{VERSION 2 3 "IBM INTEL NT" "2.3" }
{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 "Heading 1" 0 3 1 
{CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 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 "" 11 
12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "for n to 5 do expand
(cos(n*x)) od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#-%$cosG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&
*$-%$cosG6#%\"xG\"\"#F)!\"\"\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,&*$-%$cosG6#%\"xG\"\"$\"\"%F%!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,(*$-%$cosG6#%\"xG\"\"%\"\")*$F%\"\"#!\")\"\"\"F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$-%$cosG6#%\"xG\"\"&\"#;*$F%\"\"$!#?F%F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "t:=proc(n,x) if n=0 then 1 elif n=1
 then x else 2*x*t(n-1,x)-t(n-2,x) fi;end;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&-%$cosG6#*&%\"xG\"\"\"%\"nGF*F*-F&6#F)F*F**&-%$sinG
F'F*-F0F-F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tG:6$%\"nG%\"x
G6\"F)F)@'/9$\"\"!\"\"\"/F,F.9%,&*&F0F.-F$6$,&F,F.!\"\"F.F0F.\"\"#-F$6
$,&F,F.!\"#F.F0F6F)F)" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t(3,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&%\"xG\"\"\",&*$F%\"\"#F)!\"\"F&F&F)F%F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t(7,x);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,**&%\"xG\"\"\",**&F%F&,(*&F%F&,(*&F%F&,&*&F%F&,&*$F%\"
\"#F1!\"\"F&F&F1F%F2F&F1F0!\"#F&F&F&F1F.F3F%F&F&F1F,F3F0F1F2F&F&F1F*F3
F.F1F%F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$%\"xG\"\"(\"#k*$F%\"\"&!$7\"*$F%
\"\"$\"#cF%!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(ort
hopoly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(%\"GG%\"HG%\"LG%\"PG%\"T
G%\"UG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "T(7,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,**$%\"xG\"\"(\"#k*$F%\"\"&!$7\"*$F%\"\"$\"#cF%!\"(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 10 "?orthopoly" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "plot(\{T(n,x)$n=1..6\}, x=-1..1);" }}{PARA 13 "" 1 "
" {INLPLOT "6*-%'CURVESG6$7S7$$!\"\"\"\"!F(7$$!1nmm;p0k&*!#;F,7$$!1LL$
3<XZ=*F.F07$$!1nmmT%p\"e()F.F37$$!1mmm\"4m(G$)F.F67$$!1ML$3i.9!zF.F97$
$!1nm;/R=0vF.F<7$$!1++]P8#\\4(F.F?7$$!1nm;/siqmF.FB7$$!1++](y$pZiF.FE7
$$!1LLL$yaE\"eF.FH7$$!1nmm\">s%HaF.FK7$$!1+++]$*4)*\\F.FN7$$!1+++]_&\\
c%F.FQ7$$!1+++]1aZTF.FT7$$!1nm;/#)[oPF.FW7$$!1MLL$=exJ$F.FZ7$$!1MLLL2$
f$HF.Fgn7$$!1++]PYx\"\\#F.Fjn7$$!1MLLL7i)4#F.F]o7$$!1++]P'psm\"F.F`o7$
$!1++]74_c7F.Fco7$$!1JLL$3x%z#)!#<Ffo7$$!1MLL3s$QM%FhoFjo7$$!1^omm;zr)
*!#>F]p7$$\"1<LLezw5VFhoFap7$$\"1!****\\PQ#\\\")FhoFdp7$$\"1KLLe\"*[H7
F.Fgp7$$\"1*******pvxl\"F.Fjp7$$\"1)****\\_qn2#F.F]q7$$\"1)***\\i&p@[#
F.F`q7$$\"1)****\\2'HKHF.Fcq7$$\"1lmmmZvOLF.Ffq7$$\"1+++]2goPF.Fiq7$$
\"1KL$eR<*fTF.F\\r7$$\"1+++])Hxe%F.F_r7$$\"1lm;H!o-*\\F.Fbr7$$\"1****
\\7k.6aF.Fer7$$\"1mmm;WTAeF.Fhr7$$\"1****\\i!*3`iF.F[s7$$\"1MLLL*zym'F
.F^s7$$\"1LLL3N1#4(F.Fas7$$\"1mm;HYt7vF.Fds7$$\"1*******p(G**yF.Fgs7$$
\"1mmmT6KU$)F.Fjs7$$\"1LLLLbdQ()F.F]t7$$\"1++]i`1h\"*F.F`t7$$\"1++]P?W
l&*F.Fct7$$\"\"\"F*Fft-%'COLOURG6&%$RGBG$\"#5F)F*F*-F$6$7aoF'7$$!1MLLe
%G?y*F.$!1M^c*yb[4)F.7$F,$!10OB?RD,jF.7$$!1++vV5Su$*F.$!1\\VjIXYH[F.7$
F0$!1/bD35gQMF.7$$!1***\\iId9(*)F.$!1BK1G?2p>F.7$F3$!1&ov))=N\\(fFho7$
$!1mmmmxYV&)F.$\"1p.D@C2moFho7$F6$\"1'[)=='*=w=F.7$$!1++Dc[3:\")F.$\"1
z6\")frioHF.7$F9$\"1=3a(*p8sRF.7$$!1,+]iPH.xF.$\"1r%y-!o6D[F.7$F<$\"1z
lAoh`0cF.7$F?$\"1C#eu)Q-**pF.7$FB$\"1s1\"GM%*)Q\")F.7$FE$\"18B7XFE))*)
F.7$FH$\"1V?nzzG#e*F.7$$!1++]([j5i&F.$\"1p-&f#e)*e(*F.7$FK$\"1(Q$f)fjh
))*F.7$$!1LL$3x&y8_F.$\"1?g()[l=s**F.7$FN$\"0R#zKy******!#:7$$!1++++t_
\"y%F.$\"1aP\\=*y<(**F.7$FQ$\"1]7aq^t*))*F.7$$!1+++]zCcVF.$\"1P!GHC@?w
*F.7$FT$\"1,c8xmw)e*F.7$FW$\"12f-*pOZ;*F.7$FZ$\"1s#)>_IY#\\)F.7$Fgn$\"
1\"e2Vx>bz(F.7$Fjn$\"1A&e'fEZcoF.7$F]o$\"1oMPkG:EfF.7$F`o$\"1-NJkEU;[F
.7$Fco$\"12*ppn3-p$F.7$Ffo$\"18zo%)39hCF.7$Fjo$\"1S[`@E()*H\"F.7$F]p$
\"1+g)=lL:'H!#=7$Fap$!1eWnbh-!H\"F.7$Fdp$!1\"4<w%Q7BCF.7$Fgp$!1]1x)\\D
Th$F.7$Fjp$!1*pD')y*3\"z%F.7$F]q$!1y'=K8H?(eF.7$F`q$!1#)Q-ljyMoF.7$Fcq
$!1EC)>qq$)y(F.7$Ffq$!1/HKBi@C&)F.7$Fiq$!1oVRKD)[;*F.7$F\\r$!1cP&e)=F+
'*F.7$$\"1mm\"HiBQP%F.$!1,.SeFcu(*F.7$F_r$!1\\8a\")G#3!**F.7$$\"1KLeR*
)**)y%F.$!1\\rS%*Gmt**F.7$Fbr$!12`65K%*****F.7$$\"1KL$3A_1?&F.$!1%G%)3
2?b(**F.7$Fer$!1wP:T;&e*)*F.7$$\"1KLe9as;cF.$!1b.]\"*pSi(*F.7$Fhr$!1\"
eExgI>d*F.7$F[s$!1L=7\\]:z*)F.7$F^s$!1`$3\\,;`9)F.7$Fas$!1V`p/jq2qF.7$
Fds$!1*f:V5*4xbF.7$$\"1LLek6,1xF.$!11hPj=\"R\"[F.7$Fgs$!1uk=wrj\")RF.7
$$\"1LL$3U/37)F.$!1!o_8$[bSHF.7$Fjs$!1\"yLV1OQ!=F.7$$\"1++]P$[/a)F.$!1
`7f**[')RqFho7$F]t$\"1,S;s4BjZFho7$$\"1nm\"zW?)\\*)F.$\"1tPQ#y2b#=F.7$
F`t$\"1`4r&yV0F$F.7$$\"1++++PDj$*F.$\"1g&o[n\"\\XZF.7$Fct$\"1Ae(pf/BJ'
F.7$$\"1++v=5s#y*F.$\"1+.gW5t+\")F.Fet-Fit6&F[uF*F\\uF*-F$6$7hrF'7$$!1
MLe9r]X**F.$!1Ga^tn9n')F.7$$!1nm;HU,\"*)*F.$!1G!4JkLBR(F.7$$!1++vV8_O)
*F.$!1eDnSmAuhF.7$Fbu$!1n$>Pa3:,&F.7$$!1nm\"HdNvs*F.$!1fq7$yyG!RF.7$$!
1++](oUIn*F.$!1#o!)3N`q%GF.7$$!1ML3-)\\&='*F.$!1R^\"yqkF%=F.7$F,$!1IDe
8ph()))Fho7$$!1L$3-)*G#p%*F.$\"1$)QO/q`^lFho7$Fju$\"1J$yOF8p0#F.7$$!1n
;H2Jdz#*F.$\"1,$>U%3wALF.7$F0$\"1C#o`o%zeWF.7$$!1m;aQ75y!*F.$\"10Na-Aq
)e&F.7$Fbv$\"10/z5(4-d'F.7$$!1L$eRP8['))F.$\"1\"3')=FX8T(F.7$F3$\"1@6(
3:9*>\")F.7$Fjv$\"1Pt<(*[*[<*F.7$F6$\"1Z]zuNJ#y*F.7$$!1+D\"GyX`F)F.$\"
1hvO'G\"[q)*F.7$$!1M$eRZD>A)F.$\"1QDLU`BN**F.7$$!1nT5l^]o\")F.$\"1Hubw
&)Qx**F.7$Fbw$\"1aJ2n4u(***F.7$$!1LeRZXmh!)F.$\"1pAg>(zq***F.7$$!1m;aQ
UC3!)F.$\"1Sr3^$zh(**F.7$$!1+voHR#[&zF.$\"1X#=Kx,e$**F.7$F9$\"1%QifP'p
w)*F.7$Fjw$\"1t;D<#*41&*F.7$F<$\"16Z24\"4S#*)F.7$$!1LL$3i_+I(F.$\"1Xi'
*H%yW8)F.7$F?$\"1[u!RgA&*=(F.7$$!1ML$3FuF)oF.$\"1#>T,r%R$3'F.7$FB$\"1W
&)\\,3=z[F.7$$!1ML$e\\g\"fkF.$\"1,tE#)Ho6OF.7$FE$\"17dwEj'\\I#F.7$$!1n
mT&Gu,.'F.$\"1m&37()ocY*Fho7$FH$!1\"3'3Qin;SFho7$F^y$!1$[Kd/tHc\"F.7$F
K$!1Mg#3z>ao#F.7$Ffy$!1F\\D[_S()QF.7$FN$!1\"*o:O'*\\4]F.7$F_z$!1rp$f&z
jUgF.7$FQ$!1#Q#*)e+!4(pF.7$Fgz$!1qE&>)*zwv(F.7$FT$!1*R)y)G=@V)F.7$FW$!
1.bTQO'[N*F.7$$!1++v$>BJa$F.$!1_#pn<]Jr*F.7$FZ$!1]Adh)Hz#**F.7$$!1ML$3
K,BA$F.$!1l*HUNrd(**F.7$$!1MLLeW%o7$F.$!1Go#R%*Q\")***F.7$$!1ML$ef(QJI
F.$!1wvg(oM_***F.7$Fgn$!1#e%)))[5t'**F.7$$!1nmT&o_Qr#F.$!1rB+TJH2)*F.7
$Fjn$!1<**4cLJ=&*F.7$$!1nmTNz>&H#F.$!1abvX0rf\"*F.7$F]o$!1\\_*3P$o4()F
.7$F`o$!11xhD..IuF.7$Fco$!1xQppd%3*eF.7$Ffo$!1$e\"=L)\\o-%F.7$$!1LL$e9
d;J'Fho$!18%Q+K,d5$F.7$Fjo$!1fRNW1bb@F.7$$!1,+]ivF@AFho$!1Gs!plZ%36F.7
$F]p$!1[\"yFfwe$\\F\\]l7$$\"1CL$3-Dg5#Fho$\"16GJ&)\\9^5F.7$Fap$\"1/mPP
mQR@F.7$$\"1`mmmJ+IiFho$\"1m)H')z!zmIF.7$Fdp$\"1(*3S7f&p'RF.7$Fgp$\"1%
p%R`5B!y&F.7$Fjp$\"1wA1u]s(R(F.7$F]q$\"1=dKc4Da')F.7$$\"1)**\\P/q%zAF.
$\"1U=e*4**p7*F.7$F`q$\"1y8n/J*H]*F.7$$\"1)**\\(=GB2FF.$\"1Dm40q^+)*F.
7$Fcq$\"1\"eJ+kcd'**F.7$$\"1lm\"zu5M.$F.$\"1a*)[Qnb&***F.7$$\"1KL$3UDX
8$F.$\"1?qQ%3xs***F.7$$\"1***\\P4ScB$F.$\"1Lvgq7iq**F.7$Ffq$\"1x-\\,eN
:**F.7$$\"1KLLexn_NF.$\"1]GQuF(3q*F.7$Fiq$\"1C*[h%*[YN*F.7$F\\r$\"1'*
\\@&o^`R)F.7$F_r$\"1Ei\"p71&yoF.7$$\"1LLeR*)**)y%F.$\"1**3DdOo3gF.7$Fb
r$\"12O#*e\\c[]F.7$F\\`l$\"1(*)[eke\"eRF.7$Fer$\"10?I^l\"4z#F.7$Fd`l$
\"1XxtCk'))e\"F.7$Fhr$\"1eQ(QlPrT$Fho7$$\"1KLeR<vPgF.$!1@sV7u`Q**Fho7$
F[s$!1u`NT2eQBF.7$$\"1mm\"z\\%[gkF.$!14ICN&o(>OF.7$F^s$!1\"4&GA33j[F.7
$$\"1LL$3sr*zoF.$!1M$[U^b!ogF.7$Fas$!1d2V<tTvrF.7$$\"1++vo!*R-tF.$!1yS
l-HXW\")F.7$Fds$!1vvHc*e'\\*)F.7$Fhal$!1*)HB'4$p7&*F.7$Fgs$!14U7Z+)R()
*F.7$$\"1L$3-)omazF.$!1)y*)R4bc$**F.7$$\"1nmTgg/5!)F.$!1Rw:Uf?x**F.7$$
\"1**\\iS_Ul!)F.$!1h!H')[(z(***F.7$F`bl$!1odFl,e'***F.7$$\"1n;/,O=w\")
F.$!1,>$)Q)*os**F.7$$\"1***\\7yi:B)F.$!1Uj)3rZ_#**F.7$$\"1L$e9'>%pG)F.
$!1e[(y@gL&)*F.7$Fjs$!1JC2J*=hv*F.7$Fhbl$!1W1*3W0k=*F.7$F]t$!1Qd#>(*)G
O#)F.7$$\"1+]i!*z>W))F.$!1b')QFqTevF.7$F`cl$!1.<y57'>v'F.7$$\"1L$3_!HW
b!*F.$!1K#p8)4Q4eF.7$F`t$!1y0(H$>#Hs%F.7$$\"1++DJ&f@E*F.$!1Jp98p#4a$F.
7$Fhcl$!1yrWm\"[E@#F.7$$\"1++voyMk%*F.$!1[e$QBKsI(Fho7$Fct$\"1a]F#e\")
R7*Fho7$$\"1+D\"Gyh(>'*F.$\"1)=]?!)\\X'=F.7$$\"1+]7G:3u'*F.$\"1!)o;,bp
mGF.7$$\"1+vVt7SG(*F.$\"1*QhS'[2?RF.7$F`dl$\"1@NSqO%f-&F.7$$\"1+D1k2/P
)*F.$\"1i)\\='Rd&='F.7$$\"1+]P40O\"*)*F.$\"1kY%G8a-S(F.7$$\"1+voa-oX**
F.$\"1'p?9-*Gr')F.Fet-Fit6&F[uF\\uF\\uF*-F$6$7gp7$F(Fft7$F_el$\"1<AJTh
K.$)F.7$Fbu$\"1Wu*zy0#*p'F.7$Fafl$\"1B<M!4%>&=&F.7$F,$\"1F([oGt)ePF.7$
F^gl$\"1#)>$fC@te#F.7$Fju$\"1MU`\"[)yy9F.7$Ffgl$\"1)f;HCCtJ%Fho7$F0$!1
WwH'pRPb&Fho7$F^hl$!1EUrZ%Qdf\"F.7$Fbv$!1QK.8,KkDF.7$Ffhl$!14CCZ0AjMF.
7$F3$!1dd/)\\;XH%F.7$Fjv$!1#\\0Vmp8x&F.7$F6$!1V.k;y$*)*pF.7$Fbw$!1V[^1
F0*)zF.7$F9$!1Jm#oOFNw)F.7$Fjw$!13\"e%)Q0?I*F.7$F<$!1A@(=0t'z'*F.7$$!1
++]i#=ES(F.$!1tuERax:)*F.7$F^\\m$!1Mmq`nO8**F.7$$!1mm;zp[(>(F.$!1<LX,*
pR(**F.7$F?$!1rCATl3****F.7$$!1nm;/y%)))pF.$!1al<%>4$*)**F.7$Ff\\m$!1&
[pIQtZ%**F.7$$!1,+]P2qwnF.$!1;M0e%oq')*F.7$FB$!1&*=Ri%fxv*F.7$F^]m$!1W
1cEFj^%*F.7$FE$!1&*o4&>=z.*F.7$FH$!1;_5Qv4(*yF.7$FK$!1QB=CP;JmF.7$FN$!
