{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 "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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 641 "y := (x^2)*ln(x) -2 *x;\nA(0,0) := 1/y;\nB(0,0) := diff(y,x)/y;\nfor i from 1 to 6 do w := i;\nA(0,w):= simplify(sum('(-1)^(a-1)*y^(a-1)*diff(y,x$a)*y^(w-a+1)*A (0,w-a)/a!','a'=1..w)/y^(w+1));B(0,w):= simplify(sum('(-1)^(a)*y^(a)*d iff(y,x$(a+1))*y^(w-a+1)*A(0,w-a)/a!','a'=0..w)/y^(w+1));A(l,0) := sim plify(x^l*y*A(0,0)/y);\nB(l,0) := simplify(x^l*y*B(0,0)/y);\nA(l,w) := simplify(sum('(-1)^(a)*l!/(a!*(l-a)!)*x^(l-a)*y^a*y^(w-a+1)*A(0,w-a)' ,'a'=0..w)/y^(w+1));\nB(l,w) := simplify(sum('(-1)^(a)*l!/(a!*(l-a)!)* x^(l-a)*y^a*y^(w-a+1)*B(0,w-a)','a'=0..w)/y^(w+1));\nxprimeA := x - si mplify(A(l,w-1)/A(l,w));\nxprimeB := x - simplify(B(l,w-1)/B(l,w));\no d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&*&%\"xG\"\"#-%#lnG6#F'\" \"\"F,F'!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$,&*& %\"xG\"\"#-%#lnG6#F+\"\"\"F0F+!\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F'*&,(*&%\"xG\"\"\"-%#lnG6#F+F,\"\"#F+F,!\"#F,F,,& *&F+F0F-F,F,F+F1!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\"*(,(*&%\"xGF(- %#lnG6#F,F(\"\"#F,F(!\"#F(F(F,F1,&F+F(F1F(F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"\"*(,.*&%\"xG\"\"#-%#lnG6#F,F-F-*&F,F -F.F(F(*&F,F(F.F(!\"%*$F,F-F(F,F-\"\"%F(F(F,!\"#,&F2F(F6F(F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xG,&F'\"\"\"!\"\"F- F-,&*&F+F--%#lnG6#F+F-F-!\"#F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>- %\"BG6$%\"lG\"\"!*()%\"xG,&F'\"\"\"!\"\"F-F-,(*&F+F--%#lnG6#F+F-\"\"#F +F-!\"#F-F-,&F0F-F5F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$% \"lG\"\"\",$*(,,*&)%\"xG,&F'F(F(F(F(-%#lnG6#F.F(!\"#F-!\"\")F.F'\"\"#* (F'F(F-F(F0F(F(*&F'F(F5F(F3F(F.F3,&*&F.F(F0F(F(F3F(F3F4" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"\",$*(,8*&)%\"xG,&F'F(\"\"#F(F (-%#lnG6#F.F0!\"#*&F-F(F1F(!\"\"*&)F.,&F'F(F(F(F(F1F(\"\"%F-F6F8F4)F.F '!\"%*(F'F(F-F(F1F0F0*(F'F(F-F(F1F(F(*(F'F(F8F(F1F(!