{VERSION 6 0 "IBM INTEL LINUX" "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 "" 0 1 0 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 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 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f := x -> 4*x^3 - 2* x^2 + 3 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)ope ratorG%&arrowGF(,(*&\"\"%\"\"\")9$\"\"$F/F/*&\"\"#F/)F1F4F/!\"\"F2F/F( F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "You can change your funct ion, by modifying the line above." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Df := D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DfG f*6#%\"xG6\"6$%)operatorG%&arrowGF(,&*&\"#7\"\"\")9$\"\"#F/F/*&\"\"%F/ F1F/!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot(f,- 2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 384 384 384 {PLOTDATA 2 "6%-%'CUR VESG6$7S7$$!\"#\"\"!$!#PF*7$$!3MLLL$Q6G\">!#<$!3i/1E^MCJK!#;7$$!3bmm;M !\\p$=F0$!325c[sKIaGF37$$!3MLLL))Qj^r\"e+\"F37$$!35++]d(Q&\\7F0$!3KR9*o5\\l#zF07$$!3hmmmc4`i6F0$!3\"[ **yma(\\()fF07$$!3KLLLQW*e3\"F0$!3/@=`Ve8![%F07$$!3w++++()>'***!#=$!3) [sjF%*>R*HF07$$!3E++++0\"*H\"*Fco$!3b0sKy(47r\"F07$$!35++++83&H)Fco$!3 IZrjPp^#f'Fco7$$!3\\LLL3k(p`(Fco$\"3j5ED;S(H^\"Fco7$$!3Anmmmj^NmFco$\" 3SJf7FD\\2&*Fco7$$!3(zmmmYh=(eFco$\"3=m:xIP?3?F07$$!3commmCC(>%Fco$\"3Fq*=]W%*=N#F07$$!39*****\\FRXL$Fc o$\"38_/#z&zIHEF07$$!3t*****\\#=/8DFco$\"3PR>Hn\"4-\"GF07$$!3=mmm;a*el \"Fco$\"3xx:8:%)*p#HF07$$!3jomm;Wn(o)!#>$\"3fqQ()H?G#)HF07$$!3IqLLL$eV (>!#?$\"3#4VLI<#****HF07$$\"3)Qjmm\"f`@')F[s$\"3Bbz94sp()HF07$$\"3%z** **\\nZ)H;Fco$\"3&oEKI1!>kHF07$$\"3ckmm;$y*eCFco$\"3-Tnu$4U&QHF07$$\"3f )******R^bJ$Fco$\"3P+'ytAKf#HF07$$\"3&e*****\\5a`TFco$\"39^VM))yeTHF07 $$\"3'o****\\7RV'\\Fco$\"3!ex?!*f%['*HF07$$\"3X'*****\\@fkeFco$\"3#RA( p'>X*=JF07$$\"3_ILLL&4Nn'Fco$\"3#o&=^rQ7)H$F07$$\"3A*******\\,s`(Fco$ \"3:fC0XwawNF07$$\"3%[mm;zM)>$)Fco$\"3#4X/@A\">>RF07$$\"3L*******pfa<* Fco$\"3LQ/k?@61WF07$$\"38HLLeg`!)**Fco$\"3$R\"Rn,nY%)\\F07$$\"3w****\\ #G2A3\"F0$\"343\\[s3YFdF07$$\"3;LLL$)G[k6F0$\"3:1hmU$4Ug'F07$$\"3#)*** *\\7yh]7F0$\"3ghz\"[))**fp(F07$$\"3xmmm')fdL8F0$\"37t`k.#4)H*)F07$$\"3 bmmm,FT=9F0$\"3A1X<>)*4R5F37$$\"3FLL$e#pa-:F0$\"3!=^)yH*e`?\"F37$$\"3* )******Rv&)z:F0$\"3z6hc/\"3\"y8F37$$\"3HLLLGUYo;F0$\"3n3xg7c4,;F37$$\" 3_mmm1^rZF0$\"3q))ex0!4(oBF37$$\"\"#F*$\"#FF*-%'COLOURG6&%$RGBG$\"*++ ++\"!\")$F*F*Fc[l-%+AXESLABELSG6$Q!6\"Fg[l-%%VIEWG6$;F(Fhz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "newt := x -> x - f(x)/Df(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%newtGf*6#%\"xG6\"6$%)operatorG% &arrowGF(,&9$\"\"\"*&-%\"fG6#F-F.-%#DfGF2!\"\"F5F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x_0:=-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$x_0G!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Th is is our starting value." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf(newt(x_0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!++++D\")!#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(newt(%));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!+UQK)o(!#5" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 111 "Execute the last line a few times thus doing more step s of the Newton's method (I think I did it 2 times here)." }}{PARA 0 " " 0 "" {TEXT -1 27 " This is our approximation." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "fsolve(f(x)=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+e3G)o(!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Th is is the actual root." }}}}{MARK "12" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }