{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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 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 23 "f:=x^2*ln(x+11)+sin( x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&)%\"xG\"\"#\"\"\"-%#l nG6#,&F(F*\"#6F*F*F*-%$sinG6#F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a:=-2;b:=16;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"a G!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "N:=7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"NG\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "g[1]:=evalf(\nmtaylor(f,x=(a+b)/2,7 )\n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"gG6#\"\"\",0$\"+45/`;!\" (!\"\"*&$\"+3H8%R%!\")F'%\"xGF'F'*&$\"+`*QSE$!\"*F'),&F1F'$\"\"(\"\"!F ,\"\"#F'F'*&$\"+F=\"**)))!#6F')F7\"\"$F'F,*&$\"+H@Z^EF?F')F7\"\"%F'F'* &$\"+C,_6j!#7F')F7\"\"&F'F'*&$\"+N<@O\"*!#8F')F7\"\"'F'F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(\{f,g[1]\},x=a..b);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$!\"# \"\"!$\"3K'>>D)3gzy!#<7$$!38+++D7l2;F-$\"39U_0HQy*y%F-7$$!3#****\\Plqi E\"F-$\"3k9-cbsz%p#F-7$$!3)))****\\(\\_B))!#=$\"3Xp?I\\&Q&H5F-7$$!3y** ***\\#[*)e\\F;$\"3^74iGC+D5F;7$$!30-+](eKE6\"F;$!3O]h%Rf\"\\Z\")!#>7$$ \"3%)****\\i[M`CF;$\"3k^'RN/a`)QF;7$$\"3u(***\\izqXhF;$\"3'*e-ca*>G]\" F-7$$\"3U++]i^Nk**F;$\"3')f[Dx\"okI$F-7$$\"3o***\\7fvqP\"F-$\"3mC.M+r= _dF-7$$\"3Y+++&p5'o2gZA#Fao7$$\"3_+++:M@nKF-$\"3A8wOGNwCGFao7$$\"3r***\\ihg$3OF-$ \"3q%*=;(e1lW$Fao7$$\"33+++Nw,9SF-$\"3OKO0sy@)G%Fao7$$\"33+++SBmdVF-$ \"3%p`p:1\\L4&Fao7$$\"3))***\\i#GSdZF-$\"3jKQX4!*oShFao7$$\"3[*******) 3C6^F-$\"3+sw8'zx#prFao7$$\"3%3+]iKd%*\\&F-$\"3E$H%pT)*z2%)Fao7$$\"3!4 +](y68peF-$\"3+=uZ!eKEp*Fao7$$\"3W,+]iq%[D'F-$\"3'3Bs(*HzR6\"!#:7$$\"3 8++D^Y04mF-$\"3#4z&*4&G6c7Fir7$$\"3%*)***\\(Q:6*pF-$\"3xWvn(e]*=9Fir7$ $\"3')***\\i6pzQ(F-$\"3MdZ^g%)>)f\"Fir7$$\"3j++v`9VLxF-$\"3'=19pLFCw\" Fir7$$\"3\\****\\U-a1\")F-$\"3?oILzZK[>Fir7$$\"3#*)*****H\")*>\\)F-$\" 3ql,A]C#)\\@Fir7$$\"3Y****\\sM4p))F-$\"3)3())\\gsdcBFir7$$\"3#****\\ig _RB*F-$\"3Yp.r-/:mDFir7$$\"3H****\\nk1R'*F-$\"3Z)p!QF-[5GFir7$$\"3()** ****GzI+5Fao$\"3M^Ng4%y5/$Fir7$$\"37++]nS4,I\"Fao$\"3=ZdA`<5w`Fir7$$\"3-++v:d GQ8Fao$\"3&4\"*)*zsavs&Fir7$$\"37+]i;h9w8Fao$\"3/R5k*z#)p3'Fir7$$\"3\" ******H*e$4T\"Fao$\"3X$3:P^ImU'Fir7$$\"3))***\\F!*33X\"Fao$\"3#\\DVnV3 p#oFir7$$\"3=+++)zrk[\"Fao$\"35vx_ug-&>(Fir7$$\"3()**\\i#)e\\C:Fao$\"3 qpf'4Li$)f(Fir7$$\"3'***\\P$y*)3c\"Fao$\"3w0_*yAS`*zFir7$$\"#;F*$\"3/K W!QMjWV)Fir-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fc[l-F$6$7U7$F($!3y%pD8iPD 3'Fir7$$!31++]7c#Q!=F-$!3'[2')>j]$3`Fir7$F/$!3P==xaq!ph%Fir7$$!3-+]PR4 'pV\"F-$!31eA@p.,xSFir7$F4$!3G-7bD=()*e$Fir7$F9$!3Kz')z'>Dcm#Fir7$F?$! 3`D%))*RIwR>Fir7$FD$!3#*z8*[dyGQ\"Fir7$FJ$!3'*zHlv`%G&)*Fao7$FO$!3#eq8 +I@=p'Fao7$FT$!3U$\\&pm*[&>UFao7$FY$!37VH;,YkjBFao7$Fhn$!36]j]D+zI\"*F -7$F]o$\"3UVZIQ#)*Qr*F;7$Fco$\"3>!*=%4C=D/\"Fao7$Fho$\"3[ukou8oy=Fao7$ F]p$\"3'HLjB^rnk#Fao7$Fbp$\"3%*\\(ooEn_N$Fao7$Fgp$\"3YKxtxz%3D%Fao7$F \\q$\"3k'puT&)Rv2&Fao7$Faq$\"3%Qfjm(=sNhFao7$Ffq$\"3Gy'enP.y;(Fao7$F[r $\"3U9Dm)p5vS)Fao7$F`r$\"3EY\\)*GNf#p*Fao7$Fer$\"3D=rR%4zR6\"Fir7$F[s$ \"3kfn4[G6c7Fir7$F`s$\"3lo=#pe]*=9Fir7$Fes$\"33[Eih%)>)f\"Fir7$Fjs$\"3 %=w*)>\\FCw\"Fir7$F_t$\"3eaIi.uK[>Fir7$Fdt$\"3oHZk5C%)\\@Fir7$Fit$\"3) G'GFtumcBFir7$F^u$\"3]#=g8UUkc#Fir7$Fcu$\"3$z6#pcqL6GFir7$Fhu$\"3`:X&Fir7$Fex$\"3rXq%)ee8< eFir7$Fjx$\"35cu^0')[%='Fir7$F_y$\"3X!R9z3v5_'Fir7$Fdy$\"3-A\"pF^Zv*oF ir7$Fiy$\"3y!4%\\:/n;sFir7$F^z$\"39W5!3W#QEvFir7$Fcz$\"3wup*=Hl#zxFir7 $Fhz$\"3#RARZ]JX)zFir-F][l6&F_[lFc[lF`[lFc[l-%+AXESLABELSG6$Q\"x6\"Q!F jel-%%VIEWG6$;F(Fhz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "g[2]:=Fourier(unapply(f,x),N,a,b)(x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%\"gG6#\"\"#,0*&$\"++O2fu!\"(\"\"\"%#PiG!\"\" F-*&$\"+TxPg6F,F--%$cosG6#,&*&#F-\"\"*F-*&F.F-%\"xGF-F-F-*&#F'F9F-F.F- F-F-F-*&$\"+Xh]VDF,F--%$sinGF5F-F/*&$\"+nQ!4&G!\")F--F46#,&*($\"+AAAAA !#5F-F.F-F;F-F-*&$\"+cbbb:!\"*F-F.F-F/F-F-*&$\"+&*)\\?J\"F,F--FBFHF-F/ *&$\"+!e(*H>\"FFF--F46#,&*($\"+LLLLLFMF-F.F-F;F-F-*&$\"+LLLLBFQF-F.F-F /F-F/*&$\"+IjW&)))FFF--FBFZF-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(\{f,g[2]\},x=a..b);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6&-%'CURVESG6$7_p7$$!\"#\"\"!$\"3<5Z)[vk!RR!#:7$$ !31++]7c#Q!=!#<$\"3%HK\"yzFu'R$F-7$$!38+++D7l2;F1$\"3Uy8cqoe]GF-7$$!3- +]PR4'pV\"F1$\"3A3;='yN:Q#F-7$$!3#****\\PlqiE\"F1$\"3V\">pA@&=E>F-7$$! 3!***\\iv:Ju5F1$\"3pC*36tF$R9F-7$$!3)))****\\(\\_B))!#=$\"33*))y#>xI!) )*!#;7$$!3K********)47*oFK$\"37!e:q:`rx&FN7$$!3y*****\\#[*)e\\FK$\"3E1 \\&ePt5=#FN7$$!3\"4+]iqjd.