\"'*&F'F(F8F(F4*&F 'F(F;F(F:F(F.F4,&*&F.F(F1F(F(F4F(F4F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"*()F&,&%\"lGF'F'F'F',&*&F&F'-%#lnG6#F&F'F'! \"#F'F',,*&F)F'F.F'F1F)!\"\")F&F+\"\"#*(F+F'F)F'F.F'F'*&F+F'F5F'F1F4F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**)F&,&%\" lGF'F'F'F',(*&F&F'-%#lnG6#F&F'\"\"#F&F'!\"#F'F',&F-F'F2F'F',8*&)F&,&F+ F'F1F'F'F.F1F2*&F6F'F.F'!\"\"*&F)F'F.F'\"\"%F6F9F)F2)F&F+!\"%*(F+F'F6F 'F.F1F1*(F+F'F6F'F.F'F'*(F+F'F)F'F.F'!\"'*&F+F'F)F'F2*&F+F'F%\"wG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"#,$*(,.*&%\"xGF(-%#lnG6#F-F(\"\"'*&F- F(F.\"\"\"\"\"&*&F-F3F.F3!#7*$F-F(F(F-!\"#\"\")F3F3F-!\"$,&F5F3F8F3F:# F3F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"#,$*(,6*&%\" xG\"\"$-%#lnG6#F-F.\"\"%*&F-F.F/F(F(*&F-F(F/F(!#7*&F-F.F/\"\"\"F.*&F-F (F/F7\"#5*&F-F7F/F7\"#C*$F-F.F(*$F-F(\"\"'F-!\"%!#;F7F7F-!\"$,&F:F7!\" #F7FA#F7F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)% \"xG,&F'\"\"\"!\"\"F-F-,&*&F+F--%#lnG6#F+F-F-!\"#F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xG,&F'\"\"\"!\"\"F-F-,(*& F+F--%#lnG6#F+F-\"\"#F+F-!\"#F-F-,&F0F-F5F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"#,$*(,>*&)%\"xG,&F'\"\"\"F(F0F0-%#lnG 6#F.F(\"\"'*&F-F0F1F0\"\"&*&)F.,&F'F0F0F0F0F1F0!#7F-F(F8!\"#)F.F'\"\") *(F'F0F-F0F1F(!\"&*(F'F0F-F0F1F0F;*(F'F0F8F0F1F0\"#;*&F'F0F8F0\"\"%*&F 'F0F-%\"BG6$%\"lG\" \"#,$*(,V*&F'\"\"\")%\"xG,&F'F-F-F-F-!\"%*(F'F-)F/,&F'F-F(F-F--%#lnG6# F/F-F1*(F'F-F3F-F5F(!#E*&F3F-F5F-!#5*(F'F(F.F-F5F-!#;*(F'F(F3F-F5F(\"# 5)F/F'\"#;*(F'F-)F/,&F'F-\"\"$F-F-F5FE\"\"'*(F'F(FCF-F5FE!\"#*(F'F(FCF -F5F(!\"\"*&F'F-F3F-F1*&FCF-F5FEF1*&FCF-F5F(FH*&FCF-F5F-!\"$FCFH*(F'F( F3F-F5F-\"\"%*(F'F-FCF-F5F(FE*(F'F-FCF-F5F-F(*&F'F(F.F-F1*&F.F-F5F-!#C *&F'F-F@F-FVF.FQF3!\"'*&F3F-F5F(\"#7*(F'F-F.F-F5F-\"#S*&F'F(F@F-\"\")F -F/FO,&*&F/F-F5F-F-FHF-FO#FJF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(x primeAG,&%\"xG\"\"\"**F&F',&*&F&F'-%#lnG6#F&F'F'!\"#F'F',,*&)F&,&%\"lG F'F'F'F'F+F'\"\"#F1F')F&F3F.*(F3F'F1F'F+F'!\"\"*&F3F'F5F'F4F',>*&)F&,& F3F'F4F'F'F+F4\"\"'*&F;F'F+F'\"\"&F0!