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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 44 "Etude local des fonctio
ns a 1 et 2 variables" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT 257 21 "ProcŽdures dans Maple" }}{PARA 0 "" 0 "
" {TEXT -1 63 "Voici une procŽdure qui calcule la somme des nombres de
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "local i,temp;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "temp:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i f
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"nG6$%\"iG%%te
mpG6\"F+C$>8%\"\"!?(8$\"\"\"F29$%%trueG>F.,&F.F2F1F2F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(1);" }}{PARA 11 "" 1 "" {XPPMATH 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#b" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 42 "Un autre exemple, ˆ comprendre et tester :" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "g:=proc(start,n_pas)" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "local i,temp;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "t
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{MPLTEXT 1 0 3 "fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "print(temp);
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{MPLTEXT 1 0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"gG:6$%&sta
rtG%&n_pasG6$%\"iG%%tempG6\"F,C$>8%9$?(8$\"\"\"F39%%%trueGC$@%/-%$modG
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g(1,10);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 
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3 "" 0 "" {TEXT 258 24 "DŽveloppements de Taylor" }}{SECT 1 {PARA 5 "
" 0 "" {TEXT 266 14 "A une variable" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 5 "" 0 "" {TEXT 259 96 "Pour avoir les 5  premier termes du dŽv
eloppement de Taylor d'une fonction d'une variable en x=0" }}{PARA 0 "
" 0 "" {TEXT -1 11 " on Žcrit :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "taylor(exp(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+3%\"xG\"
\"\"\"\"!F%\"\"\"#F%\"\"#\"\"##F%\"\"'\"\"$#F%\"#C\"\"%#F%\"$?\"\"\"&#
F%\"$?(\"\"'-%\"OG6#F%\"\"(" }}}{PARA 0 "" 0 "" {TEXT -1 59 "Mais on p
eut aussi en demander plus, et en un autre point :" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 21 "taylor(exp(x),x=1,8);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#+5,&%\"xG\"\"\"!\"\"F&-%$expG6#F&\"\"!F(\"\"\",$F(#F&\"
\"#\"\"#,$F(#F&\"\"'\"\"$,$F(#F&\"#C\"\"%,$F(#F&\"$?\"\"\"&,$F(#F&\"$?
(\"\"',$F(#F&\"%S]\"\"(-%\"OGF*\"\")" }}}{PARA 5 "" 0 "" {TEXT 268 51 
