{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 
11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "
Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }
}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "f := expand((t-1)^5*(t+5));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fG,.*$)%\"tG\"\"'\"\"\"F**&\"#:F*)F(\"\"%F*!\"
\"*&\"#SF*)F(\"\"$F*F**&\"#XF*)F(\"\"#F*F/*&\"#CF*F(F*F*\"\"&F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g := diff(f,t);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"gG,,*&\"\"'\"\"\")%\"tG\"\"&F(F(*&\"#gF()F*
\"\"$F(!\"\"*&\"$?\"F()F*\"\"#F(F(*&\"#!*F(F*F(F0\"#CF(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(f,t=-6..3);" }}{PARA 13 "" 1 "
" {GLPLOT2D 490 253 253 {PLOTDATA 2 "6%-%'CURVESG6$7gn7$$!\"'\"\"!$\"&
2o\"F*7$$!3u**\\7.k&4&f!#<$\"3Nsa!3>iIa\"!#87$$!3[***\\i!G\">!fF0$\"3_
)=QcBwDT\"F37$$!3A**\\P4#pG&eF0$\"3A[^jma(*)G\"F37$$!3%)****\\7c#Q!eF0
$\"3IbC\\i-+s6F37$$!3,+vop/[=dF0$\"3&GFF362\\$)*!#97$$!3=+](oKNJj&F0$
\"3k.c#pT0+8)FH7$$!3&**\\7yybr`&F0$\"32yZtN=v7kFH7$$!3s***\\([i<TaF0$
\"3%3+-Bsa9*[FH7$$!3j*****\\\\gXM&F0$\"35')[Ne4?UNFH7$$!3W++DTZ%zC&F0$
\"3Yb_f/+qgBFH7$$!3G+DJ&=)y^^F0$\"3M&z;iC\\tL\"FH7$$!35+]PH;jb]F0$\"3y
F=&z=<-`%!#:7$$!3++](ovKt([F0$!3H:1mNag-')Ffo7$$!35+](=g9Fp%F0$!3jSP!y
:Er$=FH7$$!3U+](=C#y,XF0$!30=Yr(Q<:^#FH7$$!3&)**\\7BAi1WF0$!3>!Q\"RJ0L
TFFH7$$!3;+]P/AY6VF0$!3\\[$)))paq5HFH7$$!3j+vVG%yN@%F0$!3_m8#))**[#HIF
H7$$!3A++]_Yp:TF0$!3Ke+>PKJ)4$FH7$$!3r**\\Pp&y%HSF0$!37\\aCk[MBJFH7$$!
34++D'[iK%RF0$!3`zi)4VW\">JFH7$$!3u****\\2Z9\\PF0$!3kXkf/y#>-$FH7$$!3=
++]i)HUb$F0$!3Sl0:7l_KGFH7$$!3u****\\#H$RmLF0$!3I@ex\"pcFf#FH7$$!39+](
=p>e>$F0$!3Er@vbX>YBFH7$$!3'*****\\#=\"*H*HF0$!3#z-1icMs.#FH7$$!3'****
***H)o6#GF0$!3oisqrf-v<FH7$$!31+](oe)H@EF0$!3M`pg'Qj8[\"FH7$$!3E+++b&z
VW#F0$!3\\*eir6V*Q7FH7$$!3e**\\(oLr-D#F0$!3y6WJ6kUu**Ffo7$$!3c**\\i5WV
l?F0$!3X)HO$3[NVzFfo7$$!3G***\\(okds=F0$!3$3mkJ\\(3<hFfo7$$!3#***\\PuE
Z&p\"F0$!3ib(=-0:?q%Ffo7$$!3`++D1BW/:F0$!32$*Ga?t1WMFfo7$$!32+](=W:gI
\"F0$!3O^\"e&*))H)3CFfo7$$!3p**\\7tUGL6F0$!35\"GJXg&Q3<Ffo7$$!3a-+](y)
Hn%*!#=$!3DnfKQ;FL6Ffo7$$!3Q0++]$4+a(Fbw$!3!R&HNCT-\\q!#;7$$!3o-+]PE`a
cFbw$!3Oc]Gw:<pTFjw7$$!3T++vopBIQFbw$!3KyVyYq<OBFjw7$$!3a.+]iwm/=Fbw$!
