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TG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" 
}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g(x+2*Pi)-g(x); " }
{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 5 " est " }{XPPEDIT 18 0 "2*Pi;
" "6#*&\"\"#\"\"\"%#PiGF%" }{TEXT -1 11 "-p\351riodique" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
58 "g(Pi/3);limit(g(x),x=Pi/3,right);limit(g(x),x=Pi/3,left); " }
{TEXT -1 3 "en " }{XPPEDIT 18 0 "Pi/3;" "6#*&%#PiG\"\"\"\"\"$!\"\"" }
{TEXT -1 14 "  la fonction " }{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 
83 " admet une limite qui co\357ncide avec sa valeur ; elle est donc c
ontinue en ce point " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"&
\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"&\"\"'" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"&\"\"'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 22 "iscont(g(x),x=-3..3); " }{XPPEDIT 18 0 "g;" "6#%
\"gG" }{TEXT -1 74 " est m\352me continue sur un intervalle de longueu
r strictement sup\351rieure \340 " }{XPPEDIT 18 0 "2*Pi;" "6#*&\"\"#\"
\"\"%#PiGF%" }{TEXT -1 30 " ; elle est donc continue sur " }{XPPEDIT 
18 0 "R;" "6#%\"RG" }{MPLTEXT 1 0 2 "  " }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "isdifferen
tiable(g(x),x,1); " }{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 29 " serai
t d\351rivable selon Maple" }{MPLTEXT 1 0 1 " " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 0 "" {TEXT -1 2 "  " }}{PARA 0 "
" 0 "" {TEXT -1 43 "Ce r\351sultat est surprenant :  la courbe de " }
{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 51 " pr\351sente apparemment pl
usieurs point anguleux, en " }{XPPEDIT 18 0 "0;" "6#\"\"!" }{TEXT -1 
60 " par exemple. Etudions la limite du taux d'accroissement de " }
{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 7 " entre " }{XPPEDIT 18 0 "0;
" "6#\"\"!" }{TEXT -1 4 " et " }{XPPEDIT 18 0 "0+h;" "6#,&\"\"!\"\"\"%
\"hGF%" }{TEXT -1 25 " (lorsque h tend vers 0)." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "delta:=h->(g
(h)-g(0))/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deltaGf*6#%\"hG6\"6
$%)operatorG%&arrowGF(*&,&-%\"gG6#9$\"\"\"-F/6#\"\"!!\"\"F2F1F6F(F(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "limit(delta(h),h=0);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*undefinedG" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "Il semble que la limite d
e ce taux d'accroissement n'existe pas (et donc que " }{XPPEDIT 18 0 "
g;" "6#%\"gG" }{TEXT -1 30 " ne soit pas d\351rivable en 0). " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "limit(delta(h),h=0,right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"
\"&\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(delta(h),
h=0,left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"&\"\"#" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "g;" "6#%\"gG" }
{TEXT -1 23 " est donc d\351rivable en " }{XPPEDIT 18 0 "0;" "6#\"\"!
" }{TEXT -1 56 " \340 droite et \340 gauche, mais elle n'est pas d\351
rivable en " }{XPPEDIT 18 0 "0;" "6#\"\"!" }{TEXT -1 57 ". (Il faut se
 m\351fier de la fonction 'isdifferentiable'). " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "On pourra encore montrer \+
(\340 la main) que " }{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 52 " est \+
affine par morceaux et \351tudier sa monotonie.   " }}}}{MARK "0" 0 }
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