1'H5h&fR#*\\F.7$FQ$!1(*[Z%)H+(>$F.7$FT$!1\\v./'yVR\"F.7$FW$\"18%o4-*eA
DFho7$FZ$\"1!en(p$3L;#F.7$Fgn$\"1'Gu#G4k)p$F.7$Fjn$\"1$\\sf*[DT`F.7$F]
o$\"1J)prt2=j'F.7$F`o$\"1t(esL()z$yF.7$Fco$\"1/(pW;mov)F.7$Ffo$\"1]0QF
8Ob%*F.7$F\\cm$\"1az&GYtDo*F.7$Fjo$\"1hYUbML\\)*F.7$Fdcm$\"1R<*R)oag**
F.7$F]p$\"13%f#Q?#*****F.7$$\"1GL3_Nl.5Fho$\"1?Z8[A%>***F.7$F\\dm$\"1x
bp1I`k**F.7$$\"1@Le*['R3KFho$\"19@r0Vt<**F.7$Fap$\"1YH(3\\9;&)*F.7$Fdd
m$\"1-?wR;q!p*F.7$Fdp$\"1ys)3bZAZ*F.7$Fgp$\"1Y#*Qec'*3))F.7$Fjp$\"1Sv2
+b%='yF.7$F]q$\"1zi8KMV)p'F.7$F`q$\"1c#4j6ZZP&F.7$Fcq$\"17Vpxhw7PF.7$F
fq$\"1a9P-(pX3#F.7$Fiq$\"1[Ar./t<DFho7$F\\r$!1**)pD:]#[9F.7$F_r$!1c#e*
pJ\"RH$F.7$Fbr$!1F(o&zV.h\\F.7$Fer$!1ij2CdAllF.7$Fhr$!1-O.\"G^k#zF.7$F
[s$!1)\\U.\"er\\!*F.7$Fajm$!13b1Mj*QX*F.7$F^s$!1tIO-C_a(*F.7$$\"1ML3Fe
#Rx'F.$!1)feFr/Y')*F.7$Fijm$!1rN2;+9V**F.7$$\"1LLe9w,')pF.$!1QvnI^c))*
*F.7$Fas$!17hP$f#H****F.7$$\"1m;a)GJs>(F.$!1#=*3>g2u**F.7$Fa[n$!1$)z6*
G`:\"**F.7$$\"1M$e*[oc2uF.$!196s$H0,\")*F.7$Fds$!1XK\"fV*3o'*F.7$Fhal$
!1#)ejELt&H*F.7$Fgs$!1in\"yuo,x)F.7$F`bl$!1ub6BqUlzF.7$Fjs$!1A#eKN+&Gp
F.7$Fhbl$!1r+m5OK!z&F.7$F]t$!1J]p(Rj+W%F.7$F`cl$!1'fnU$QE_FF.7$F`t$!13
@Ooj!p#zFho7$Fi_n$\"1)G\"y=/=gCFho7$Fhcl$\"16P\\EXa_8F.7$Fa`n$\"1i?t$>
O(GDF.7$Fct$\"1!)*GXZgkx$F.7$F^an$\"1SC4@x?*>&F.7$F`dl$\"1)z6`E7\"4nF.