$FK$!3yzIWBe%yX)F17$$!30-+](eKE6\"FK$!3+!4]O *>B\"H$FN7$$\"3%*))***\\PhNq'!#>$!3fKZu:'>\"G]FN7$$\"3%)****\\i[M`CFK$ !3E7G+P)H(eiFN7$$\"3I****\\PcVwLFK$!3k9driv1-nFN7$$\"3y)***\\7k_*H%FK$ !37LqXqlsLN%FN7$$\"3m**** *\\FS:*GF1$\"3'p?@J!>^&Q'FN7$$\"33+++XoPzIF1$\"33EUzOs#z,(FN7$$\"3_+++ :M@nKF1$\"3*ysr\\w?gT(FN7$$\"36+]i:qyPMF1$\"3-+2U06(=e(FN7$$\"3r***\\i hg$3OF1$\"3I^nTDNewvFN7$$\"3!***\\iD\"*=6QF1$\"3kh+4Y8#yP(FN7$$\"33+++ Nw,9SF1$\"3>eXLE)>Y,(FN7$$\"33+++SBmdVF1$\"3EsAm/(zB='FN7$$\"3))***\\i #GSdZF1$\"3QVmD.r]=_FN7$$\"3C**\\7e=KM\\F1$\"3DyV&R#=-3\\FN7$$\"3[**** ***)3C6^F1$\"37$f:R?l/s%FN7$$\"3;+]73\"\\`I&F1$\"3#ze#y(=3631Z)yFN7$$\"38 ++D^Y04mF1$\"3&yx5(R%eP/\"F-7$$\"3%*)***\\(Q:6*pF1$\"3wB(=\\2)pr8F-7$$ \"3')***\\i6pzQ(F1$\"3G$)QzXM;L\\)F1$\"3II4 6)pYAPt$F-7$$\"3%***\\7xK*p=\"FN$\"3C[33ZQuPUF-7$$\"3 -++](H\"[F-7$$\"3#***\\i:!yFE\"FN$\"3WRFn3;r[aF-7$ $\"3?+++%>4,I\"FN$\"3zZf@%[_K.'F-7$$\"3-++v:dGQ8FN$\"3R7U@YLqIlF-7$$\" 3)**\\(=;f@d8FN$\"3RB3\\_9>=nF-7$$\"37+]i;h9w8FN$\"3%)R([%*yXh&oF-7$$ \"31](=2cV[Q\"FN$\"3aFEV<`5,pF-7$$\"3++D\"[+TNR\"FN$\"3$=>u)HPpLpF-7$$ \"3)\\Pfos*)yR\"FN$\"3aD`!)*)y>XpF-7$$\"3'*\\i!*[%QAS\"FN$\"3-C27&QOM& pF-7$$\"3$\\7`4<(e19FN$\"3GJmU-.OepF-7$$\"3\"******H*e$4T\"FN$\"3G3$=$ 3^#*fpF-7$$\"3#)\\(=#>+#fT\"FN$\"3/$*QLEf`dpF-7$$\"3!**\\Pa9/4U\"FN$\" 3INtAS*G1&pF-7$$\"3**\\ilr#))eU\"FN$\"3qa&=)*Hf\"RpF-7$$\"3*)**\\(yRs3 V\"FN$\"39*=EhN!4BpF-7$$\"3*)*\\7.lS3W\"FN$\"3I/M_>(\\q(oF-7$$\"3))*** \\F!*33X\"FN$\"30%yA^D#Q7oF-7$$\"3/+]P].ko9FN$\"3w!4P^_n.l'F-7$$\"3=++ +)zrk[\"FN$\"34\"HeJV\\+V'F-7$$\"3-+DJSQ[0:FN$\"32VLu9t&Q8'F-7$$\"3()* *\\i#)e\\C:FN$\"3%)yu+NH;zdF-7$$\"3\"******H$GpU:FN$\"3K>/io=\"3R&F-7$ $\"3'***\\P$y*)3c\"FN$\"31\\*Q2OO;'\\F-7$$\"3)**\\(o\"*[W!e\"FN$\"3ADH vZf&RY%F-7$$\"#;F*$\"37^$3#eZ1RRF--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F]f l-F$6$7S7$F($\"3K'>>D)3gzyF17$F5$\"39U_0HQy*y%F17$F?$\"3k9-cbsz%p#F17$ FI$\"3Xp?I\\&Q&H5F17$FU$\"3^74iGC+D5FK7$Fin$!3O]h%Rf\"\\Z\")F`o7$Fdo$ \"3k^'RN/a`)QFK7$Fhp$\"3'*e-ca*>G]\"F17$F\\r$\"3')f[Dx\"okI$F17$Ffr$\" 3mC.M+r=_dF17$F[s$\"3%oe%[\"[Tu%*)F17$F`s$\"3hq*yE]?_B\"FN7$Fes$\"3!e% Qddsp)o\"FN7$Fjs$\"3MY%3>2gZA#FN7$Fdt$\"3A8wOGNwCGFN7$F^u$\"3q%*=;(e1l W$FN7$Fhu$\"3OKO0sy@)G%FN7$F]v$\"3%p`p:1\\L4&FN7$Fbv$\"3jKQX4!