{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title
" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 
12 12 0 0 0 0 0 0 19 0 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 42 "Approximation par des s
\351ries de Tchebychef" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "D'apr
\350s ENS Saint-Cloud option P' 1982." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "restart:with(orthopoly):interface(plotdevice=gdi);" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 126 "Le paquet nomm\351 orthopoly fo
urnit toutes sortes de polyn\364mes orthogonaux, notamment ceux de Tch
ebychef dont nous avons besoin." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
74 "Nous d\351finissons d'abord la fonction auxiliaire fc; c'est une h
omographie." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "c:=2.*sqrt(2
.)-3.:fc:=x->(1-c^2)/(2*(1-2*c*x+c^2)):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 244 "Cette fonction a un d\351veloppement en s\351rie de poly
n\364mes de Tchebychef. Quand on prend n termes, l'erreur commise est \+
de l'ordre de grandeur de c^n. La th\351orie des polyn\364mes de meill
eure approximation montre que le meilleur choix pour approcher " }}
{PARA 0 "" 0 "" {TEXT -1 45 "fc avec un polyn\364me de degr\351 n au p
lus est..." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "P:=(n,x)->-1/2+sum(c^k*T(k,x),k=0..n-1)+c^n/(1-c^2)*T(n,x):" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 109 "Nous prendrons pour nos essais une petite valeur de
 n, qui mettra bien en \351vidence les approximations faites." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Digits:=9:P(4,x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,,$\"*#eb9Z!\"*\"\"\"%\"xG$!*u4Uc\"F&*$)F(\"
\"#\"\"\"$\"*&G=t^!#5*$)F(\"\"$F.$!*e`--#F1*$)F(\"\"%F.$\"*1vE9(!#6" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Un changement de variable affine
 ram\350ne l'intervalle [-1,1]  \340 [0,1]." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 40 "Q:=(n,t)->expand(P(n,(2*t-1))*sqrt(2.)):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "On constate que l'\351cart entre \+
la fonction 1/(1+t) et Qn est petit, et qu'il y a bien une alternance \+
\340 l'ordre 4+2=6." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot
(1/(1+t)-Q(4,t),t=0..1);" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7
`s7$\"\"!$\"1n/+++Qm@!#>7$$\"1LL$3FWYs#!#=$\"1Dl*o$zHH=F+7$$\"1mmmT&)G
\\aF/$\"1')od'H/)4:F+7$$\"1++]7G$R<)F/$\"1`Z-b:P27F+7$$\"1LLL3x&)*3\"!
#<$\"1YU*4BH[@*!#?7$$\"1nmTN@Ki8F?$\"1,bUN<K;lFB7$$\"1++]ilyM;F?$\"1j'
3tqMK(RFB7$$\"1LLe*)4D2>F?$\"1Uz&>.72e\"FB7$$\"1nmm;arz@F?$!1^%*p>\"=+
m'!#@7$$\"1L$e*)4bQl#F?$!1`#)y,i&=C%FB7$$\"1++D\"y%*z7$F?$!1Tq')p]09uF
B7$$\"1n;ajW8-OF?$!1'f/_-d0-\"F+7$$\"1LL$e9ui2%F?$!1<m'*pH&QE\"F+7$$\"
1++voMrU^F?$!1pU]Vo&4p\"F+7$$\"1nmm\"z_\"4iF?$!1Pys*>4,(>F+7$$\"1mm;zp
!fu'F?$!1AS4+8Ih?F+7$$\"1nmmm6m#G(F?$!1&)GZ!>>G7#F+7$$\"1omTg#Q5b(F?$!
1#HMe1(>V@F+7$$\"1nm;a`T>yF?$!1#3C*o)Qq:#F+7$$\"1nm\"zW#z(3)F?$!1.D>`Z
ik@F+7$$\"1mmmT&phN)F?$!1]?=R$Gi;#F+7$$\"1,v$f3rKi)F?$!1*)o\\l%\\@;#F+
7$$\"1L$3-js.*))F?$!1&p]3(om_@F+7$$\"1m\"zW<uu:*F?$!1&R%zL;.Q@F+7$$\"1
++v=ddC%*F?$!1<tbF))[=@F+7$$\"1m;H2)y(e**F?$!1JkJb8jl?F+7$$\"1LLe*=)H
\\5!#;$!1jv+!fQf*>F+7$$\"1++v=JN[6Fjs$!1(eYE8g!G=F+7$$\"1nm\"z/3uC\"Fj
s$!1)\\F7]p'=;F+7$$\"1LLe*ot*\\8Fjs$!1cBqD:;o8F+7$$\"1++DJ$RDX\"Fjs$!1
Cq')G#)p#4\"F+7$$\"1LLekGhe:Fjs$!1fv9?Be0zFB7$$\"1nm\"zR'ok;Fjs$!1qJ!3
B,5z%FB7$$\"1LL3_(>/x\"Fjs$!1@;dmlqm;FB7$$\"1++D1J:w=Fjs$\"1Ky^:c\\89F
B7$$\"1n;HdG\"\\)>Fjs$\"1Vp]X1sxWFB7$$\"1LLL3En$4#Fjs$\"1hal$>)R&Q(FB7
$$\"1++Dc#o%*=#Fjs$\"1V$QLMy@y*FB7$$\"1nm;/RE&G#Fjs$\"1QYbIu!**>\"F+7$
$\"1LLe9r5$R#Fjs$\"15W*fg;aU\"F+7$$\"1+++D.&4]#Fjs$\"1#zCmS@Ki\"F+7$$
\"1+++]jB4EFjs$\"16K/'Q8Az\"F+7$$\"1+++vB_<FFjs$\"1CjHq)4.$>F+7$$\"1++
+Dg(=#GFjs$\"1<]\\)>\"\\L?F+7$$\"1+++v'Hi#HFjs$\"1(G<N](32@F+7$$\"1m\"
H2B6O(HFjs$\"1D\"\\*f.wI@F+7$$\"1L$eky#*4-$Fjs$\"1=sQo:R[@F+7$$\"1+v=U
VPoIFjs$\"1wr$GnH+;#F+7$$\"1nm\"z*ev:JFjs$\"1F\"Gj)ftl@F+7$$\"1](=U_ER
9$Fjs$\"1\\C3KlMm@F+7$$\"1L3_]r4sJFjs$\"1CelNM!\\;#F+7$$\"1<H#oxn-?$Fj
s$\"1.x4?bUh@F+7$$\"1+]7.%Q%GKFjs$\"16yWxH$f:#F+7$$\"1m\"HdlzZG$Fjs$\"
1O%*\\\"Q\"**Q@F+7$$\"1LLL347TLFjs$\"1clvPgE9@F+7$$\"1LL$3xxlV$Fjs$\"1
Y1/I#*>b?F+7$$\"1LLLLY.KNFjs$\"1aZVqA^v>F+7$$\"1++D\"o7Tv$Fjs$\"1u)*\\
>,b<<F+7$$\"1LLL$Q*o]RFjs$\"1$R%)))\\rjT\"F+7$$\"1++D\"=lj;%Fjs$\"1IId
(\\>Z-\"F+7$$\"1++]iB0pUFjs$\"1Hyt%pqJ@)FB7$$\"1++vV&R<P%Fjs$\"1s_<mLK
+hFB7$$\"1n;zWG))yWFjs$\"1^lDKJ8OQFB7$$\"1LL$e9Ege%Fjs$\"1:kvTqIO:FB7$
$\"1M$3F9<Wo%Fjs$!1V'*e%zO=&eFW7$$\"1LLeR\"3Gy%Fjs$!1&\\ahl*p&p#FB7$$
\"1+](=7O*))[Fjs$!1g$=YZ@y$\\FB7$$\"1nm;/T1&*\\Fjs$!1yT%f]&R@rFB7$$\"1
m;/^7I0^Fjs$!111wx(oJI*FB7$$\"1mm\"zRQb@&Fjs$!1)yZ=e%GP6F+7$$\"1LLLe,]
6`Fjs$!1Fh)eY8lI\"F+7$$\"1***\\(=>Y2aFjs$!1FQhn:/k9F+7$$\"1mm;zXu9cFjs
$!1l1gQ_2e<F+7$$\"1+++]y))GeFjs$!1\"e3JKM^)>F+7$$\"1***\\ibOO$fFjs$!1Q
c*RQ7X1#F+7$$\"1****\\i_QQgFjs$!1G[oKVn@@F+7$$\"1*\\(=U,1*3'Fjs$!1],B8
w5T@F+7$$\"1**\\(=-N(RhFjs$!1`<HT\\2b@F+7$$\"1*\\i:!*4/>'Fjs$!11!Rs:7N
;#F+7$$\"1***\\7y%3TiFjs$!1gcKGiOm@F+7$$\"1*\\7`f]tH'Fjs$!1&3[9%Q%H;#F
+7$$\"1**\\P4kh`jFjs$!1&ptZ%pa_@F+7$$\"1+vVBA))4kFjs$!1%)y&z;`^8#F+7$$
\"1****\\P![hY'Fjs$!1?F=^%e26#F+7$$\"1mmT5FEnlFjs$!1PpQN>Q\\?F+7$$\"1L
LL$Qx$omFjs$!1)RJVJ%pl>F+7$$\"1+++v.I%)oFjs$!1xyMm4i9<F+7$$\"1mm\"zpe*
zqFjs$!1)HW&*[.vS\"F+7$$\"1L$e9\"=\"p=(Fjs$!1K^RdIz57F+7$$\"1+++D\\'QH
(Fjs$!15kIPU2g**FB7$$\"1n;zp%*\\%R(Fjs$!1+h06bQ$z(FB7$$\"1KLe9S8&\\(Fj
s$!1]O#)e@G1bFB7$$\"1mmT5hK+wFjs$!1EdY)Rx<,$FB7$$\"1***\\i?=bq(Fjs$!1k
]m\"ox#)R%FW7$$\"1m;H2FO3yFjs$\"1)HAjVL)=@FB7$$\"1LLL3s?6zFjs$\"1j+YG@
2)o%FB7$$\"1m;zpe()=!)Fjs$\"1z=kixL]tFB7$$\"1++DJXaE\")Fjs$\"1=.3\"oC3
%**FB7$$\"1L$e*[ACI#)Fjs$\"1[,9e:LK7F+7$$\"1nmmm*RRL)Fjs$\"1`!o%3#3\\X
\"F+7$$\"1nmTge)*R%)Fjs$\"1a+X&Q:7m\"F+7$$\"1mm;a<.Y&)Fjs$\"1>L1:,WS=F
+7$$\"1+]PM&*>^')Fjs$\"1=xS)H-c)>F+7$$\"1LLe9tOc()Fjs$\"1(p$fes=#4#F+7
$$\"1+vV[ko/))Fjs$\"1K4Rz.YE@F+7$$\"1m;H#e0I&))Fjs$\"1;Ul8&z0:#F+7$$\"
1](=#\\^;x))Fjs$\"1%R+AaB'e@F+7$$\"1Le9;ZK,*)Fjs$\"1F;-ox(Q;#F+7$$\"1;
H2$G%[D*)Fjs$\"1oiU$Qci;#F+7$$\"1+++]Qk\\*)Fjs$\"1c$o\")fsc;#F+7$$\"1n
T5SMLx*)Fjs$\"1M%\\3(pCh@F+7$$\"1L$3-.B]+*Fjs$\"1*p&3O4o_@F+7$$\"1+DJ?