#7F;F4F1F.F5\"\")*(F3F'F;F'F+F4! \"&*(F3F'F;F'F+F'F.F6\"#;*&F3F'F1F'\"\"%F8F@*(F3F4F;F'F+F4F'*(F3F4F1F' F+F'!\"%*&F3F4F5F'FGF7F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xprimeB G,&%\"xG\"\"\"**,8*&)F&,&%\"lGF'\"\"#F'F'-%#lnG6#F&F.!\"#*&F+F'F/F'!\" \"*&)F&,&F-F'F'F'F'F/F'\"\"%F+F4F6F2)F&F-!\"%*(F-F'F+F'F/F.F.*(F-F'F+F 'F/F'F'*(F-F'F6F'F/F'!\"'*&F-F'F6F'F2*&F-F'F9F'F8F'F&F',&*&F&F'F/F'F'F 2F'F',VF?F:FF*\"#7F=\"#S*&F-F .F9F'\"\")F4F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"$,$*(,4*&%\"xGF(-%#l nG6#F-F(\"#7*&F-F(F.\"\"#\"#8*&F-F3F.F3!#O*&F-F(F.\"\"\"\"\"**&F-F3F.F 8!#5*&F-F8F.F8\"#[*$F-F(F(F-\"\"%!#CF8F8F-!\"%,&F-%\"BG6$\"\"!\"\"$,$*(,@\"#'*\"\"\"% \"xG\"#;*&F.F--%#lnG6#F.F-!$#>*$F.\"\"%\"\"'*$F.F(\"#C*$F.\"\"#!\"%*&F .F6F1F6\"#7*&F.F6F1F(F7*&F.F6F1F;\"#6*&F.F6F1F-F>*&F.F;F1F-!#S*&F.F;F1 F;\"$W\"*&F.F(F1F(!#[*&F.F(F1F;\"#_*&F.F(F1F-FJF-F.F<,&F0F-!\"#F-F<#F- F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xG,&F' \"\"\"!\"\"F-F-,&*&F+F--%#lnG6#F+F-F-!\"#F-F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xG,&F'\"\"\"!\"\"F-F-,(*&F+F-- %#lnG6#F+F-\"\"#F+F-!\"#F-F-,&F0F-F5F-F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"$,$*(,fn*&F'\"\"\")%\"xG,&F'F-F-F-F-\"#C*(F'F- )F/,&F'F-\"\"#F-F--%#lnG6#F/F-!#[*(F'F-F3F-F6F5!$9\"*&F3F-F6F-\"#?*(F' F5F.F-F6F-!#%)*(F'F5F3F-F6F5\"#[)F/F'FA*(F'F-)F/,&F'F-F(F-F-F6F(\"#E*( F'F5FDF-F6F(!\"**(F'F5FDF-F6F5!\"$*&F'F-F3F-!#7*&FDF-F6F(!#C*&FDF-F6F5 !#E*&FDF-F6F-!#=FD!\"'*(F'F5F3F-F6F-\"#7*(F'F-FDF-F6F5\"#=*(F'F-FDF-F6 F-\"\"'*&F'F5F.F-FL*&F.F-F6F-!#'**&F'F-FBF-!#))F.!\")*(F'F(FDF-F6F(F-* &F3F-F6F5\"#s*(F'F-F.F-F6F-\"$o\"*&F'F5FBF-FA*(F'F(F.F-F6F-FU*(F'F(F3F -F6F5FS*&F'F(FBF-FinF-F/!\"%,&*&F/F-F6F-F-!\"#F-Fco#!\"\"FY" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"$,$*(,\\q*&F'\"\"\")%\"xG, &F'F-F-F-F-!#K*(F'F-)F/,&F'F-\"\"#F-F--%#lnG6#F/F-\"#g*(F'F-F3F-F6F5!$ +$*&F3F-F6F-!#S*(F'F5F.F-F6F-!$;#*(F'F5F3F-F6F5\"$#>)F/F'\"#'**(F'F-)F /,&F'F-F(F-F-F6F(\"$C\"*(F'F5FEF-F6F(!#y*(F'F5FEF-F6F5!#C*&F'F-F3F-\"# C*&FEF-F6F(!#[*&FEF-F6F5\"#_*&FEF-F6F-FQFEFM*(F'F5F3F-F6F-FM*(F'F5FEF- F6F-!#7*(F'F-FEF-F6F-\"#7*(F'F-)F/,&F'F-\"\"%F-F-F6F-!\"'*(F'F(FEF-F6F 5\"\"'*(F'F(FYF-F6F(!\"\"*&F.F-F6F-!$#>*&F'F-FBF-!$w\"*(F'F(F3F-F6F-FU F.\"#;*(F'F(FEF-F6F(\"#9F3!\"%*&F3F-F6F5\"$W\"*(F'F-F.F-F6F-\"$o$*&FYF -F6F5\"#6*&FYF-F6F-FW*(F'F5FYF-F6F5F(*&F'F5F3F-FW*&F'F-FEF-FW*&FYF-F6F enFW*&FYF-F6F(Fhn*&F'F(F.F-\"\")*&F'F5FBF-FCFYFhn*(F'F-FYF-F6F5FU*(F'F -FYF-F6Fen!#A*(F'F(F.F-F6F-\"#S*(F'F(F3F-F6F5!#O*&F'F(FBF-!#;*(F'F(FYF -F6Fen!\"#*(F'F-FYF-F6F(!#6*(F'F5FYF-F6F(Fhn*(F'F5FYF-F6FenFWF-F/Fco,& *&F/F-F6F-F-F]qF-Fco#F-Fhn" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xprim eAG,&%\"xG\"\"\"**F&F',&*&F&F'-%#lnG6#F&F'F'!\"#F'F',>*&)F&,&%\"lGF'\" \"#F'F'F+F4!\"'*&F1F'F+F'!\"&*&)F&,&F3F'F'F'F'F+F'\"#7F1F.F9F4)F&F3!\" )*(F3F'F1F'F+F4\"\"&*(F3F'F1F'F+F'F4*(F3F'F9F'F+F'!#;*&F3F'F9F'!\"%*&F 3F'F!$9\"F6\"#?FH!#%)FF\"#[F%(xprimeBG,&%\"xG\"\"\"**F&F',&*&F&F'-%#lnG6#F&F'F'!\" #F'F',V*&%\"lGF')F&,&F1F'F'F'F'!\"%*(F1F')F&,&F1F'\"\"#F'F'F+F'F4*(F1F 'F6F'F+F8!#E*&F6F'F+F'!#5*(F1F8F2F'F+F'!#;*(F1F8F6F'F+F8\"#5)F&F1\"#;* (F1F')F&,&F1F'\"\"$F'F'F+FF\"\"'*(F1F8FDF'F+FFF.*(F1F8FDF'F+F8!\"\"*&F 1F'F6F'F4*&FDF'F+FFF4*&FDF'F+F8F.*&FDF'F+F'!\"$FDF.*(F1F8F6F'F+F'\"\"% *(F1F'FDF'F+F8FF*(F1F'FDF'F+F'F8*&F1F8F2F'F4*&F2F'F+F'!#C*&F1F'FAF'FVF 2FQF6!\"'*&F6F'F+F8\"#7*(F1F'F2F'F+F'\"#S*&F1F8FAF'\"\")F',\\qF0\"#KF5 !#gF9\"$+$F;FfnF=\"$;#F?!$#>FA!#'*FC!$C\"FH\"#yFI\"#CFKFVFL\"#[FM!#_FN FdoFDFVFPFV*(F1F8FDF'F+F'FZFS!#7*(F1F')F&,&F1F'FQF'F'F+F'FG*(F1FFFDF'F +F8FX*(F1FFFhoF'F+FFF'FU\"$#>FW\"$w\"*(F1FFF6F'F+F'FZF2F>*(F1FFFDF'F+F F!#9F6FQFY!$W\"Fen!$o$*&FhoF'F+F8!#6*&FhoF'F+F'Ffo*(F1F8FhoF'F+F8FO*&F 1F8F6F'Ffo*&F1F'FDF'Ffo*&FhoF'F+FQFfo*&FhoF'F+FFFX*&F1FFF2F'!\")FgnF_o FhoFX*(F1F'FhoF'F+F8FZ*(F1F'FhoF'F+FQ\"#A*(F1FFF2F'F+F'!#S*(F1FFF6F'F+ F8\"#O*&F1FFFAF'FB*(F1FFFhoF'F+FQF8*(F1F'FhoF'F+FF\"#6*(F1F8FhoF'F+FFF X*(F1F8FhoF'F+FQFfoFJFO" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"%,$*(,@\"$#>\"\" \"%\"xG!#C*$F.F(\"#7*$F.\"\"$F1*$F.\"\"#!\"%*&F.F5-%#lnG6#F.F-\"#o*&F. 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