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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::<:J\\;E_>L<;:E_ymy;:::::::::::BsZ>W=vY::::::::::::::::::::::::::::: ::t@W\\HKAsyvY:::XGW\\H;jUsyvY:::::::::::::::::::::::::::::::::::::::: ::::::::::::::tBW\\HKqryvY:::::::::::::::::JA;W\\h;xI::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::bC :vY:::::::::::J\\CkdB:jysy^VLFC@:nTjy;::::::::::::C`>=Je;yA::::::::::Z ::xI::::::::::::::bMnCJA;W\\Hlysy:::::::::::::::::::::::vPt>W:RlvYxI:::::::::::::::::::::::i?nCjysy:ZqryvY::::::::::::::::: ::tBbMnGxIyA:vPJa:yay=::::::::::::::::::::::::::t@W\\H;:::::JqryvY:::: :::::::::::::::::::::::::::::::::::::::::::::::::::tBbMnGjy;:::::::::: :::::::W>nCt@ry::vPJa:yay=:::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::<:ry::::::::::::::ZZ@NbM:Zymy;:::::::::::::::::::::::i? nCjysy:ZqryvY:::::::::::::::::::XGi_ql^;yA:vPt>W:::::b]vYxI::::::::::::::::::::::::::::::::::::::::: ::::::::::::::roZql^;yA:::::::::::::::::vTjUSlZy=:jUcMnCjysy:::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::Z::xI:::::::::::::::W \\H;JqryvY:::::::::::::::::::::::jU;W:1:" }{TEXT -1 0 "" }}{PARA 18 "" 0 "" {TEXT 271 16 "Travail \+ dirig\351 1" }}{PARA 18 "" 0 "" {TEXT 272 39 "\251 Apprendre Maple. Al ain Le Stang. 2006" }}{EXCHG {PARA 0 "" 0 "" {TEXT 262 7 "TD 1.1:" } {TEXT -1 24 "\n1\260 D\351finir la fonction " }{TEXT 258 1 "f" }{TEXT -1 7 " qui \340 " }{TEXT 257 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 Cal culer 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 259 1 "f" }{TEXT -1 10 " au point " }{TEXT 260 1 "x" } {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 41 " (on les \351crira so us 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 Repr\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 261 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 263 7 "TD 1.2:" }{TEXT -1 17 "\n\n1\260 D\351vel opper " }{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\351terminer les polyn\364mes " }{XPPEDIT 18 0 "T[ n]" "6#&%\"TG6#%\"nG" }{TEXT -1 16 " de la variable " }{TEXT 256 1 "X " }{TEXT -1 14 " d\351finis par " }{XPPEDIT 18 0 "T[n](cos(x)) = cos( n*x)" "6#/-&%\"TG6#%\"nG6#-%$cosG6#%\"xG-F+6#*&F(\"\"\"F-F1" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 13 " lorsque " }{XPPEDIT 18 0 "n=3,4,5" "6%/%\"nG\"\"$\"\"%\"\"&" }{TEXT -1 30 " (polyn\364mes de \+ Tch\351bychev) ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "3\260 Repr\351senter " }{XPPEDIT 18 0 "T[3],T[4],T[5]" "6 %&%\"TG6#\"\"$&F$6#\"\"%&F$6#\"\"&" }{TEXT -1 5 " sur " }{XPPEDIT 18 0 "[-1,1]" "6#7$,$\"\"\"!\"\"F%" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "4\260 Calculer les racine s de " }{XPPEDIT 18 0 "T[3], T[4], T[5]" "6%&%\"TG6#\"\"$&F$6#\"\"%&F$ 6#\"\"&" }{TEXT -1 2 " ." }}}{PAGEBK }{PARA 257 "" 0 "" {TEXT -1 28 "C orrig\351 du Travail dirig\351 1:" }}{EXCHG {PARA 0 "" 0 "" {TEXT 270 7 "TD 1.1:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "1\260 D\351finition de " }{TEXT 265 1 "f " }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->e xp(-x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)ope ratorG%&arrowGF(-%$expG6#,$*$)9$\"\"#\"\"\"!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "2\260 Calcul de " }{TEXT 266 8 "f1,f2,f3 " }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f1:=dif f(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G,$*&%\"xG\"\"\"-%$ expG6#,$*$)F'\"\"#F(!\"\"F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f2:=factor(diff(f1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# f2G,$*&-%$expG6#,$*$)%\"xG\"\"#\"\"\"!\"\"F/,&F0F/*&F.F/F,F/F/F/F." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f3:=factor(diff(f2,x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3G,$*(%\"xG\"\"\"-%$expG6#,$*$)F' \"\"#F(!\"\"F(,&!\"$F(*&F/F(F.F(F(F(!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "3\260 Calcul de " }{TEXT 267 8 "h1,h2,h3" }{TEXT -1 1 ": " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h1:=simplify(exp(x^2)*f 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h1G,$%\"xG!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h2:=simplify(exp(x^2)*f2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h2G,&!\"#\"\"\"*&\"\"%F')%\"xG\"\"# F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "h3:=simplify(exp(x^ 2)*f3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h3G,$*&%\"xG\"\"\",&!\"$ F(*&\"\"#F()F'F,F(F(F(!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "4 \260 Racines de " }{TEXT 268 8 "h1,h2,h3" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve(h1);solve(h2);solve(h3);" }} {PARA 11 "" 1 "" 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