"Pour en faire un vrai polyn™me, il faut convertir :" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 42 "t3:=convert(taylor(exp(x),x=1,3),polynom)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t3G,(-%$expG6#\"\"\"F)*&F&F),&
%\"xGF)!\"\"F)F)F)*&F&F)F+\"\"##F)F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "subs(x=0.5,t3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$
-%$expG6#\"\"\"$\"*+++D'!\"*" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 265 
11 "Exercice 1." }}{PARA 0 "" 0 "" {TEXT -1 177 "Ecrire une procŽdure \+
ayant comme param�tre une fonction d'une variable f(x), une valeur a, \+
et qui dessine le graphe de f pr�s de a et de sa sŽrie de Taylor tronq
uŽe ˆ l'ordre 3." }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 260 21 "A plusieurs
 variables" }}{PARA 0 "" 0 "" {TEXT -1 117 "Voici les commandes pour c
alculer la sŽrie de Taylor ˆ un ordre voulu d'une fonction de deux ou \+
plusieurs variables :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "rea
dlib(mtaylor);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#:6\"6*%\"fG%\"kG%\"v
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n-negative~integerG@$54-F>6$Ffq-FI6#%'posintG0-F_p6#FfqF]p-FW6#%en4th~
argument~(weights)~must~be~a~list~of~positive~integersG>F2-%%subsG6$7#
-%$seqG6$/&F86#8%,&*&F[uF6)8*&FfqF\\uF6F6&FenF\\uF6/F]u;F6F]pF2>F2-Fgn
6&%(collectG-Fdt6$/-%\"OGF5Fdo-%'taylorG6%F2FauF\\qF8.%,distributedG>F
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0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "mtaylo
r(exp(x+y),[x,y]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,L\"\"\"F$%\"xGF
$%\"yGF$*$F%\"\"##F$F(*&F%F$F&F$F$*$F&F(F)*$F%\"\"$#F$\"\"'*&F%F(F&F$F
)*&F&F(F%F$F)*$F&F-F.*$F%\"\"%#F$\"#C*&F&F$F%F-F.*&F&F(F%F(#F$F4*&F&F-
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(FB*&F&F4F%F$F5*$F&F=F>" }}}{PARA 0 "" 0 "" {TEXT -1 63 "Par dŽfaut, l
a sŽrie est tronquŽe ˆ partir de l'ordre 6. Mais :" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 31 "mtaylor(exp(x+y),[x=1,y=-2],7);" }}{PARA 0 "" 0 "" 
{XPPMATH 20 "6#,Z-%$expG6#!\"\"\"\"\"*&F$F(,&%\"yGF(\"\"#F(\"\"$#F(\"
\"'*&F$F(,&%\"xGF(F'F(F-F.*&F$F(F1F(F(*&F$F(F*F(F(*&F$F(F1F,#F(F,*&F$F
(F*\"\"%#F(\"#C*&F$F(F*F,F6*&F$F(F1F8F9*&F$F(F*\"\"&#F(\"$?\"*&F$F(F1F
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(F*F(F1F(F(*(F$F(F*F-F1F(F.*(F$F(F*F(F1F-F.*(F$F(F*F,F1F,#F(F8*(F$F(F*
F(F1F8F9*(F$F(F*F,F1F-#F(\"#7*(F$F(F*F-F1F,FO*(F$F(F*F8F1F(F9*(F$F(F*F
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(F*F>F1F(F?" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 263 33 "Etude des fonct
ions ˆ 2 variables" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 261 16 "Points cri
tiques" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 267 27 "Calcul des points crit
iques" }}{PARA 0 "" 0 "" {TEXT -1 91 "Les points critiques d'une fonct
ion sont ceux o� les dŽrivŽes du premier ordre sont nulles." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:
=y^2-x*(x-1)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$%\"yG\"\"
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{TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 11 "Exercice 2." }}
{PARA 0 "" 0 "" {TEXT -1 95 "Trouvez les points singuliers des fonctio
ns g(x,y)=y^2-(x-1)*x^2*(x+1), u(x,y)=x^3-y^3+x^2-y^2." }}{PARA 0 "" 
0 "" {TEXT -1 116 "Ecrire une procŽdure qui admet comme param�tre une \+
fonction f(x,y) et qui calcule la liste de ses points singuliers." }}
{PARA 0 "" 0 "" {TEXT -1 2 "- " }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 264 
47 "Etude locale aux voisinage des points critiques" }}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 113 "On va faire tracer les niveaux de f et de sa hes
sienne, convenablement translatŽs, pour juger de l'approximation." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ff2:=subs(x=x-1/3,hess(f,1/3
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124 "p1:=contourplot(f,x=1/3-1..1/3+1,y=-1..1,color=blue):p2:=contourp
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$FebclF_fmF\\dcl7$Fbdcl7$$\"1KekLLL.QF*$\"1$pTN******p\"F-7$7$$\"15OUL
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Ffr$!1)********>Yt(F2F[il7$F[hl7$$\"1m([:z/Yh*F*$\"1YB^%3_R&yF27$7$$\"
1++++++S'*F*$\"1'********>Yt(F2Feil7$7$Ffr$!1'********>Yt(F27$$\"1.tuE
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F27$7$F^w$\"1XWWWW/$*oF2Fb`m7$Fi_m7$$\"1*['QyaIp**F*$!1u['QyaI*oF27$7$
Fjw$!1LLLLL8$*oF2F\\am7$Fh`m7$$\"1^m8q(oI+\"F\\x$\"1^[L')H7$*oF27$7$Fj
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'*R5F\\x$\"1+gB*oaK+)F27$7$Fb_l$\"1.++++-<#)F2Fchm7$7$$\"1++++++_5F\\x
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$Fa^nFBFd^nF\\al-F$6cr7$7$$\"1Y-EPj@o!*F*F+7$$\"1s]bybcu!*F*$!1:2b&ybc
%**F27$7$$\"1++++++!3*F*$!1kmmm;9**)*F2Fa_n7$7$Fh_n$\"1nmmm;9**)*F27$F
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*****\\ni#*F2Fb`n7$F]`n7$$\"1RE=%eR$H\"*F*$\"1KO<eTg1&*F27$7$$\"1+++++
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hB*F27$7$$\"1!)HAivao\"*F*F[qF[bn7$7$$\"1\")HAivao\"*F*F[q7$$\"1sv#fOX
#3#*F*$!1>dFfOX#)))F27$7$$\"1************R#*F*$!1^aaaaWG')F2Fhbn7$7$$
\"1++++++S#*F*$\"1`aaaaWG')F27$$\"1yHAivao\"*F*Fbr7$FicnFdan7$F^cn7$$
\"1$)3g@q?`#*F*$!1F)3g@q?`)F27$7$$\"1F:i$f08F*F*F^glF^dn7$Fddn7$$\"1HW
rBvJ)H*F*$!1\"GWrBvJ=)F27$7$Fgbl$!1&********H\"4!)F2Fhdn7$7$F\\el$\"1'
********H\"4!)F27$$\"1E:i$f08F*F*Fahl7$Feen7$F_cn$\"1^aaaaWG')F27$F^en
7$$\"1TzyLQuV$*F*$!1+%zyLQu$yF27$7$$\"1pew-+ew$*F*F][mF]fn7$Fcfn7$$\"1
g54iic*Q*F*$!1*f54iic\\(F27$7$Fadl$!1HLLLL$=T(F2Fgfn7$7$$\"1-++++++%*F
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1ySQr4tN%*F*$!1f2%Qr4t:(F27$7$F5$!1jmmmm'>%oF2F]hn7$7$FadlFdgn7$$\"14e
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*F*$!1&4c%o%Gf#oF27$7$$\"1I_nBYy'[*F*$!1)************z'F2Fbin7$Fhin7$$
\"1Pw?\\s&*H&*F*$!1ej2#\\s&*\\'F27$7$Ffo$!1&******\\70H'F2F^jn7$7$F\\h
l$\"1&******\\70H'F27$$\"1G_nBYy'[*F*$\"1.++++++oF27$F[[oF^in7$Fdjn7$$
\"1^$e5W,$y&*F*$!12Ne5W,$='F27$7$$\"1g%f%f%f%4'*F*$!1)*************fF2
Fb[o7$Fh[o7$$\"1!e%eRJtF'*F*$!1&zXeRJt(eF27$7$F`o$!14dG9d)\\z&F2F^\\o7
$7$F`o$\"16dG9d)\\z&F27$Fi[o$\"1/++++++gF27$7$Fi[o$\"1.++++++gF2Fhjn7$
Fd\\o7$$\"1kd'*4*Q&y'*F*$!1Ewl*4*Q&e&F27$7$$\"1++++++?(*F*$!1'********
**)f`F2Fc]o7$7$F\\jlFi\\o7$$\"1M)3E>X\\o*F*$\"1q;\"R2[0b&F27$7$F[r$\"1
(**********)f`F2F`^o7$7$F[rF\\^o7$$\"1I`>[jJJ(*F*$!1(G`>[jJJ&F27$7$$\"
1#z@qq;(e(*F*$!1)************>&F2F[_o7$Fa_o7$$\"1Lc78jd'y*F*$!1BjDJJwl
]F27$7$Fcs$!1ILLLL3,]F2Fg_o7$7$Fd^m$\"1ILLLL3,]F27$$\"1\"z@qq;(e(*F*$
\"1.++++++_F27$Fd`oFf^o7$7$Fd^mF^`o7$$\"1t-Lu!f`%)*F*$!1EFIV2f`[F27$7$
Fjt$!1(********\\4u%F2F\\ao7$7$FcsFb`o7$$\"1o$HRTw%H)*F*$\"1UjqgeB0\\F
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F*$\"11K%=_o0l%F27$7$Fbv$\"1+++++N4YF2F^co7$7$F^wF[co7$$\"1#H[(*[Q4)**
F*$!18H[(*[Q4YF27$7$Fjw$!1KLLLL[4YF2Fico7$Fdco7$$\"1wtu:b!>+\"F\\x$\"1
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27$7$F_hoFg`oFcho7$Fiho7$$\"1C*HvK@m-\"F\\x$\"1?w+Zs'yL&F27$7$F`\\l$\"
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f$f$QpF27$7$F^im$\"1fbbbbDPqF2Ff]p7$7$Fjjm$!10++++l+xF27$$\"1UaIQPne5F
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xF27$Ff_p7$$\"1gX*34EP1\"F\\x$\"1()Ra54RF!)F27$7$$\"1[Zt`_(z1\"F\\xFah
lFe`p7$F[ap7$$\"1q\"=K-*)z1\"F\\x$\"1>I=yw4,%)F27$7$Fa]n$\"1LFFFF(>S)F
2F_ap7$Fj_p7$$\"1\"3M]H6#o5F\\x$!1X!3M]H6U)F27$7$$\"1++++++w5F\\x$!1E=
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\"1EnmKTrw5F\\xF[q7$Fgcp7$F`bp$!1D====GF\"*F27$F^cp7$$\"1Fc3*Hgj2\"F\\
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++++g(*F*$!1%************R#F27$7$FcsFbhqFie\\l7$7$FcsFeiqFfe\\l7$Faf\\
lFaf\\l7$F_f\\l7$$\"1++++++S)*F*$!1%************f\"F27$7$FjtFcjqFdf\\l
7$7$FjtFi\\rFaf\\l7$F\\g\\lF\\g\\l7$Fjf\\l7$$\"1++++++?**F*$!1Q*******
*****zF[[r7$7$F^wF`[rF_g\\l7$7$F^wFj[rFeg\\l7$Fgg\\lF\\g\\l7$Fgg\\lFgg
\\l7$7$FjwF`[rFeg\\l7$Feg\\lF[h\\l7$F[h\\lFgg\\l7$Feg\\lFgg\\l7$7$FjwF
j[rF[h\\lF]h\\l7$F`h\\lFgg\\l7$Fgg\\lF`h\\l7$7$FayFcjqFdh\\l7$Fdh\\lF[
h\\l7$F[h\\lF`h\\l7$F`h\\l7$$\"1++++++35F\\x$\"17++++++!)F[[r7$7$FayFi
\\rFhh\\l7$7$FjzFbhqF`i\\l7$F`i\\lFdh\\l7$F^i\\l7$Fi]x$\"1-++++++;F27$
7$FjzFeiqFci\\l7$7$F`\\lFgeqFii\\l7$Fii\\lF`i\\l7$Fgi\\l7$$\"1++++++C5
F\\x$\"1-++++++CF27$7$F`\\lFhfqF\\j\\l7$7$F`]lF[eqFdj\\l7$Fdj\\lFii\\l
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F_[]l7$F_[]lFdj\\l7$F][]l7$Ffe[l$\"1/++++++SF27$7$Fb_lF^dqFb[]l7$7$F^i
mFd_oFh[]l7$Fh[]lF_[]l7$Ff[]l7$$\"1++++++[5F\\x$\"1/++++++[F27$7$F^imF
g`oF[\\]l7$7$FjjmF[\\oFc\\]l7$Fc\\]lFh[]l7$Fa\\]l7$$\"1++++++c5F\\x$\"
10++++++cF27$7$FjjmF`]oFf\\]l7$7$Fa]nF[jnF^]]l7$F^]]lFc\\]l7$F\\]]l7$$
\"1++++++k5F\\x$\"1/++++++kF27$7$Fa]nF^[oFa]]l7$7$F`bpF][mFi]]l7$Fi]]l
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)F27$$\"1zM/8R<7!*F*$!1!yM/8R<_)F27$7$$\"1KLLLLLB!*F*F^glFj`]l7$F`a]l7
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%ot%*y:*F*$!1]5Uot%*ynF27$7$Fean$!1&***********\\nF2Fjc]l7$7$Fean$\"1&
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\"*F*$\"1S++++++qF27$7$F^c]lF`\\mF\\e]l7$Fbe]l7$$\"1,+++++!3*F*$\"1)**
*********>xF27$7$FbesFad]l7$$\"1LLLLLL$>*F*$!1ILLLLLLjF27$7$$\"1******
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14dG9dG9dF2Fef]l7$7$F_\\q$\"14dG9dG9dF27$Fbf]lF`]o7$7$$\"1++++++?#*F*F
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Fd_oFig]l7$F_h]l7$$\"1,+++++'H*F*$!1'***********f\\F27$7$Fgbl$!1#*****
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*H$F2Fdj]l7$7$Fbgn$\"1!************H$F27$Faj]lFegq7$Fa[^l7$Fgb\\l$\"1A
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F*$!1$***********\\7F27$7$$\"1ommmmm'[*F*FcjqF[_^l7$Fa_^l7$$\"1dG9dG9(
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$$\"1nmmmmm'[*F*Fi\\rFe`^l7$7$Fb_^lFi\\rFg]^l7$7$F^im$!1:++++++9F27$$
\"1LLLLLL^5F\\xFcjq7$Fda^l7$$\"1+++++?^5F\\x$!1#***********>6F27$7$Ffc
xF`[rFha^l7$F^b^l7$Ffcx$!1G************>F[[r7$7$FfcxFj[rF`b^l7$Fdb^l7$
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$Fch[lFgeq7$F[d^l7$$\"1++++++b5F\\x$!1()***********H#F27$7$$\"1'G9dG9P
0\"F\\xFbhqF]d^l7$Fcd^lFaa^l7$Fdc^l7$$\"1LLLLLL`5F\\x$\"1smmmmmm=F27$7
$Fdd^lFeiqFhd^l7$F^e^l7$$\"1+++++gb5F\\x$\"10+++++SCF27$7$Fch[lFhfqF`e
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**RF27$7$$\"1+++++]h5F\\xF[eqFif^l7$F]g^lFhc^l7$F^f^l7$$\"1++++++h5F\\
x$\"11++++++NF27$7$F^g^lFegqFbg^l7$Fhg^l7$Fb]]l$\"11++++++SF27$7$Fff^l
FjjsFjg^l7$7$Fff^lF^dq7$$\"1dG9dG9n5F\\x$\"1\"H9dG9d[%F27$7$Fa]n$\"14+
+++++YF2Fah^l7$7$F`bp$!1BdG9dG9dF27$F]^]lFd_o7$F^i^lFbf^l7$Fgh^l7$$\"1
+++++Sq5F\\x$\"11+++++g\\F27$7$F]^]lFg`oFai^l7$Fgi^l7$$\"1+++++vt5F\\x
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7$Fgj^lF\\]oF[[_l7$7$Fgj^lF`]o7$$\"1nmmmmm!3\"F\\x$\"1RLLLLLLjF27$7$Fc
cp$\"15+++++]nF2Fd[_l7$7$Fj]s$!15+++++?xF27$$\"1\"4444444\"F\\xF][m7$F
a\\_l7$$\"1***********f3\"F\\x$!1X************pF27$7$$\"1OOOOOO%3\"F\\
xF[jnFe\\_l7$F[]_l7$Fccp$!15+++++]nF27$Fj[_l7$$\"1!z:j_5U3\"F\\x$\"1e5
Uot%*ynF27$7$F\\]_lF^[oFc]_l7$Fi]_l7$$\"1+++++!y3\"F\\x$\"12+++++?sF27
$7$Fb\\_lF`\\mF[^_l7$Fa^_l7$$\"1r&G9dG94\"F\\x$\"1iG9dG9dwF27$7$Fj]s$
\"15+++++?xF2Fc^_l7$7$Fc^u$!1laaaaaa')F27$$\"1nmmmmm(4\"F\\xF^gl7$F`__
lF^\\_l7$Fi^_l7$$\"1444444&4\"F\\x$\"1*4444444)F27$7$Fa__lFahlFe__l7$F
[`_l7$$\"1_cp3Ey)4\"F\\x$\"1\"zM/8R<_)F27$7$Fc^u$\"1laaaaaa')F2F]`_lFc
dx-F$6[p7$7$Fchp$!1jmmmmmmqF27$$\"1s&G9dG9,*F*$!17dG9dG9pF27$7$$\"1***
*********>!*F*F[jnF\\a_l7$7$$\"1++++++?!*F*F[jn7$$\"1++++++W!*F*$!1'**
*********RkF27$7$$\"1LLLLLLt!*F*F[\\oFia_l7$F_b_l7$$\"15Uot%*yv!*F*$!1
-@%ot%*y&fF27$7$Fh_n$!1!G9dG9d)eF2Fcb_l7$7$Fh_n$\"1#G9dG9d)eF27$F`b_lF
\\]o7$7$F`b_lF`]o7$$\"1************f!*F*$\"1<++++++iF27$7$Fga_lF^[oFcc
_l7$7$Fca_lF^[o7$Fchp$\"1jmmmmmmqF27$Fib_l7$$\"1nmmmmm1\"*F*$!1jmmmmmm
aF27$7$$\"1kjjjjjB\"*F*Fd_oF`d_l7$Ffd_l7$$\"1&HN#)eqk8*F*$!1QHN#)eqk\\
F27$7$Fbes$!1FLLLLLLXF2Fjd_l7$7$Fean$\"1GLLLLLLXF27$Fgd_lFg`o7$Fge_lF]
c_l7$7$FeanFae_l7$$\"1,+++++l\"*F*$!1'***********\\WF27$7$$\"1,+++++o
\"*F*FhbqF[f_l7$Faf_l7$$\"1++++++#>*F*$!1'***********>RF27$7$$\"1,++++
+3#*F*F[eqFef_l7$F[g_l7$$\"1dG9dG9<#*F*$!1n&G9dG9P$F27$7$FecnFgeqF_g_l
7$7$FecnFhfq7$$\"1++++++3#*F*Fegq7$Fhg_l7$$\"1++++++w\"*F*$\"18+++++SU
F27$7$$\"1***********z;*F*F^dqF\\h_l7$Fbh_lFde_l7$Feg_l7$$\"1++++++g#*
F*$!1&************>#F27$7$$\"1mmmmmmm#*F*FbhqFgh_l7$F]i_l7$$\"1OOOOOOw
#*F*$!1ejjjjjj:F27$7$$\"1WWWWWW%G*F*FcjqFai_l7$Fgi_l7$$\"1++++++)G*F*$
!1V***********z)F[[r7$7$FidxF`[rF[j_l7$Faj_l7$Fidx$!1jKLLLLL8F[[r7$7$F
idxFj[rFcj_l7$Fgj_l7$$\"1++++++!H*F*$\"1\"3++++++(F[[r7$7$$\"1XWWWWW%G
*F*Fi\\rFij_l7$F_[`l7$$\"1:dG9dGu#*F*$\"1mG9dG9d;F27$7$$\"1nmmmmmm#*F*
FeiqFc[`l7$Fi[`lFgg_l7$7$F`bpFgeq7$$\"1LLLLLLt5F\\xFbhq7$F_\\`l7$$\"1H
9dG9ds5F\\x$!1YG9dG9d;F27$7$$\"1bbbbbbr5F\\xFcjqFc\\`l7$Fi\\`l7$$\"1++
++++r5F\\x$!1+************pF[[r7$7$Fg[zF`[rF]]`l7$Fc]`l7$Fg[z$\"1?MLLL
LL8F[[r7$7$Fg[zFj[rFe]`l7$Fi]`l7$$\"1+++++?r5F\\x$\"1t++++++))F[[r7$7$
$\"1cbbbbbr5F\\xFi\\rF[^`l7$Fa^`l7$$\"1OOOOOOs5F\\x$\"1rjjjjjj:F27$7$F
`\\`lFeiqFe^`l7$F[_`l7$$\"1++++++u5F\\x$\"12++++++AF27$7$F`bpFhfqF]_`l
7$7$Fccp$!1[LLLLLLXF27$$\"1+++++?$3\"F\\xFhbq7$Fh_`l7$$\"1+++++S#3\"F
\\x$!1z**********RUF27$7$$\"1+++++?z5F\\xF[eqF\\``l7$Fb``lF^\\`l7$Fc_`
l7$$\"19dG9dGy5F\\x$\"1z&G9dG9P$F27$7$Fc``lFegqFg``l7$F]a`l7$$\"1+++++
!33\"F\\x$\"13+++++?RF27$7$Fi_`lF^dqF_a`l7$Fea`l7$$\"1+++++]$3\"F\\x$
\"12+++++]WF27$7$Fccp$\"1[LLLLLLXF2Fga`l7$7$Fj]s$!1*H9dG9d)eF27$$\"1kj
jjjj(3\"F\\xFd_o7$Fdb`lFe_`l7$F]b`l7$$\"1rk<THN'3\"F\\x$\"1\\HN#)eqk\\
F27$7$Feb`lFg`oFib`l7$F_c`l7$$\"1LLLLLL*3\"F\\x$\"1ummmmmmaF27$7$Fj]s$
\"1+Vr&G9d)eF2Fac`l7$7$Fc^u$!1zmmmmmmqF27$$\"1++++++)4\"F\\xF[jn7$F^d`
l7$$\"1++++++%4\"F\\x$!1p***********>'F27$7$$\"1nmmmmm#4\"F\\xF[\\oFbd
`l7$7$Fid`lFi^qFab`l7$Fgc`l7$$\"1z:j_5U#4\"F\\x$\"18@%ot%*y&fF27$7$Fid
`lF`]oF^e`l7$Fde`l7$$\"1+++++g&4\"F\\x$\"12+++++SkF27$7$F_d`lF^[oFfe`l
7$F\\f`l7$$\"1Vr&G9d))4\"F\\x$\"1@dG9dG9pF27$7$Fc^u$\"1zmmmmmmqF2F^f`l
Fcdx-F$6Y7$7$Fchp$!1&*************\\F27$Fca_l$!1'************f%F27$7$F
bhvFhbqF]g`l7$Fag`l7$$\"1THN#)eqW!*F*$!13%HN#)eq/%F27$7$$\"1LLLLLLj!*F
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1#************4$F2F]h`l7$7$Fh_n$\"1!************4$F27$Fjg`lFegq7$Fjh`l
7$$\"1q&G9dG90*F*$\"1&H9dG9d)QF27$7$FbhvF^dqF\\i`l7$Fbi`l7$F`fp$\"1&**
***********\\F27$Fch`l7$$\"1***********z3*F*$!1'***********zGF27$7$$\"
1#4444444*F*FgeqFhi`l7$F^j`l7$$\"1'G9dG9d5*F*$!1`G9dG9dAF27$7$$\"1ssss
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$7$$\"1FFFFFFF\"*F*FcjqF\\[al7$7$$\"1EFFFFFF\"*F*Fcjq7$$\"1++++++I\"*F
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[[r7$7$$\"1baaaaaM\"*F*Fj[rFa\\al7$Fe\\al7$$\"1++++++K\"*F*$\"1h++++++
oF[[r7$7$Fc[alFi\\rFi\\al7$F_]al7$F][al$\"12++++++;F27$7$Fij`lFeiqFa]a
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l$\"1\"************4$F27$7$Fj]s$!1C++++++JF27$Fb\\_lFgeq7$Ff^al7$$\"1+
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\"1+++++!o3\"F\\x$!1*))**********z'F[[r7$7$$\"1aaaaaa'3\"F\\xF`[rFj_al
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dal7$$\"11Zw6%Hb4\"F\\x$\"1?%HN#)eq/%F27$7$F_calFjjsFedal7$7$F_calF^dq
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\"xG%\"yG" 2 329 329 329 2 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 10030 0 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 12 "Exercice 3
. " }}{PARA 0 "" 0 "" {TEXT -1 329 "Ecrire une procŽdure qui admet com
me param�tres une fonction f(x,y) et un point singulier (a,b) de f et \+
qui, apr�s avoir vŽrifiŽ que (a,b) est bien un point singulier, trace \+
les contours de f et de sa hessienne translatŽe en (a,b), sur un recta
ngle centrŽ en (a,b) dont les dimensions sont de prŽfŽrence Žtablies i
ntŽractivement." }}{PARA 0 "" 0 "" {TEXT -1 94 "Testez cette procŽdure
 sur les fonctions de l'exercice 2 ou d'autres fonctions de votre choi
x." }}}}}}{MARK "2" 0 }{VIEWOPTS 1 1 0 1 1 1803 }