3oK'3F\"\\x/6Fjw7$$\"3yn$*****\\kR:!#?$!3QAu*o/bJ'\\F07$$\"3-1++vLqe>F
bw$!3y\\=DbJ)pu\"F07$$\"3*e**\\7GG'>PFbw$!3]y)o.i'z[_Fbw7$$\"3:0++DVyW
cFbw$!3C%>NU%G7>()!#>7$$\"3)Q**\\781iX(Fbw$!3RwWD=5$*>hF]y7$$\"3u'**\\
i&Qm\\$*Fbw$!3Xx([KH5T!p!#B7$$\"31++](['3?6F0$\"3%zM+L<p$G:!#@7$$\"3e*
*\\7y+*QJ\"F0$\"3iI%3+\"4\"R#>F_z7$$\"3,,++qfa+:F0$\"3w\"H?0\"e`U?Fbw7
$$\"31++vy&G9p\"F0$\"3aq7Tv$Ru0\"F07$$\"3_+]7$eI2)=F0$\"3yDt1o$zik$F07
$$\"3a*****\\YzY0#F0$\"3G$p&zJe=1#*F07$$\"3Q***\\P^WSD#F0$\"3!\\j'>Db!
)\\AFjw7$$\"3*3+++**eBV#F0$\"37+;'=z96[%Fjw7$$\"3L**\\78%zCi#F0$\"3co:
#e@D-d)Fjw7$$\"3v**\\(o\"*[W!GF0$\"3As)=Oa=I\\\"Ffo7$$\"\"$F*$\"$c#F*-
%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fj^l-%+AXESLABELSG6$Q\"t6\"Q!F__l-%%VI
EWG6$;F(F_^l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
x[0] := 0.9:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "for k from
 0 to 9 do\n   x[k+1] := evalf( x[k] - subs(t=x[k],f)/subs(t=x[k],g)):
\n   print(x[k+1]):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+s-
o+#*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+[-+h$*!#5" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+'p%)*)[*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#$\"+Bo>\"f*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+vD#=n*!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+,NPQ(*!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+r6s&z*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+;o
DM)*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&o0&z)*!#5" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#$\"+&o0&z)*!#5" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Example:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "F := Vect
or([x^2-y^2+2*y,2*x+y^2-6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG
-%'RTABLEG6%\"*S[nY\"-%'MATRIXG6#7$7#,(*$)%\"xG\"\"#\"\"\"F3*$)%\"yGF2
F3!\"\"*&F2F3F6F3F37#,(*&F2F3F1F3F3F4F3\"\"'F7&%'VectorG6#%'columnG" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plots[implicitplot](\{F[1]
=0,F[2]=0\},x=-3..3,y=-3..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 490 260 
260 {PLOTDATA 2 "6%-%'CURVESG6cq7$7$$!3++++++++:!#<$!\"$\"\"!7$$!3#)=t
d_<Rm8F*$!3e!oAuC3O&HF*7$7$$!3<************>8F*$!3++++++]PHF*F.7$7$F5$
\"3++++++]PHF*7$$!3K0++++++:F*$\"3y,++++++IF*7$F47$$!3#=T!oAuC)=\"F*$!
3c(e>td_<*GF*7$7$$!3=************z5F*$!3_mmmmm;aGF*FC7$F:7$$!3\\K*[\">
`DC7F*$\"3([$*[\">`D/HF*7$7$FJ$\"3_mmmmm;aGF*FO7$7$FJ$!33mmmmm;aGF*7$$
!3T/Ny#4.,,\"F*$!3c%\\;s!p*)HGF*7$7$$!3#>************R)!#=$!3/LLLLL$3x
#F*Ffn7$FU7$$!39t%3oWdfc)F_o$\"3!)\\3oWdfwFF*7$7$F]o$\"3/LLLLL$3x#F*Fc
o7$F\\o7$$!3#4(f')Gwe>$)F_o$!3+-M6P7/oFF*7$7$$!3w!**********z3)F_o$!3!
)************fFF*F]p7$Fcp7$$!3gljitjitlF_o$!3aitjitj-FF*7$7$$!3+#*****
********fF_o$!3o!444444o#F*Fip7$7$F`q$\"3o!444444o#F*7$$!3/W+++++)3)F_
o$\"3c,+++++gFF*7$FhqFio7$F_q7$$!3!\\-nH.nH$[F_o$!3S'H.nH.nj#F*7$7$$!3
3#************f$F_o$!3U*************e#F*F_r7$Feq7$$!3gYEHo#Hos%F_o$\"3
km#Ho#HoKEF*7$7$Ffr$\"3')*************e#F*F[s7$Fer7$$!3?%o2Bp2B4$F_o$!
3qI#p2Bp2d#F*7$7$$!3o*)*********>v\"F_o$!3d************>DF*Fes7$F[t7$$
!3yhk<THNi8F_o$!3X_B)eqkP]#F*7$7$$!3=#************>\"F_o$!3))*********
**p\\#F*Fat7$7$Fht$\"3))***********p\\#F*7$$!33M+++++_<F_o$\"3N,+++++?
DF*7$F`u7$$!3_\"************f$F_o$\"3U*************e#F*7$7$Fht$!3W****
*******p\\#F*7$$\"3zDO#)eqk<L!#>$!3\\N#)eqk<LCF*7$7$$\"3s2++++++7F_o$!
3y***********pR#F*F_v7$F]u7$$!3=#\\Ur&G9d!)Fbv$\"35F9dG9d![#F*7$7$Fgv$
\"3y***********pR#F*F\\w7$Ffv7$$\"3z'=THN#)e-#F_o$!3?<THN#)eiBF*7$7$$
\"3i2++++++OF_o$!3q***********pH#F*Ffw7$Fbw7$$\"3ef9dG9d3LF_o$\"3$e&G9
dG94BF*7$7$F]x$\"3q***********pH#F*Fbx7$F\\x7$$\"3(*4+++++?PF_o$!3#)**
*********>H#F*7$7$$\"3W:+++++3SF_o$!3O************zAF*F\\y7$Fby7$$\"3g
nX;`-ip`F_o$!3DbkJD?'p@#F*7$7$$\"3a2++++++gF_o$!3Qxxxxxx(=#F*Fhy7$7$F_
z$\"3#yxxxxxx=#F*7$$\"3.w*********z+%F_o$\"39,+++++!G#F*7$FgzFhx7$7$F_
z$!3#yxxxxxx=#F*7$$\"3&>\\yAeE,,(F_o$!3qZyAeE,T@F*7$7$$\"3Y2++++++%)F_
o$!3mmmmmmmw?F*Fa[l7$Fdz7$$\"3dv.Jz8C<xF_o$\"3ck*o?'eF3@F*7$7$Fh[l$\"3
mmmmmmmw?F*F]\\l7$7$Fh[l$!3Ammmmmmw?F*7$$\"3I;CR6Hj]')F_o$!39S#R6Hj]1#
F*7$7$$\"3#z,++++?>*F_o$!3:************R?F*Fj\\l7$F`]l7$$\"36;$\\o]J\\
-\"F*$!3_9$\\o]J\\)>F*7$7$$\"3u++++++!3\"F*$!3Q*********\\i&>F*Ff]l7$7
$F]^l$\"3g*********\\i&>F*7$$\"3S#)*********>>*F_o$\"3#4++++++/#F*7$Fe
^l7$Fh[l$\"3Ammmmmmw?F*7$F\\^l7$$\"3S)RFgsRF=\"F*$!3$oRFgsRF!>F*7$7$$
\"3t++++++?8F*$!3Q*********\\7$=F*F__l7$7$F]^l$\"3Q*********\\i&>F*7$$
\"3]bcp3Eya7F*$\"3;YVI\"R<_'=F*7$7$Ff_l$\"3g*********\\7$=F*F^`l7$Fe_l
7$$\"3[![0_%zaS8F*$!3pya?Xza?=F*7$7$$\"3A,+++++!Q\"F*$!3;*************
z\"F*Fh`l7$F^al7$$\"3CBb*3#e$G\\\"F*$!3\">_&*3#e$Gt\"F*7$7$$\"3s++++++
g:F*$!3QUr&G9dGp\"F*Fdal7$7$F[bl$\"3QUr&G9dGp\"F*7$$\"3c)***********z8
F*$\"3q+++++++=F*7$Fcbl7$Ff_l$\"3Q*********\\7$=F*7$7$$\"3%4++++++c\"F
*$!3gUr&G9dGp\"F*7$$\"3F`&*3#e$GV;F*$!3]^&*3#e$GV;F*7$7$$\"3C,++++?$y
\"F*$!3%*)***********f:F*Fbcl7$7$Ficl$!3;************f:F*7$$\"3ih$)4aZ
6$z\"F*$!33g$)4aZ6`:F*7$7$Ffbl$!3!HLLLLL$[:F*Fadl7$7$$\"3[+++++++=F*$
\"3!HLLLLL$[:F*7$$\"3+**********>$y\"F*F[bl7$F`elF`bl7$7$$\"3#4++++++!
=F*Fhdl7$$\"3fc1O)4aZ$>F*$!31b1O)4aZX\"F*7$7$Fh^l$!3#fmmmmm;Q\"F*Fhel7
$7$FfblF^el7$$\"3!G#=====Q=F*$\"3Ty\"=====_\"F*7$7$Fh^l$\"3;mmmmmm\"Q
\"F*Fcfl7$F^fl7$$\"3c^HiUMRw?F*$!3-]HiUMRc8F*7$7$$\"3#4+++++)G@F*F5F]g
l7$7$Fdgl$!3&*)***********>8F*7$$\"3RGFFFFF6AF*$!3?EFFFFF^7F*7$7$Fjz$!
3/***********R>\"F*Fjgl7$7$Fjz$\"3/***********R>\"F*7$$\"39**********z
G@F*Ff_l7$FghlFifl7$F`hl7$$\"3D>=====UBF*$!33<=====U6F*7$7$$\"3s+++++!
oT#F*FJF\\il7$Fbil7$$\"3;6bxQpMnCF*$!3)*3bxQpMF5F*7$7$Fcu$!3)e)*******
**\\s*F_oFfil7$7$Fcu$\"3)e)*********\\s*F_o7$$\"3R**********z;CF*F]^l7
$FcjlFdhl7$F\\jl7$$\"3[uO=fz*[e#F*$!3IBn$=fz*[!*F_o7$7$$\"3m+++++?ZEF*
F]oFhjl7$F^[m7$$\"3cj6l/'=Wp#F*$!389;^Yg=WxF_o7$7$F[r$!314LLLLLLoF_oFb
[m7$7$F[r$\"3G6LLLLLLoF_o7$$\"3M**********>ZEF*Fh[l7$F_\\mF`jl7$Fh[m7$
$\"3IL-$4s$)[z#F*$!3W5BI4s$)[jF_o7$7$$\"3G++++++?GF*F`qFd\\m7$Fj\\m7$$
\"3'*y$y$y$y$yGF*$!37nPy$y$y$y%F_o7$7$$\"3Z+++++?NHF*FfrF^]m7$Fd]m7$$
\"3UrQ[N>uZHF*$!3A!pQ[N>u2$F_o7$7$$\"3!***********z#*HF*FhtFh]m7$F^^m7
$F_^m$!3ht*********z7\"F_o7$7$F_^m$\"3e2++++++7F_oFb^m7$7$F_^mFgv7$$\"
3#GZ*y:j_!*HF*$\"3q&H0@%ot%H\"F_o7$7$$\"3f**********>NHF*F]xF[_m7$Fa_m
7$$\"3)Hh%Q:YQvGF*$\"3c&*Q:YQ:Y[F_o7$7$$\"3S************>GF*F_zFe_m7$F
[`mF\\\\m-%'COLOURG6&%$RGBG\"\"\"F-F--F$6fq7$7$F+$!39++++++g@F*7$$!3)o
NYIa=s$HF*$!3FUO&pX\"y-@F*7$7$$!3GKLLLLLoGF*Fc]lFj`m7$F`am7$$!3Fv#[M5$
z8GF*$!3oB<b'*o?')>F*7$7$Ffp$!3b1:$\\o]J$>F*Fdam7$Fjam7$$!3kUgWU>2!p#F
*$!3IcRbd!G*p=F*7$7$$!3!>FFFFFFh#F*FaalF^bm7$Fdbm7$$!3_%)RfP],mDF*$!3U
9gSi\\)Rv\"F*7$7$F^t$!3G5zT;nl3<F*Fhbm7$7$F^t$!3%)4zT;nl3<F*7$$!3i0'\\
J![dTCF*$!37$R]o>D%Q;F*7$7$$!3?***********RN#F*F_dlFecm7$F[dm7$$!36Kg(
[@%p;BF*$!3>mR7&y0L_\"F*7$7$Fey$!3!z4aZ68s[\"F*F_dm7$7$Fey$!3o(4aZ68s[
\"F*7$$!3G'3EyM/8>#F*$!3C7R<_cp39F*7$7$$!3C566666\"4#F*F5F\\em7$Fbem7$
$!3%*Hu\"45@`1#F*$!3%zc#3**)yYH\"F*7$7$Fc]l$!33\"=====)p7F*Ffem7$7$Fc]
l$!3%3=====)p7F*7$$!37G!*pw2kQ>F*$!3?q4IB#f8=\"F*7$7$$!37**********\\A
=F*FJFcfm7$Fifm7$$!3xb&=1-M6\"=F*$!3MU9Qzf')o5F*7$7$Faal$!3woMn$=fz0\"
F*F]gm7$7$$!3Q*************z\"F*Fdgm7$$!3ihtjitj#o\"F*$!3#\\OEOPEOd*F_
o7$7$F_dl$!37I=fz*[C_)F_oFjgm7$7$F_dl$\"3;fw7-<O\\GF*7$$!3(3Vr&G9dG<F*
F@7$F`hm7$$!3Q(eqk<THb\"F*$!3w4THN#)eq%)F_o7$7$$!3MKLLLLLV:F*F]oF[im7$
7$$!36KLLLLLV:F*F]o7$$!3SL()*=:s<U\"F*$!3s]E,\"[yAQ(F_o7$7$F5$!3>G&R\"
eDBIlF_oFhim7$7$Fhgl$\"3)*pJ2<tq^EF*7$$!38NLLLLLV9F*F[r7$7$$!3\"\\LLLL
LLW\"F*F[rFdhm7$F^jm7$$!3IqwGBrw)G\"F*$!3%3GBrwGBJ'F_o7$7$$!3*))******
****RC\"F*F`qF][n7$Fc[n7$$!3u%*3#e$GV`6F*$!3kP5zT;nl_F_o7$7$FJ$!3?k-Fq
-FqYF_oFg[n7$7$FJ$\"3)zUr&G9doCF*7$$!3o,+++++S6F*Fcu7$Fd\\n7$F5Fcjm7$F
]\\n7$$!3&R68s'>3:5F*$!3eX)oyK!=\\UF_o7$7$$!39))**********\\\"*F_oFfrF
j\\n7$7$$!3E*)**********\\\"*F_oFfr7$$!3(zrssssss)F_o$!3gmssssssKF_o7$
7$F]o$!3Zs'4(Q[N>IF_oFg]n7$Fa\\n7$$!3=2jjjjjj\"*F_o$\"3)GjjjjjjN#F*7$7
$F]o$\"3$)***********RI#F*Fa^n7$F]^n7$$!3#RsO=fz*[sF_o$!3kfK;3/-^BF_o7
$7$F`q$!3%*)*Gh^k!ei\"F_oF[_n7$7$F`q$\"3q************f@F*7$$!36^LLLLLL
zF_oFjz7$7$$!3+]LLLLLLzF_oFjzFg^n7$Fa_n7$$!3kUR\"eDBIp&F_o$!3bTg=Wn(p]
\"F_o7$7$$!39#)************[F_oFhtF``n7$Ff`n7$$!3'*4;i@;i@SF_o$!3QSPy$
y$y$y(Fbv7$7$Ffr$!3kx**********fdFbvFj`n7$Fe_n7$$!3?g0Zw6%H&RF_o$\"3%y
0Zw6%Hv?F*7$7$Ffr$\"3k8C<b'*og?F*Fdan7$7$Fgu$!3cv**********fdFbv7$$!3'
y&Q[N>un@F_o$!3yj7;X1eABFbv7$7$Fht$\"31u')o%osmK)!#MFabn7$7$$!3/#*****
*******>\"F_o$\"3Ql&p3EyM+#F*7$$!3sO++++++EF_oFh^l7$FacnFjan7$Fgbn7$$
\"3;>_ZMAJa:!#K$F-F-7$7$Fgv$!3RGs!R!R*)QpFjbnFfcn7$7$FhtF_cn7$$!3Ooj&p
3EyM)FbvF_cn7$7$FgvF_cnFadn7$7$Fgv$!3t>,Zl9X9(*Fjbn7$$\"3et5Uot%*yFF_o
$!3[$e5Uot%*y$Fbv7$7$F]x$!3QI+++++gdFbvFjdn7$Fedn7$$\"3'o!QTs^l*[\"F_o
$\"32@'eF[M5,#F*7$7$$\"3;J++++++EF_oFh^lFden7$7$$\"3iI++++++EF_oFh^l7$
$\"3:R9dG9dGMF_o$\"3#y&G9dG9d?F*7$7$F]x$\"359C<b'*og?F*Fafn7$7$F_z$!3r
1Hh^k!ei\"F_o7$$\"3/\")************[F_oFht7$F^gnF`en7$7$$\"332++++++OF
_oFhfn7$$\"3=L^>7&>7:&F_o$\"3O)[!y[!y[7#F*7$7$F_z$\"39++++++g@F*Ffgn7$
7$F_z$!3W1Hh^k!ei\"F_o7$$\"3>_YQ:YQ:qF_o$!3FOYQ:YQ:AF_o7$7$Fh[l$!3Z#o4
(Q[N>IF_oFchn7$F\\hn7$$\"3B/\\\">`D/u'F_o$\"3p6&3oWdf?#F*7$7$$\"3*)[LL
LLLLzF_oFjzF]in7$Fcin7$$\"3?vA'RV4:C)F_o$\"39uPgc!\\eH#F*7$7$Fh[l$\"3r
++++++/BF*Fgin7$7$F]^l$!3Iv-Fq-FqYF_o7$$\"3E*)**********\\\"*F_oFfr7$F
djnFihn7$7$Fh[l$\"3;,+++++/BF*7$$\"3_,M?KfN\"o*F_o$\"3]h'znSk=R#F*7$7$
F]^l$\"3')G9dG9doCF*F\\[o7$7$Ff_l$!3SS&R\"eDBIlF_o7$$\"3*))**********R
C\"F*F`q7$Fi[o7$F]^l$!3'eFq-Fq-n%F_o7$7$F]^l$\"3KH9dG9doCF*7$$\"3k3Bp2
Bp26F*$\"3m$p2Bp2B\\#F*7$7$$\"3Y,+++++S6F*FcuFd\\o7$Fj\\o7$$\"3EK=(>mV
RC\"F*$\"3#)p\"G!Qj0'f#F*7$7$Ff_l$\"3KrJ2<tq^EF*F^]o7$7$F[bl$!3LU=fz*[
C_)F_o7$$\"3MKLLLLLV:F*F]o7$F[^oFf[o7$Fd]o7$$\"3#*QBmPBmx8F*$\"3PjwLiw
L-FF*7$7$$\"38NLLLLLV9F*F[rF`^o7$Ff^o7$$\"3%pWh.f(R4:F*$\"3Mb&Q'4Cg5GF
*7$7$F[bl$\"3/gw7-<O\\GF*Fj^o7$Fh]o7$$\"3c'H9dG9dk\"F*$!3;[H9dG9d#*F_o
7$7$Ffbl$!33qMn$=fz0\"F*Fd_o7$F`_o7$$\"3;axzh0bR;F*$\"3M[A?Q%\\/#HF*7$
7$$\"3(3Vr&G9dG<F*F@F^`o7$7$Fh^l$!3i#=====)p7F*7$$\"3M**********\\A=F*
FJ7$F[aoFj_o7$7$Fjz$!3C*4aZ68s[\"F*7$$\"3C566666\"4#F*F57$FcaoFh`o7$7$
Fcu$!3h6zT;nl3<F*7$$\"3?***********RN#F*F_dl7$F[boF`ao7$7$F[r$!3K3:$\\
o]J$>F*7$$\"3!>FFFFFFh#F*$!3#*)************z\"F*7$FcboFhao7$7$F@$!3#>+
+++++;#F*7$$\"3GKLLLLLoGF*Fc]l7$F]coF`boF_`m-%+AXESLABELSG6$%\"xG%\"yG
" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "C
urve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "z[0] := Vector([
2,-2]): # initial guess" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
J := Matrix(2,2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J[1,1]
 := diff(F[1],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6$\"\"\"F'
,$*&\"\"#F'%\"xGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J[1
,2] := diff(F[1],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6$\"\"
\"\"\"#,&*&F(F'%\"yGF'!\"\"F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 23 "J[2,1] := diff(F[2],x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%
\"JG6$\"\"#\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "J[2,
2] := diff(F[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"JG6$\"\"#F
',$*&F'\"\"\"%\"yGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 221 "
for k from 0 to 9 do\n   A := evalf(subs(\{x=z[k][1],y=z[k][2]\},J)):
\n   b := - evalf(subs(\{x=z[k][1],y=z[k][2]\},F)):\n   u[k] := Linear
Algebra[LinearSolve](A,b):\n   z[k+1] := z[k]+u[k]:\n   print(z[k+1][1
],z[k+1][2]):\nend do:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$$\"3zUr&G9dG9#!#<$!3gG9dG9dG9F%" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6$$\"3*emg&G?Y5@!#<$!3:Xkq$HipL\"F%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$$\"3M:0>3E^4@!#<$!3ZKbp!)Q`M8F%" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$$\"3*H$)3&>>^4@!#<$!3yd6t(=KXL\"F%" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$$\"3MxQw=>^4@!#<$!3S4Z\"z=KXL\"F%" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$$\"3/:,7>>^4@!#<$!3MMC-)=KXL\"F%" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6$$\"3v_jZ>>^4@!#<$!3Gf,8)=KXL\"F%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$$\"3X!fK)>>^4@!#<$!3A%)yB)=KXL\"F%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$$\"3![j(3>>^4@!#<$!3%eV@%)=KXL\"F%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$$\"3^sQW>>^4@!#<$!3yg\"H&)=KXL\"F%" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "An experiment \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x, y, z := 'x','y','z':" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "F := Vector([2*x-3*y+z-4,2*x
+y-z+4, x^2+y^2+z^2-4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'R
TABLEG6%\"*sPNZ\"-%'MATRIXG6#7%7#,**&\"\"#\"\"\"%\"xGF1F1*&\"\"$F1%\"y
GF1!\"\"%\"zGF1\"\"%F67#,**&F0F1F2F1F1F5F1F7F6F8F17#,**$)F2F0F1F1*$)F5
F0F1F1*$)F7F0F1F1F8F6&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 86 "plots[implicitplot3d](\{F[1]=0,F[2]=0,F[3]=0\},x=-2
..2,y=-2..2,z=-2..2,grid=[30,30,30]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "J := VectorCalculus[Jac
obian](F,[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'RTABLEG