7$F`bn$\"1*46\"4\"p&3$)F.Fet-Fit6&F[uF*F*F\\u-F$6$7SF^cn7$F,$\"1,z/TpB
%H)F.7$F0$\"1X#H1x3>(oF.7$F3$\"1i()y$R16M&F.7$F6$\"1'GR>#*oO(QF.7$F9$
\"1BO'e$eV'[#F.7$F<$\"1#[sq3dbE\"F.7$F?$\"14eD1d<enF\\]l7$FB$!1>jgSla+
6F.7$FE$!1!yEvYkK>#F.7$FH$!1D%eR()3EC$F.7$FK$!1tO)RMmT5%F.7$FN$!1:f]x0
!Q+&F.7$FQ$!1)[*48nBKeF.7$FT$!1;&>8J\"eflF.7$FW$!1Q8,J$*pfrF.7$FZ$!1S
\\QFh\\)z(F.7$Fgn$!1eP\"e9igF)F.7$Fjn$!1\\B=J=@e()F.7$F]o$!1'\\+Qyd\">
\"*F.7$F`o$!1CT<\"RUSW*F.7$Fco$!1L+HR5B%o*F.7$Ffo$!1;JX=0!H')*F.7$Fjo$
!1)*\\hc@Ei**F.7$F]p$!1eea40)*****F.7$Fap$!19)=#fX$G'**F.7$Fdp$!1b[\"y
#)zr')*F.7$Fgp$!1f\"3>Grwp*F.7$Fjp$!1-zpXfN]%*F.7$F]q$!1Y#)HP[SP\"*F.7
$F`q$!18(*f_own()F.7$Fcq$!1AzqXzK!G)F.7$Ffq$!1eaUDN@txF.7$Fiq$!1)))>un
H&frF.7$F\\r$!1X'o>X<!RlF.7$F_r$!1'z$okpa!z&F.7$Fbr$!15aT**\\W>]F.7$Fe
r$!1H)>&))p8WTF.7$Fhr$!1L%=@2)*)>KF.7$F[s$!1x&)GNaxz@F.7$F^s$!1K,$*Qa(
y5\"F.7$Fas$\"1YgmChHZfF\\]l7$Fds$\"1-gl@jB)G\"F.7$Fgs$\"1bUZL#\\(zCF.
7$Fjs$\"1E(RhSk)=RF.7$F]t$\"1)Qa.ZSDF&F.7$F`t$\"1a%*>:P-&y'F.7$Fct$\"1
JWbui`*H)F.Fet-Fit6&F[uF\\uF*F\\u-F$6$7\\tF^cn7$Fjdl$\"1PKeeR*)*4)F.7$
F_el$\"1Bb$)3$4-K'F.7$Fdel$\"1iY&>@Knl%F.7$Fbu$\"1X7x]!Q`5$F.7$F\\fl$
\"1@UuP.*>m\"F.7$Fafl$\"1U,!**G'RFKFho7$Fffl$!1;kccbxi\"*Fho7$F,$!1O![
l!)R)e?F.7$F^gl$!1MYEF83GQF.7$Fju$!1+!p%pWDN`F.7$Ffgl$!1@voeG\\)f'F.7$
F0$!1R[?@Y?NwF.7$Fbv$!1o(f'p5bC#*F.7$F3$!1'[x*)H+'G**F.7$$!1nm\"H-%\\/
()F.$!1a!pa<\"p&)**F.7$$!1mm;/'=3l)F.$!1[\\I&4h$****F.7$$!1mmT&=Vrf)F.
$!1JghmX%>(**F.7$Fjv$!1'G7!*49d!**F.7$$!1mm;Hp6O%)F.$!1f]!*)p'fl'*F.7$
F6$!1k.K.D)fH*F.7$Fbw$!10j?d0XP#)F.7$F9$!1)\\`X`DW%oF.7$Fjw$!1!4MFd\\O
M&F.7$F<$!1f2M`Gf:PF.7$F^\\m$!1:3lit0j>F.7$F?$!1e$ybCHt-#Fho7$Ff\\m$\"
1<G,lokq:F.7$FB$\"1?roC-K[KF.7$F^]m$\"1XP0=Z%fy%F.7$FE$\"1R22NMxdhF.7$
Ff]m$\"1WO'[gl1P(F.7$FH$\"1pM2&e[SO)F.7$F^y$\"1Y'>-(3cZ!*F.7$FK$\"1'fI
'RhCZ&*F.7$$!1++D\")*G;K&F.$\"19_]??@Z(*F.7$Ffy$\"1yn684!*)))*F.7$$!1,
]ilT')f^F.$\"1f'Hyhe!Q**F.7$$!1nmTgD%f5&F.$\"14O7j<)G(**F.7$$!1M$3_&4-
_]F.$\"1kg)\\<$[$***F.7$FN$\"0\\q6L\"******F]z7$$!1,+]Pj&R%\\F.$\"1LqF
G2\\#***F.7$$!1+++DL\")*)[F.$\"1]F#f&e3r**F.7$$!1++]7.nN[F.$\"1mUV&=^f
$**F.7$F_z$\"1,L')f\\F())*F.7$$!1+++v7CtYF.$\"1GnR_l6](*F.7$FQ$\"18\")
o[BPh&*F.7$Fgz$\"1dcZ\\<Tf!*F.7$FT$\"1:#4xF*)))Q)F.7$$!1LL3FW,eRF.$\"1
wKu$HU([wF.7$FW$\"1bW\\_(z%)z'F.7$Fi_m$\"1/SREw=lcF.7$FZ$\"1f0fQdQCWF.
7$Ff`m$\"1\"4(31y]4LF.7$Fgn$\"1,TK5d-a@F.7$Fcam$\"1$[GV3:;\"yFho7$Fjn$
!1x.rM`cxfFho7$F[bm$!1*Q__R#*H!=F.7$F]o$!1GchXC9wHF.7$$!1nmTNa%H)=F.$!
1L95q&\\s?%F.7$F`o$!1YutVXTg`F.7$$!1+++v_*=Y\"F.$!1S[E2;EpjF.7$Fco$!1-
K3%)>ZwsF.7$Ffo$!1>N94rb)y)F.7$F\\cm$!1k!pU-J0H*F.7$Fjo$!1HobLi1i'*F.7
$$!1omT&QdDG$Fho$!1#=*z2Og1)*F.7$Fdcm$!1k=!e[.8\"**F.7$$!1o;/^wj!p\"Fh
o$!1l<s/1f[**F.7$$!1NLeRx**f6Fho$!1bkh%)zyv**F.7$$!1<+D\"GyNH'F\\]l$!1
\\\"z+6rG***F.7$F]p$!1v&ojeC)****F.7$$\"1(H$3x\"yY_%F\\]l$!1&[6H6:j***
F.7$F_\\o$!1B&f?5t=)**F.7$$\"1E$ekGR[b\"Fho$!1ZG,&f7l&**F.7$F\\dm$!1KP
!RDe-#**F.7$Fg\\o$!189EE(>_\")*F.7$Fap$!1c^`.l;n'*F.7$Fddm$!1QE-7$z&3$
*F.7$Fdp$!1p=#Q;%pD))F.7$$\"1lm\"z\\1A-\"F.$!1<n<%o67<)F.7$Fgp$!1fr#eP
>wQ(F.7$$\"1mm;HCjV9F.$!1W\\)*R2DakF.7$Fjp$!17`YF<44aF.7$$\"1****\\7JF
n=F.$!14jv%R-RH%F.7$F]q$!1?isrZ&Q5$F.7$Feem$!17Jg>[D)*=F.7$F`q$!1gs'*)
o!RrlFho7$F]fm$\"1T:=26<+uFho7$Fcq$\"1T'*HQOuJ@F.7$Fjfm$\"1&p4LGf_N$F.
7$Ffq$\"1uARWCXKXF.7$Fggm$\"1]Up0%3cr&F.7$Fiq$\"1#[<lO9!*z'F.7$$\"1mm
\"H2fU'RF.$\"1M7udZ'\\n(F.7$F\\r$\"13GYcS/L%)F.7$F\\_l$\"1A7eBaT3\"*F.
7$F_r$\"1\\0LY(e_g*F.7$$\"1m;z%Rk$)o%F.$\"1]d1hLTs(*F.7$Fehm$\"1,[D1.z
%*)*F.7$$\"1m\"z>@;$R[F.$\"1`Q!>]W(Q**F.7$$\"1**\\P%[L'*)[F.$\"1.%o#z<
*4(**F.7$$\"1K3xc2&*R\\F.$\"1h))*fQ\"Q\"***F.7$Fbr$\"1^i5TGx****F.7$$
\"1KL3xS'G/&F.$\"1B/t`!yb***F.7$$\"1*****\\7ga4&F.$\"1GK=Zl*z(**F.7$$
\"1lm\"H<c![^F.$\"1l)**H\\1p%**F.7$F\\`l$\"1TI#p8+A!**F.7$$\"1mmm;V%eI
&F.$\"1z3!ys!er(*F.7$Fer$\"1q^uSfd&e*F.7$Fd`l$\"1+!RN0=41*F.7$Fhr$\"1#
fE=6rVK)F.7$Fiim$\"1#[n&=`,KtF.7$F[s$\"1:SBz]/DhF.7$Fajm$\"1(ooCj/ox%F
.7$F^s$\"1'[WlfM#pKF.7$Fijm$\"1B&y$[*HNf\"F.7$Fas$!1?gE%p/Ty\"Fho7$Fa[
n$!1AfCpdD$)>F.7$Fds$!1D%Gh6$>zPF.7$Fhal$!1O$HV^]_O&F.7$Fgs$!1\")>WzIJ
HoF.7$F`bl$!1x;wcuiq#)F.7$Fjs$!1%y,14N#\\$*F.7$$\"1LLeRZQT%)F.$!1V0gkb
`!o*F.7$Fhbl$!1\"*4R/1)3!**F.7$$\"1L$ek8!)**e)F.$!176'GO,`'**F.7$$\"1m
mTN>^R')F.$!1aoT4X#p***F.7$$\"1**\\PMP/*o)F.$!1oI`tD(R***F.7$F]t$!1>;T
hKia**F.7$F`cl$!1R7HnU]L$*F.7$F`t$!1#\\\\\"p'32'yF.7$Fi_n$!1a3\\LSM0oF
.7$Fhcl$!1j1v_<1'\\&F.7$Fa`n$!1wt5]***=\"RF.7$Fct$!17'**\\8i4.#F.7$Fi`
n$!1[#>*G4$y*))Fho7$F^an$\"1s3FyZ@tMFho7$Fcan$\"1Gln*)f4%o\"F.7$F`dl$
\"1Q-R\"poV7$F.7$F[bn$\"1;R(\\s_?n%F.7$F`bn$\"151o)=Z6L'F.7$Febn$\"1se
!f?Qd5)F.Fet-Fit6&F[uF*F\\uF\\u-%+AXESLABELSG6$%\"xG%!G-%%VIEWG6$;F(Ff
t%(DEFAULTG" 2 299 299 299 2 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 10030 10061 10056 10074 0 0 0 20030 0 12020 0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 0 0 0 1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "f
or n from 1 to 7 do combine(2^(n-1)*cos(x)^n) od ;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%$cosG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-
%$cosG6#,$%\"xG\"\"#\"\"\"F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%
$cosG6#,$%\"xG\"\"$\"\"\"-F%6#F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,(-%$cosG6#,$%\"xG\"\"%\"\"\"-F%6#,$F(\"\"#F)\"\"$F*" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,(-%$cosG6#,$%\"xG\"\"&\"\"\"-F%6#,$F(\"\"$F)-F%6#F(
\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*-%$cosG6#,$%\"xG\"\"'\"\"\"-
F%6#,$F(\"\"%F)-F%6#,$F(\"\"#\"#:\"#5F*" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,*-%$cosG6#,$%\"xG\"\"(\"\"\"-F%6#,$F(\"\"&F)-F%6#,$F(\"\"$\"#@-
F%6#F(\"#N" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "for n from 1 \+
to 7 do chebyshev(2^(n-1)*x^n,x) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,$-%\"TG6$\"\"\"%\"xG$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,&-%\"TG6$\"\"!%\"xG$\"+++++5!\"*-F%6$\"\"#F(F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&-%\"TG6$\"\"\"%\"xG$\"+++++I!\"*-F%6$\"\"$F($\"+++++5
F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%\"TG6$\"\"!%\"xG$\"+++++I!\"
*-F%6$\"\"#F($\"+++++SF+-F%6$\"\"%F($\"+++++5F+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(-%\"TG6$\"\"\"%\"xG$\"+++++5!\")-F%6$\"\"$F($\"+++++]
!\"*-F%6$\"\"&F($F*F1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,*-%\"TG6$\"
\"!%\"xG$\"+++++5!\")-F%6$\"\"#F($\"+++++:F+-F%6$\"\"%F($\"+++++g!\"*-
F%6$\"\"'F($F*F6" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,*-%\"TG6$\"\"\"%
\"xG$\"+++++N!\")-F%6$\"\"$F($\"+++++@F+-F%6$\"\"&F($\"+++++q!\"*-F%6$
\"\"(F($\"+++++5F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "u:=pr
oc(n,x) if n=0 then 1 elif n=1 then 2*x else 2*x*u(n-1,x)-u(n-2,x) fi;
 end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG:6$%\"nG%\"xG6\"F)F)@'/
9$\"\"!\"\"\"/F,F.,$9%\"\"#,&*&F1F.-F$6$,&F,F.!\"\"F.F1F.F2-F$6$,&F,F.
!\"#F.F1F8F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "u(4,x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"\",&*&F%F&,&*$F%\"\"#\"
\"%!\"\"F&F&F+F%!\"#F&F+F*!\"%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$
%\"xG\"\"%\"#;*$F%\"\"#!#7\"\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "U(4,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$%\"xG\"
\"%\"#;*$F%\"\"#!#7\"\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }