5F6F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, &*&%\"xG\"\"\"-%$expG6#,$*$)F%\"\"#F&!\"\"F&!\"%#F&F-F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%$expG6#,$*$)%\"xG\"\"#\"\"\"!\"\"F-,&F.F-*&F ,F-F*F-F-F-\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor( diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"xG\"\"\"-%$expG6 #,$*$)F%\"\"#F&!\"\"F&,&!\"$F&*&F-F&F,F&F&F&!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(int(f(x),x=-1..2));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+[5\"y]#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(\{f(x),x\},x=-1..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 185 147 147 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"\"\"\"!F(7$$! 3[*****\\P&3Y$*!#=F,7$$!3C++Dcx6x()F.F07$$!3b++]iTDP\")F.F37$$!3A**** \\P\"\\J\\(F.F67$$!3g***\\7V0@&oF.F97$$!3w++DcexdiF.F<7$$!3j***\\i+#QU cF.F?7$$!3$****\\i!3%f+&F.FB7$$!3;++D\"oS:P%F.FE7$$!3h*****\\<#)*=PF.F H7$$!3#*****\\(G3U9$F.FK7$$!3Y*****\\-\\r\\#F.FN7$$!3?+++vGVZ=F.FQ7$$! 3_*****\\(4J@7F.FT7$$!3;,+]iIKFl!#>FW7$$\"3(R,++]siL#!#?Fen7$$\"3K,+++ !R5'fFYFin7$$\"3!)***\\P/QBE\"F.F\\o7$$\"39******\\\"o?&=F.F_o7$$\"3k+ +vVb4*\\#F.Fbo7$$\"3w++DJ'=_6$F.Feo7$$\"3#4++vVy!ePF.Fho7$$\"3'4+](=WU [VF.F[p7$$\"3s****\\7B>&)\\F.F^p7$$\"3w***\\P>:mk&F.Fap7$$\"3d***\\iv& QAiF.Fdp7$$\"3j++]PPBWoF.Fgp7$$\"3%*)*****\\Nm'[(F.Fjp7$$\"36****\\(yb ^6)F.F]q7$$\"3')***\\PMaKs)F.F`q7$$\"3a****\\7TW)R*F.Fcq7$$\"3z*****\\ @80+\"!#+++!*>=+:FhqF_s7$$\" 3-++DE&4Qc\"FhqFbs7$$\"3=+]P%>5pi\"FhqFes7$$\"39+++bJ*[o\"FhqFhs7$$\"3 3++Dr\"[8v\"FhqF[t7$$\"3++++Ijy5=FhqF^t7$$\"31+]P/)fT(=FhqFat7$$\"31+] i0j\"[$>FhqFdt7$$\"\"#F*Fgt-%'COLOURG6&%$RGBG$\"#5F)$F*F*F_u-F$6$7S7$F ($\"3n%)GM#))edB\"Fhq7$F,$\"3Ql\"*eybG-8Fhq7$F0$\"3+z*R()3KXO\"Fhq7$F3 $\"3z3dc!GY$Q9Fhq7$F6$\"3,u_)RA%R::Fhq7$F9$\"3G14y(4=Kf\"Fhq7$F<$\"3;& )Q&[&4%[m\"Fhq7$F?$\"3C]r*>*RzO^.8$[4w#>Fhq7$FK$\"3M#Rpri[*o>Fhq7$FN$\"3,&p[vE^R+#Fhq 7$FQ$\"3Rrpt,KED?Fhq7$FT$\"3#HP2R#\\XJ?Fhq7$FW$\"3(pv`HbLT-#Fhq7$Fen$ \"39.9WZ4#))*>Fhq7$Fin$\"3!R72&>15j>Fhq7$F\\o$\"3Tnm0JdE0>Fhq7$F_o$\"3 x;aqAn&*R=Fhq7$Fbo$\"3#4,#z+j&Rv\"Fhq7$Feo$\"3m'oQ7#yEf;Fhq7$Fho$\"3' \\>$*fds'[:Fhq7$F[p$\"3\"eHSC>1!Q9Fhq7$F^p$\"3_`*pjoY1J\"Fhq7$Fap$\"3u 43hJ\"\\;<\"Fhq7$Fdp$\"3)3f'z.t\"o/\"Fhq7$Fgp$\"3W;P&\\%>](4*F.7$Fjp$ \"3%G)GFoQ7vwF.7$F]q$\"3eJ8Bf.P%H'F.7$F`q$\"3%HG&[\"Q/G)\\F.7$Fcq$\"3C )Qz'pM/pNF.7$Ffq$\"33!33rjsuM#F.7$Fjq$\"3>d>#f0,I5\"F.7$F]r$\"3vG2YYV* zT$Fgn7$F`r$!3W@i2&QPj1\"F.7$Fcr$!3Y(\\4U![:N?F.7$Ffr$!3[x))*z'*H&yHF. 7$Fir$!34;0e*pRO$QF.7$F\\s$!3wujDKwQgYF.7$F_s$!3kPUr5h2%R&F.7$Fbs$!3oA r8%Q#R&3'F.7$Fes$!3K-g1G*\\qr'F.7$Fhs$!35Y(oVPDYD(F.7$F[t$!3%z(o7SNtDy F.7$F^t$!3s2'Gbut0I)F.7$Fat$!3ovq.%yQVx)F.7$Fdt$!3-vNsQgm+#*F.7$Fgt$!3 q;`AAsoL'*F.-Fjt6&F\\uF_uF]uF_u-%+AXESLABELSG6$Q\"x6\"Q!F\\_l-%%VIEWG6 $;F(Fgt%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "fsolve(f(x)=x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+CXRXv!#5" }}}{PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 17 "Travail dirig\351 1:" }}{EXCHG {PARA 0 "" 0 "" {TEXT 320 7 "TD 1.1:" }{TEXT -1 24 "\n1\260 D\351finir la fonction " }{TEXT 307 1 "f" }{TEXT -1 7 " qui \340 " }{TEXT 306 1 "x" }{TEXT -1 9 " associe \+ " }{XPPEDIT 18 0 "exp(- x^2)" "6#-%$expG6#,$*$%\"xG\"\"#!\"\"" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "2\260 Calculer les 3 premiers nombres d\351riv\351s successifs " }{XPPEDIT 18 0 "f[1],f[2],f[3];" "6%&%\"fG6#\"\"\"&F$6#\"\"#&F$6#\"\"$ " }{TEXT -1 4 " de " }{TEXT 308 1 "f" }{TEXT -1 10 " au point " } {TEXT 309 1 "x" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 41 " (on les \351crira sous forme factoris\351e)" }}{PARA 0 "" 0 "" {TEXT -1 16 "3\260 On pose pour " }{XPPEDIT 18 0 "n=1,2,3" "6%/%\"nG\"\"\"\"\"# \"\"$" }{TEXT -1 4 " : " }{XPPEDIT 18 0 "h[n] = exp(x^2)*f[n];" "6#/& %\"hG6#%\"nG*&-%$expG6#*$%\"xG\"\"#\"\"\"&%\"fG6#F'F/" }{TEXT -1 11 ". Calculer " }{XPPEDIT 18 0 "h[1],h[2],h[3];" "6%&%\"hG6#\"\"\"&F$6#\" \"#&F$6#\"\"$" }{TEXT -1 38 " (on les \351crira sous forme simplifi \351e)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "4\260 Calculer les racines des polyn\364mes " }{XPPEDIT 18 0 "h[1], \+ h[2], h[3]" "6%&%\"hG6#\"\"\"&F$6#\"\"#&F$6#\"\"$" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "5\260 Rep r\351senter " }{XPPEDIT 18 0 "h[1], h[2], h[3]" "6%&%\"hG6#\"\"\"&F$6# \"\"#&F$6#\"\"$" }{TEXT -1 26 " dans un m\352me rep\350re pour " } {TEXT 310 1 "x" }{TEXT -1 15 " compris entre " }{XPPEDIT 18 0 "-2;" "6 #,$\"\"#!\"\"" }{TEXT -1 6 " et 2." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 27 "6\260 Calculer l'int\351grale de " } {XPPEDIT 18 0 "h[3]-h[2];" "6#,&&%\"hG6#\"\"$\"\"\"&F%6#\"\"#!\"\"" } {TEXT -1 5 " sur " }{XPPEDIT 18 0 "[-1,1]" "6#7$,$\"\"\"!\"\"F%" } {TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 322 7 "TD 1.2:" }}{PARA 0 "" 0 "" {TEXT -1 16 "\n1\260 D\351velopper " }{XPPEDIT 18 0 "cos (3 *x) , cos(4*x) , cos (5*x)" "6%-%$cosG6#*&\"\"$\"\"\"%\"xGF(-F$6#*&\" \"%F(F)F(-F$6#*&\"\"&F(F)F(" }{TEXT -1 16 " en fonction de " } {XPPEDIT 18 0 "cos(x)" "6#-%$cosG6#%\"xG" }{TEXT -1 2 " ." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "2\260 D\351termine r les polyn\364mes " }{XPPEDIT 18 0 "T[n]" "6#&%\"TG6#%\"nG" }{TEXT -1 16 " de la variable " }{TEXT 321 1 "X" }{TEXT -1 11 " tels que " } {XPPEDIT 18 0 "T[n](cos(x)) = cos(n*x)" "6#/-&%\"TG6#%\"nG6#-%$cosG6#% \"xG-F+6#*&F(\"\"\"F-F1" }}{PARA 0 "" 0 "" {TEXT -1 13 " lorsque \+ " }{XPPEDIT 18 0 "n=3,4,5" "6%/%\"nG\"\"$\"\"%\"\"&" }{TEXT -1 17 " \+ (polyn\364mes de " }{TEXT 323 10 "Tch\351bychev" }{TEXT -1 3 ") ." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "3\260 Rep r\351senter " }{XPPEDIT 18 0 "T[3],T[4],T[5]" "6%&%\"TG6#\"\"$&F$6#\" \"%&F$6#\"\"&" }{TEXT -1 5 " sur " }{XPPEDIT 18 0 "[-1,1]" "6#7$,$\"\" \"!\"\"F%" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "4\260 Calculer les racines de " }{XPPEDIT 18 0 "T [3], T[4], T[5]" "6%&%\"TG6#\"\"$&F$6#\"\"%&F$6#\"\"&" }{TEXT -1 2 " . " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "2 0" 33 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 1 1 1 33 1 1 }