*oShFN7$ F\\w$\"3+sw8'zx#prFN7$Ffw$\"3E$H%pT)*z2%)FN7$F`x$\"3+=uZ!eKEp*FN7$Fex$ \"3'3Bs(*HzR6\"F-7$Fjx$\"3#4z&*4&G6c7F-7$F_y$\"3xWvn(e]*=9F-7$Fdy$\"3M dZ^g%)>)f\"F-7$Fiy$\"3'=19pLFCw\"F-7$F^z$\"3?oILzZK[>F-7$Fcz$\"3ql,A]C #)\\@F-7$Fhz$\"3)3())\\gsdcBF-7$F][l$\"3Yp.r-/:mDF-7$Fb[l$\"3Z)p!QF-[5 GF-7$Fg[l$\"3M^Ng4%y5/$F-7$F\\\\l$\"3!3?O,[a%*H$F-7$Fa\\l$\"36&zOIS][a $F-7$Ff\\l$\"3&G!=!eQ(pDQF-7$F[]l$\"3/wd3)\\V?5%F-7$F`]l$\"3`6SbN)eLS% F-7$Fe]l$\"3#=!H-\\U,5ZF-7$Fj]l$\"3Tj(\\w&*RM/&F-7$F_^l$\"3=ZdA`<5w`F- 7$Fd^l$\"3&4\"*)*zsavs&F-7$F^_l$\"3/R5k*z#)p3'F-7$F\\al$\"3X$3:P^ImU'F -7$Fjbl$\"3#\\DVnV3p#oF-7$Fdcl$\"35vx_ug-&>(F-7$F^dl$\"3qpf'4Li$)f(F-7 $Fhdl$\"3w0_*yAS`*zF-7$Fbel$\"3/KW!QMjWV)F--Fgel6&FielF]flFjelF]fl-%+A XESLABELSG6$Q\"x6\"Q!Fj_m-%%VIEWG6$;F(Fbel%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "evalf(Int((f-g[1])^2,x=a..b) );\nevalf(Int((f-g[2])^2,x=a..b));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+4B>?D!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+b&G;\"=!\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "In this metric the Fourier aproximation is better, that the fourie r one" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "evalf(Int((f-g[1] )^2,x=a..b))+evalf(Int((diff(f,x)-diff(g[1],x))^2,x=a..b));\nevalf(Int ((f-g[2])^2,x=a..b))+evalf(Int((diff(f,x)-diff(g[2],x))^2,x=a..b));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(4&=*)R!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+toWet!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "In that metric the Fouri er aproximation is worse, that the fourier one" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "div:=(a,b,N)->seq(a+(b- a)/N*i,i=0..N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$divGj+6%%\"aG%\" bG%\"NG6\"6$%)operatorG%&arrowGF*-%$seqG6$,&9$\"\"\"*(,&9%F3F2!\"\"F39 &F7%\"iGF3F3/F9;\"\"!F8F*F*F*6%F " 0 "" {MPLTEXT 1 0 22 "x:=div(a,b,N);\ny:=seq(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6*!\"##\"\"%\"\"(#\"#AF&#\"#SF&#\"#eF&#\"#wF&#\"#%*F&\"#;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a,b;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " Interp([div(a,b,N)], [div(a,b,N)], x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 22 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }