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{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 8 "restart:" }{MPLTEXT 1 
204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 39 "perturbee:=p
roc(u1,n) option remember; " }{TEXT 206 17 "M\351thode r\351cursive" }
{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 9 "\nlocal u;" }{MPLTEXT 1 204 0 "
" }{MPLTEXT 1 204 23 "\nif n=1 then [u1]; else" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 59 "\n  u:=perturbee(u1,n-1);[op(u),evalf(u[n-1]*(u[n-1
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204 0 "" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 204 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 15 "perturbee(1,5);" }{MPLTEXT 1 
204 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#7'\"\"\"$\"+++++:!\"*$\"++
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{PARA 203 "" 1 "" {XPPMATH 20 "6#7,\"\"\"$\"+++++:!\"*$\"++++]FF'$\"++
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{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" 
}}}{EXCHG {PARA 202 "" 0 "" {TEXT 205 11 "Question b)" }{TEXT 203 0 ""
 }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 14 "test:=proc(u1)" }
{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 28 "\nlocal l,u,n,suite,sol,maxi;"
 }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 11 "\nmaxi:=10: " }{TEXT 206 16 
"pour \351viter une " }{TEXT 208 14 "boucle infinie" }{TEXT 206 31 " o
n se fixe un nombre maximal (" }{TEXT 208 4 "maxi" }{TEXT 206 14 ") d'
it\351rations" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 11 "\nn:=1;l:=1;" 
}{TEXT 206 1 " " }{TEXT 208 10 "Par d\351faut" }{TEXT 206 26 " nous af
fectons la valeur " }{TEXT 208 3 "l=1" }{MPLTEXT 1 204 0 "" }{MPLTEXT 
1 204 7 "\nu:=u1;" }{TEXT 206 0 "" }{TEXT 206 23 "\nla limite potentie
lle " }{TEXT 208 16 "l est d\351termin\351e" }{TEXT 206 43 " lors d'un
e des conditions ci-dessous pour " }{TEXT 208 2 "u1" }{MPLTEXT 1 204 
0 "" }{MPLTEXT 1 204 27 "\nif is(u<=1-1/n) then l:=0;" }{MPLTEXT 1 
204 0 "" }{MPLTEXT 1 204 37 "\nelif is(u>=1) then l:=+infinity; fi;" }
{TEXT 206 0 "" }{TEXT 206 63 "\nN'ayons pas de r\351ponse d\351terminn
\351e pour u1, nous essayons les " }{TEXT 208 43 "valeurs successives \+
(jusqu'\340 l'indice maxi)" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 28 "
\nwhile is(l=1 and n<maxi) do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 
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29 "\n  if is(u<=1-1/n) then l:=0;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 
204 37 "\nelif is(u>=1) then l:=+infinity; fi;" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 4 "\nod;" }{TEXT 206 0 "" }{TEXT 206 79 "\nApr\350s ces
 nombreuses tentatives, on peut esp\351rer conclure sans trop se tromp
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:=true else sol:=false; fi;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "
\nend:" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 1 "\n" }{MPLTEXT 1 204 1 
"\n" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 18 "test(0.3);test(1
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{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 205 11 "Question
 c)" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "
alpha:=proc(epsilon)" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 17 "\nlocal
 a,b,m,n,t;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 17 "\nn:=0:a:=0;b:=1
; " }{TEXT 206 11 "intialement" }{TEXT 208 7 " (n=0) " }{TEXT 206 30 "
on travaille sur l'intervalle " }{TEXT 208 11 "[a,b]=[0,1]" }{MPLTEXT 
1 204 0 "" }{MPLTEXT 1 204 25 "\nwhile is(b-a>epsilon) do" }{MPLTEXT 
1 204 0 "" }{MPLTEXT 1 204 31 "\n n:=n+1:m:=(a+b)/2;t:=test(m);" }
{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 2 "\n " }{TEXT 206 11 "On remplace
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{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 18 "\n if t then b:=m  " }{TEXT 
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}{TEXT 206 8 "si pour " }{TEXT 208 4 "u1=m" }{TEXT 206 9 " la suite" }
{TEXT 208 23 " u tend vers +infini, (" }{TEXT 206 9 "car alors" }
{TEXT 208 9 " alpha<m)" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 17 "\n el
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}{MPLTEXT 1 204 1 " " }{TEXT 206 8 "si pour " }{TEXT 208 4 "u1=m" }
{TEXT 206 9 " la suite" }{TEXT 208 29 " u ne tend pas vers +infini (" 
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