6%\"*;Q[Y\"-%'MATRIXG6#7%7%\"\"#!\"$\"\"\"7%F.F0!\"\"7%,$*&F.F0%\"xGF0
F0,$*&F.F0%\"yGF0F0,$*&F.F0%\"zGF0F0%'MatrixG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "v := 'v':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 32 "v[0] := Vector([-0.5,-1.5,1.5]):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 253 "for k from 0 to 9 do\n   A := evalf(subs(\{x=v[k][1]
,y=v[k][2], z=v[k][3]\},J)):\n   b := - evalf(subs(\{x=v[k][1],y=v[k][
2], z=v[k][3]\},F)):\n   u[k] := LinearAlgebra[LinearSolve](A,b):\n   \+
v[k+1] := v[k]+u[k]:\n   print(v[k+1][1],v[k+1][2],v[k+1][3]):\nend do
:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!37*************\\'!#=$!3/++++++
+8!#<$\"37+++++++9F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!35N*[\">`Dam
!#=$!3C(yHQ1^3L\"!#<$\"3uD/MsyHQ8F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
%$!3UiL)e$oemm!#=$!3qsm<ntJL8!#<$\"3![lYcElLL\"F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%$!3o$*=>kmmmm!#=$!3'*y$QGLLLL\"!#<$\"33UKKMLLL8F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%$!3!R*=pmmmmm!#=$!3+z$QLLLLL\"!#<$\"3+
UKKLLLL8F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!3!4ce3nmmm'!#=$!3S7<<M
LLL8!#<$\"3FvllKLLL8F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!35%*=>pmmm
m!#=$!3/z$QQLLLL\"!#<$\"3\">CBBLLLL\"F(" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%$!3!R*=pmmmmm!#=$!3+z$QLLLLL\"!#<$\"3+UKKLLLL8F(" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6%$!3!4ce3nmmm'!#=$!3S7<<MLLL8!#<$\"3FvllKLLL8F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%$!35%*=>pmmmm!#=$!3/z$QQLLLL\"!#<$\"3
\">CBBLLLL\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "24 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 
2 33 1 1 }{RTABLE_HANDLES 146674840 147353772 146483816 }{RTABLE 
M7R0
I6RTABLE_SAVE/146674840X*%)anythingG6"6"[gl!#%!!!"#"#,(*$%"xG""#"""*$%"yGF*!""F
-F*,(F)F*F,F+!"'F+F&
}
{RTABLE 
M7R0
I6RTABLE_SAVE/147353772X*%)anythingG6"6"[gl!#%!!!"$"$,*%"xG""#%"yG!"$%"zG"""!"%
F-,*F(F)F*F-F,!""""%F-,**$F(F)F-*$F*F)F-*$F,F)F-F.F-F&
}
{RTABLE 
M7R0
I6RTABLE_SAVE/146483816X,%)anythingG6"6"[gl!"%!!!#*"$"$""#F',$%"xGF'!"$""",$%"y
GF'F+!"",$%"zGF'F&
}