ErK!*Fjs$\"13gtY!R)R@F+7$$\"1nmT5ASg!*Fjs$\"1$=([WTeA@F+7$$\"1+]i!R\"y
:\"*Fjs$\"1RU](3yU2#F+7$$\"1LL$3dg6<*Fjs$\"1%[=%>6j1?F+7$$\"1++voTAq#*
Fjs$\"1+*Q6@5P$=F+7$$\"1mmmmxGp$*Fjs$\"1!\\X>#oJ)e\"F+7$$\"1+DJ&**)4A%
*Fjs$\"1C18JpUD9F+7$$\"1L$eRA5\\Z*Fjs$\"1-?2+*)zQ7F+7$$\"1mTg_9sF&*Fjs
$\"1\"H`.S$HF5F+7$$\"1++D\"oK0e*Fjs$\"1E$RH&fZ(*yFB7$$\"1+]il(z5j*Fjs$
\"1m(p*f@,p`FB7$$\"1+++]oi\"o*Fjs$\"1fY@s9_!e#FB7$$\"1+]PMR<K(*Fjs$!1h
E[mn,)y%FW7$$\"1++v=5s#y*Fjs$!1$>@o,j*>QFB7$$\"1+D1k2/P)*Fjs$!1%p[(H5[
PxFB7$$\"1+]P40O\"*)*Fjs$!1\">!)p,f2?\"F+7$$\"1^7.#Q?&=**Fjs$!1RU8Qn$z
U\"F+7$$\"1+voa-oX**Fjs$!1MC$GtsWm\"F+7$$\"1\\PMF,%G(**Fjs$!1x*>6p^0\"
>F+7$$\"\"\"F($!18))*****fj;#F+-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXES
LABELSG6$Q\"t6\"%!G-%%VIEWG6$;F(Ffdm%(DEFAULTG" 2 520 302 302 2 0 1 0 
2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 10056 10074 0 0 0 
20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 4 1 0 0 0 0 0 0 }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 61 "Maintenant nous pouvons approcher les logarithm
es sur [0,1]. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "L:=(n,x)-
>int(Q(n,t),t=0..x):plot(ln(1+x)-L(4,x),x=0..1);" }}{PARA 13 "" 1 "" 
{INLPLOT "6%-%'CURVESG6$7iq7$\"\"!F(7$$\"1mmmT&)G\\a!#=$\"16PU?gM%)**!
#A7$$\"1LLL3x&)*3\"!#<$\"1U6LG(oyl\"!#@7$$\"1nmTN@Ki8F3$\"1KDg0#>=(=F6
7$$\"1++]ilyM;F3$\"1,_g@MP9?F67$$\"1LLe*)4D2>F3$\"11+(\\k*p*3#F67$$\"1
nmm;arz@F3$\"1i@h1_$=5#F67$$\"1+D\"yD&y;CF3$\"1U(\\C]HS1#F67$$\"1L$e*)
4bQl#F3$\"1MCxAL%Q)>F67$$\"1nT5S\\#4*GF3$\"1\"z!=(f.P'=F67$$\"1++D\"y%
*z7$F3$\"1=$)R4z'fq\"F67$$\"1n;ajW8-OF3$\"1)Q(H,**z'G\"F67$$\"1LL$e9ui
2%F3$\"12-H%[6'QuF/7$$\"1++voMrU^F3$!1bgfywIe%)F/7$$\"1nmm\"z_\"4iF3$!
1$o*3eN<5GF67$$\"1nmmm6m#G(F3$!1K7bA#*o<]F67$$\"1mmmT&phN)F3$!1p8-O3\"
)GtF67$$\"1++v=ddC%*F3$!1#G8>\"H1D'*F67$$\"1LLe*=)H\\5!#;$!1XJ'3!***G=
\"!#?7$$\"1++v=JN[6F_q$!1K#ek&pns8Fbq7$$\"1nm\"z/3uC\"F_q$!1p1(*eqoV:F
bq7$$\"1++DJ$RDX\"F_q$!1Y(Gwu([B=Fbq7$$\"1LLekGhe:F_q$!1&*RdCr[B>Fbq7$
$\"1nm\"zR'ok;F_q$!1&[a=3u3*>Fbq7$$\"1+++vIb<<F_q$!1xY]'*)o?,#Fbq7$$\"
1LL3_(>/x\"F_q$!1vn?a;+D?Fbq7$$\"1+]i!4`oz\"F_q$!1)G\"3`.QG?Fbq7$$\"1m
m;HkGB=F_q$!1aWv`7rH?Fbq7$$\"1L$3xw>(\\=F_q$!1r`@C`+H?Fbq7$$\"1++D1J:w
=F_q$!13nw6eFE?Fbq7$$\"1L3x\")H`I>F_q$!1&*=^@\\O9?Fbq7$$\"1n;HdG\"\\)>
F_q$!1[_26&>T*>Fbq7$$\"1+D\"Gt#HR?F_q$!1**\\wsltl>Fbq7$$\"1LLL3En$4#F_
q$!1)zUyAX%H>Fbq7$$\"1++Dc#o%*=#F_q$!1poj>>3Z=Fbq7$$\"1nm;/RE&G#F_q$!1
]U&G6-Eu\"Fbq7$$\"1+++D.&4]#F_q$!1\"RhGybhV\"Fbq7$$\"1+++]jB4EF_q$!1T&
HKpf4D\"Fbq7$$\"1+++vB_<FF_q$!1^by8$G\"\\5Fbq7$$\"1+++Dg(=#GF_q$!1zyN6
#H0U)F67$$\"1+++v'Hi#HF_q$!1\\hC#\\MvD'F67$$\"1L$eky#*4-$F_q$!1ZKT'H9$
RUF67$$\"1nm\"z*ev:JF_q$!1'e\"*pBSL>#F67$$\"1+]7.%Q%GKF_q$\"1#RE=0$)fW
#F/7$$\"1LLL347TLF_q$\"1%yL:-0Ml#F67$$\"1LL$3xxlV$F_q$\"1W+C$)>6XYF67$
$\"1LLLLY.KNF_q$\"1-%Gk>*\\qlF67$$\"1++D\"o7Tv$F_q$\"1'p)*QE-*o5Fbq7$$
\"1LLL$Q*o]RF_q$\"1kK32$HzP\"Fbq7$$\"1++D\"=lj;%F_q$\"1k7(=7c@k\"Fbq7$
$\"1++]iB0pUF_q$\"1<_0\"H:qt\"Fbq7$$\"1++vV&R<P%F_q$\"1g)e-rj0\"=Fbq7$
$\"1n;zWG))yWF_q$\"1Gt;\"=QQ'=Fbq7$$\"1LL$e9Ege%F_q$\"1X<L/'RE*=Fbq7$$
\"1M3FW;ANYF_q$\"1g]u?$)e(*=Fbq7$$\"1M$3F9<Wo%F_q$\"1'37wk<t*=Fbq7$$\"
1Le9TEhLZF_q$\"1n^qN^$=*=Fbq7$$\"1LLeR\"3Gy%F_q$\"1E(4sCg6)=Fbq7$$\"1+
](=7O*))[F_q$\"10cZ>AhS=Fbq7$$\"1nm;/T1&*\\F_q$\"1wSBQ#flx\"Fbq7$$\"1m
m\"zRQb@&F_q$\"1sB5\\.'=d\"Fbq7$$\"1***\\(=>Y2aF_q$\"1(f0t3%[@8Fbq7$$
\"1mm;zXu9cF_q$\"1?'RhwwP')*F67$$\"1LLe9i\"=s&F_q$\"1w(RU@!>8zF67$$\"1
+++]y))GeF_q$\"1jjfDh#4%eF67$$\"1***\\ibOO$fF_q$\"1VK!og^!=PF67$$\"1**
**\\i_QQgF_q$\"1j5:qmeB:F67$$\"1**\\(=-N(RhF_q$!17-Jad'\\X'F/7$$\"1***
\\7y%3TiF_q$!1Kp5ooEPGF67$$\"1**\\P4kh`jF_q$!1WC^HM&*p_F67$$\"1****\\P
![hY'F_q$!1r;W'eh8n(F67$$\"1mmT5FEnlF_q$!1lRSk'4lx*F67$$\"1LLL$Qx$omF_
q$!1Xp7I)G3=\"Fbq7$$\"1+++v.I%)oF_q$!1g=]\\k*)z:Fbq7$$\"1mm\"zpe*zqF_q
$!1$4rO9)\\')=Fbq7$$\"1+++D\\'QH(F_q$!1n8'33\\[9#Fbq7$$\"1n;zp%*\\%R(F
_q$!1$R+[L*GMAFbq7$$\"1KLe9S8&\\(F_q$!1FaB86I,BFbq7$$\"1++]i+tZvF_q$!1
GJL`J-FBFbq7$$\"1mmT5hK+wF_q$!1ir[TN=YBFbq7$$\"1LLLe@#Hl(F_q$!1TNS<.ne
BFbq7$$\"1***\\i?=bq(F_q$!1/;f6;RkBFbq7$$\"1L3xc/%pv(F_q$!1%)Gj%\\wLO#
Fbq7$$\"1m;H2FO3yF_q$!1$43'45ybBFbq7$$\"1*\\7y&\\yfyF_q$!1N:y'[!eTBFbq
7$$\"1LLL3s?6zF_q$!136kZAx?BFbq7$$\"1m;zpe()=!)F_q$!1-Y\"f!*>fD#Fbq7$$
\"1++DJXaE\")F_q$!1>E!eR[F;#Fbq7$$\"1nmmm*RRL)F_q$!1<^&>#*3x!>Fbq7$$\"
1nmTge)*R%)F_q$!1Y>x;#oAu\"Fbq7$$\"1mm;a<.Y&)F_q$!1aD')eYLc:Fbq7$$\"1+
]PM&*>^')F_q$!11k>u^$[N\"Fbq7$$\"1LLe9tOc()F_q$!1\\\"=YpU+9\"Fbq7$$\"1
m;H#e0I&))F_q$!1^%))o7#3Z$*F67$$\"1+++]Qk\\*)F_q$!1c+Oi[zdsF67$$\"1nmT
5ASg!*F_q$!1KLa\\4nw[F67$$\"1LL$3dg6<*F_q$!1M-/#3(z#e#F67$$\"1++voTAq#
*F_q$!1(G]c!R/\\nF/7$$\"1mmmmxGp$*F_q$\"1^MSbzOE5F67$$\"1L$eRA5\\Z*F_q
$\"1F>iO&ox_#F67$$\"1++D\"oK0e*F_q$\"1D\"\\E#eC3OF67$$\"1+]il(z5j*F_q$
\"1fzluShWRF67$$\"1+++]oi\"o*F_q$\"1-'e8C\\m9%F67$$\"1,v=#R+pq*F_q$\"1
eS*y(37$>%F67$$\"1+]PMR<K(*F_q$\"1<\\Ppa$4?%F67$$\"1+DcwuWd(*F_q$\"1z5
$G#)H$oTF67$$\"1++v=5s#y*F_q$\"1*\\)yfc]$4%F67$$\"1+]P40O\"*)*F_q$\"1Y
EMvd`YKF67$$\"\"\"F($\"1rmKX*f8V\"F6-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%
+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F(Fa]m%(DEFAULTG" 2 496 272 272 2 
0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 10061 10056 10074 
0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 157 -28248 0 0 0 0 0 0 }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 125 "Le polyn\364me L(4,x) est donc un
e approximation honorable (mais non la meilleure) de ln(1+x) sur [0,1]
. Voici ses coefficients:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 
"L(4,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,%\"xG$\"*iLy***!\"**$)F$
\"\"#\"\"\"$!*T&\\O\\F'*$)F$\"\"$F+$\"*:%REHF'*$)F$\"\"%F+$!*W:&z8F'*$
)F$\"\"&F+$\"*s0CB$!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "A comparer avec la somme partielle de la s\351rie enti\350re:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot(ln(1+x)-x+x^2/2-x^3/3+x^4/4-x^
5/5,x=0..1);" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7U7$\"\"!F(7$
$\"1nmm;arz@!#<$!1glaJ+ua<!#E7$$\"1LL$e9ui2%F,$!1Ot*zoezQ(!#D7$$\"1nmm
\"z_\"4iF,$!1np!)34to!*!#C7$$\"1mmmT&phN)F,$!1?Wm\"=+`H&!#B7$$\"1LLe*=
)H\\5!#;$!1a\\l6*y7/#!#A7$$\"1nm\"z/3uC\"FE$!1Dno;3utcFH7$$\"1++DJ$RDX
\"FE$!1'ox<.:CR\"!#@7$$\"1nm\"zR'ok;FE$!1\"3/cj\"*\\5$FS7$$\"1++D1J:w=
FE$!1orU>#GVE'FS7$$\"1LLL3En$4#FE$!1?20]!*y!>\"!#?7$$\"1nm;/RE&G#FE$!1
/X)zdKi)>F]o7$$\"1+++D.&4]#FE$!1!*e..JjgLF]o7$$\"1+++vB_<FFE$!1$eMPU\"
f[aF]o7$$\"1+++v'Hi#HFE$!1V[:j1/t$)F]o7$$\"1nm\"z*ev:JFE$!1-1w#H>Y?\"!
#>7$$\"1LLL347TLFE$!1Q$)\\/!oU!=Fgp7$$\"1LLLLY.KNFE$!1.`nKy&o[#Fgp7$$
\"1++D\"o7Tv$FE$!1)4fBnVU`$Fgp7$$\"1LLL$Q*o]RFE$!1.'[Ix=1u%Fgp7$$\"1++
D\"=lj;%FE$!1m2oRHMLkFgp7$$\"1++vV&R<P%FE$!18NsXOcx%)Fgp7$$\"1LL$e9Ege
%FE$!1X77.R%\\6\"!#=7$$\"1LLeR\"3Gy%FE$!1&o1'3+g<9F[s7$$\"1nm;/T1&*\\F
E$!1j(3.5*H;=F[s7$$\"1mm\"zRQb@&FE$!1^h#fUxJK#F[s7$$\"1***\\(=>Y2aFE$!
1_FNKSc`GF[s7$$\"1mm;zXu9cFE$!1x)oMA8O`$F[s7$$\"1+++]y))GeFE$!1GMND\"z
(pVF[s7$$\"1****\\i_QQgFE$!108'o;/xL&F[s7$$\"1***\\7y%3TiFE$!1l3%y$oDM
kF[s7$$\"1****\\P![hY'FE$!1R(4f@</'yF[s7$$\"1LLL$Qx$omFE$!1.P:T+^_$*F[
s7$$\"1+++v.I%)oFE$!1wA$z$eF>6F,7$$\"1mm\"zpe*zqFE$!1;l*owe0J\"F,7$$\"
1+++D\\'QH(FE$!1*)f8UyL\\:F,7$$\"1KLe9S8&\\(FE$!1^8nx+F0=F,7$$\"1***\\
i?=bq(FE$!1@ZcSEd3@F,7$$\"1LLL3s?6zFE$!1w<iw<*RW#F,7$$\"1++DJXaE\")FE$
!1QE:>BUSGF,7$$\"1nmmm*RRL)FE$!1`13([3-F$F,7$$\"1mm;a<.Y&)FE$!1;h3W#))
Hw$F,7$$\"1LLe9tOc()FE$!1.@%Rb(p4VF,7$$\"1+++]Qk\\*)FE$!1j%)zD8Qn[F,7$
$\"1LL$3dg6<*FE$!1tL8))eDxbF,7$$\"1mmmmxGp$*FE$!1VJ(*)fh8G'F,7$$\"1++D
\"oK0e*FE$!1N$3D!o#*4rF,7$$\"1+++]oi\"o*FE$!1^Y?$*3pOvF,7$$\"1++v=5s#y
*FE$!1$[ST!Q-%)zF,7$$\"1+]P40O\"*)*FE$!1^ywB6`)[)F,7$$\"\"\"F($!1/)QtF
:'=!*F,-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"%!G-%%VI
EWG6$;F(Fd[l%(DEFAULTG" 2 479 229 229 2 0 1 0 2 9 0 4 2 1.000000 
45.000000 45.000000 10030 10061 10056 10074 0 0 0 20530 0 12020 0 0 0 
0 0 0 0 1 1 0 0 0 0 7 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
13 "Rien \340 voir !" }}}}{MARK "0 0 0" 24 }{VIEWOPTS 1 1 0 1 1 1803 }