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fi;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 15 "\nsuite_m:=NULL;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\nfor i from 1 to N do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 43 "\nmilieu:=(aa+bb)/2;suite_m:=suite_m,milieu;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 44 "\n if is(f(milieu)*f(bb)<0) then aa:=milieu;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 23 "\n else bb:=milieu; fi;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 11 "\n[suite_m];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 2 "\n " }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 19 "Cauchy:=proc (f,a,N)" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 20 "\nlocal aa,i,suite_m ;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 15 "\nsuite_m:=NULL;" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 7 "\naa:=a;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 "\nfor i from 1 to N do" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 42 "\n suite_m:=suite_m,aa;aa:=evalf(f(aa)+aa);" } {MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 11 "\n[suite_m];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "impact:=(f,a)->a-f(a)/D(f)(a);" }{MPLTEXT 1 202 0 " " }{MPLTEXT 1 202 1 "\n" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I'impactG 6\"f*6$I\"fGF%I\"aGF%F%6$I)operatorGF%I&arrowGF%F%,&9%\"\"\"*&-9$6#F.F /--I\"DGF%6#F2F3!\"\"F8F%F%F%" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> \+ " 0 "" {MPLTEXT 1 202 19 "Newton:=proc(f,a,N)" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 29 "\nlocal aa,i,compteur,suite_m;" }{MPLTEXT 1 202 0 " " }{MPLTEXT 1 202 15 "\nsuite_m:=NULL;" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 7 "\naa:=a;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 22 " \nfor i from 1 to N do" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 46 "\n s uite_m:=suite_m,aa;aa:=evalf(impact(f,aa));" }{MPLTEXT 1 202 0 "" } {MPLTEXT 1 202 4 "\nod;" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 11 "\n[s uite_m];" }{MPLTEXT 1 202 0 "" }{MPLTEXT 1 202 5 "\nend:" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 51 "f:=x->(exp(-0.5*x))-1;a:=5;b:=-4;N:=80;s: =0;x_0:=5;" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I \"fG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,&-I$expG6$I*protectedG F0I(_syslibGF%6#,$*&$\"\"&!\"\"\"\"\"9$F8F7F8F7F8F%F%F%" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"aG6\"\"\"&" }{TEXT 204 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"bG6\"!\"%" }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"NG6\"\"#!)" }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"sG6\"\"\"!" }{TEXT 204 0 "" }} {PARA 202 "" 1 "" {XPPMATH 20 "6#>I$x_0G6\"\"\"&" }{TEXT 204 0 "" }}} {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 23 "#f:=x->(exp(-0.001*x))-" }{MPLTEXT 1 202 1 "x" }{MPLTEXT 1 202 35 "-1;a:=10;b:=-14;N:=80;s:=0; x_0:=10;" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 69 "#f:=x->sinh(x/10^4)/10^(20);a:=-10^4;b:=5*10^3;N:=8;s:=0;x_0 :=9*10^3;" }{MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 31 "s D:=evalf(Dichotomie(f,a,b,N));" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I#sDG6\"7\\p$\"?++++++++++++++]!#I$!?+++++++++++++] FG$FK!#N$!?++++ +++]P%[@?dn'FM$!?+++++++Dc,\"z&=%Q#FM$FQ!#O$\"?++++++](oa&o-lW$)FS$\"? ++++++DJ&p(QAB!)HFS$FW!#P$!?+++++v$fLpNG\"3V5FS$!?+++++D19>Y)H!HDPFY$F gn!#Q$\"?++++v=#*p;Y/;&QI\"FY$\"?++++D\"yDRxI(GhcYFin$F]o!#R$!?+++vVBS (3xb]9)H;Fin$!?+++DcEsSnM\"4m2#eF_o$Fco!#S$\"?++voHHDf8(>8os.#F_o$\"?+ +DJ?L!fU$=9w&fF(Feo$Fio!#T$!?+v$4@;m!*>k\\;&eYDFeo$!?+D1R]\"zBGHx,Z\\4 *F[p$F_p!#U$\"?v=nj-F$)[_?c9B$=$F[p$\"?7G))z$R(Hgh@x$oo8\"F[p$FepFap$! ?W)*eHy3/hlD?$R!zRFap$!?;N&[Aur.??:Z&3@9Fap$Fjp!#V$\"?0t)py4,8q?.:*zt \\F\\q$\"?&*o1\"ynk/D+%RoNw,Zl9X9(*F^r$!?yi*[Q#))=9O&>&pWpMF^r$Fbr!#Z$\"?(p8Z $)3m\\w$=LkI97F^r$\"?[.7\")Hgt+.8R\\4/7BD#prBF`s$!?!o+DKo!R.Ias%H.Z)Ffs$Fjs!# ^$\"?Q_(G\"Rn=^+R:`hkHFfs$\"?&e7.a$QUvy1%=\"ze5Ffs$F`tF\\t$!?ZS4\"RU$) RcPU9pdq$F\\t$!?J2RD%zzU%[3!)*)[B8F\\t$Fet!#_$\"?fv')))z#z\\&pHI9@KYFg t$\"?9%QryGk-z&F]u" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "sC:=Cauchy(f,x_0 ,N);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I#sCG6 \"7\\p\"\"&$\"?Zu'G&p^z)*Qi)*\\3#3%!#H$\"?/@.7yujnSHD#y>@$F*$\"?Dd/&z/ qs,Ugr\"F*$\"?u`mvNeg-&G4yFo8\"F*$\"?Y]!3TG'G zx`m\"4D.(!#I$\"?\"pX?T!H&f6%yc\\%z1%F5$\"?^L4a%=X*fjMn`[FAF5$\"?EZu?x Q<'>:2,CN<\"F5$\">Sg$*z>@)H..gnWOgF5$\">p'p?%)\\(QMD%GpJjIF5$\">Z3B>d* Gf'3QpGLa\"F5$\"=%\\1zl+r-vkKSju(F5$\"=PvrPQW*>/B@h1)QF5$\"=)4JE#z\\zM lI=@U>F5$\"<1rv`4iT,3'Gx:(*F5$\"<)Q!*f@/%=$Q#>m!f[F5$\"S7vgF5$\";#)p_*3nftJ93w.$F5$ \";wR?5$eWd`g:)=:F5$\":o_n')fxC<'o5%f(F5$\":3$=$QBkg'R11(z$F5$\":#)eE6 $oy.A@`)*=F5$\"9*)==d6lE\\*F5$\"9C^Ju`DC%oLju%F5$\"9adHi(HQdGue#4NYF5$\"62^z$G)RHYvJ#F5$\"6%etc&eq9t(e6F5$ \"5+3G1YNd'Qz&F5$\"5-9vAxnG$p*GF5$\"5_%yi'*QVm%[9F5$\"49\\O4&p@LUsF5$ \"4z)Q7w%3m6i$F5$\"4X&eAQUIe5=F5$\"3\\!R:>@:H0*F5$\"3p>(efgdk_%F5$\"3' fhzH!)GKE#F5$\"3,s)*[,WhJ6F5$\"2,_\\u+s!ecF5$\"2,![s.g.HGF5$\"2,Ti=+=X T\"F5$\"1w?J4+fsqF5$\"1Wgl/]HONF5$\"1C!GB]Z\"oO _O\"Q\"F5$\".p4=Eo!pF5$\".&[!48MX$F5$\".V_a1ns\"F5$\"-@EF`L')F5$\"-6jj w;VF5$\"-b\"=$Qe@F5$\"-x!f\">z5F5$\",R&z&fR&F5$\",p(*yzp#F5$\",&)[*)*[ 8F5$\"+Vu%\\u'F5$\"+@PZsLF5$\"+hoB'o\"F5$\"*J%=J%)F5$\"*:#f:UF5$\"*2'z 2@F5$\"*.)*Q0\"F5" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 20 "sN:=Newton(f,x_0,N);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I#sNG6\"7\\p\"\"&$!?B!>NSh(o%pS@z)\\O_(o8\"F*$ !?j:8d)R:z;'e'\\\\bP*!#H$!?4$)GS'3Lsk+)*zjRR(F3$!?Ncu&HDhtHGVJgNW&F3$! ?'y'H\"e?m)f'zp\\v]d$F3$!?bSDSN8!*Q8BX!>)4>F3$!>%\\DC4OB#>,3rH^z'F3$!? 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