{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 0 660 "f:=y=x^x-c;\nA(0,0) := 1/y;\nB(0,0) := implicitdiff(f,y,x)/y;\nfor i from 1 to 5 do w := \+ i;\nA(0,w):= simplify(sum('(-1)^(a-1)*y^(a-1)*implicitdiff(f,y,x$a)*y^ (w-a+1)*A(0,w-a)/a!','a'=1..w)/y^(w+1));B(0,w):= simplify(sum('(-1)^(a )*y^(a)*implicitdiff(f,y,x$(a+1))*y^(w-a+1)*A(0,w-a)/a!','a'=0..w)/y^( w+1));A(l,0) := simplify(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 - simplify(A(l,w-1)/A(l,w));\nxprimeB := x - simplify(B (l,w-1)/B(l,w));\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG/%\"yG, &)%\"xGF)\"\"\"%\"cG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$ \"\"!F'*$%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F '*&,&*&)%\"xGF,\"\"\"-%#lnG6#F,F-F-F+F-F-%\"yG!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"wG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\" AG6$\"\"!\"\"\"*()%\"xGF+F(,&-%#lnG6#F+F(F(F(F(%\"yG!\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"\",$*&,0*&)*$%\"xG\"\"#F/F(-%# lnG6#F/F0!\"\"*&F-F(F1F(!\"#F-F4*(%\"yGF()F/F/F(F1F0F(*(F8F(F9F(F1F(F0 *&F8F(F9F(F(*&F8F()F/,&F/F(F4F(F(F(F(F8F6F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xG,&F'\"\"\"F+F-F-, &-%#lnG6#F+F-F-F-F-%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\" AG6$%\"lG\"\"\"*&,(*&)%\"xG,&F'F(F-F(F(-%#lnG6#F-F(F(F,F(*(F'F()F-,&F' F(!\"\"F(F(%\"yGF(F5F(F6!\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"B G6$%\"lG\"\"\",$*&,4*()%\"xGF'F()*$F.\"\"#F.F(-%#lnG6#F.F1!\"\"*(F-F(F /F(F2F(!\"#*&F-F(F/F(F5*()F.,&F'F(F.F(F(%\"yGF(F2F1F(*(F:F(F%(xprimeAG,&%\"xG\"\" \"*(F&F'%\"yGF',(*&)F&,&F&F'F'F'F'-%#lnG6#F&F'F'F,F'*&%\"lGF'F)F'!\"\" F3F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**)F&, &F&F'F'F'F',&-%#lnG6#F&F'F'F'F'%\"yGF',4*()*$F&\"\"#F&F'F,F4F&F'F'*(F2 F'F,F'F&F'F4*&F2F'F&F'F'*(F/F'F)F'F,F4!\"\"*(F/F'F)F'F,F'!\"#*&F/F'F)F 'F8*&F/F')F&F&F'F8**%\"lGF'F=F'F/F'F,F'F8*(F?F'F=F'F/F'F8F8F8" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"#,$*&,0*&)*$%\"xGF(F/\"\"\"-%#lnG6#F/ F(!\"#*&F-F0F1F0!\"%F-F4*(%\"yGF0)F/F/F0F1F(F0*(F8F0F9F0F1F0F(*&F8F0F9 F0F0*&F8F0)F/,&F/F0!\"\"F0F0F0F0F8!\"$#F?F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"#,$*(,D*(-%#lnG6#%\"xG\"\"$)*$F0F1F0 \"\"\"F0F4F(*(F-F(F2F4F0F4\"\"'*(F-F4F2F4F0F4F6**)*$F0F(F0F4F-F1%\"yGF 4F0F4!\"$**F9F4F-F(F;F4F0F4!\"***F9F4F-F4F;F4F0F4F>*(F9F4F-F4F;F4F<*&F 2F4F0F4F(*(F;F4F9F4F0F4F<*&F;F4F9F4F<*(F;F()F0,&F0F4F4F4F4F-F1F4*(F;F( FEF4F-F(F1*(F;F(FEF4F-F4F1*&F;F(FEF4F4*(F;F()F0F0F4F-F4F1*&F;F(FKF4F1* &F;F()F0,&F0F4!\"\"F4F4FPF4F0FPF;F<#F4F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xG,&F'\"\"\"F+F-F-,&-%#lnG6# F+F-F-F-F-%\"yG!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG \"\"#,$*&,8*()%\"xGF'\"\"\")*$F.F(F.F/-%#lnG6#F.F(F(*(F-F/F0F/F2F/\"\" %*&F-F/F0F/F(*()F.,&F'F/F.F/F/%\"yGF/F2F(!\"\"*(F9F/F;F/F2F/!\"#*&F9F/ F;F/F<*&)F.,(F'F/F.F/F*(F'F/FAF/F;F/F>* (F'F()F.,&F'F/F>F/F/F;F(F/*(F'F/FFF/F;F(F-%\"BG6$%\"lG\"\"#,$*(,X**)%\"xG,&F'\"\"\"F0F0F 0)*$F.F(F.F0-%#lnG6#F.F0%\"yGF0!\"**(F-F0F6F0F1F0!\"$*(F-F0F3\"\"$)*$F .F;F.F0F(*(F'F0)F.,(F'F0F.F0!\"\"F0F0F6F(F0**F'F0)F.F'F0F6F0F1F0!\"#*( )F.,(F'F0F.F0F0F0F0F6F(F3F;F0*,F'F0FCF0F6F0F1F0F3F0!\"%*(F'F0)F.,&F'F0 F.F0F0F6F(F(*,F'F0FCF0F6F0F1F0F3F(FD**F'F0F?F0F6F(F3F0FA*(F'F(F?F0F6F( F0*&F?F0F6F(FA*&FFF0F6F(F0**FCF0F1F0F3F0F6F0F9*(FCF0F6F0F1F0F9*&F-F0F< F0F(*&FKF0F6F(F;**F-F0F1F0F3F;F6F0F9*(F-F0F3F0F%(xprimeAG,&%\"xG\"\"\"*(% \"yGF',(*&)F&,&F&F'\"\"#F'F'-%#lnG6#F&F'!\"\"F,F2*(F&F'%\"lGF'F)F'F'F' ,8*()*$F&F.F&F'F/F.F&F.F.*(F7F'F/F'F&F.\"\"%*&F7F'F&F.F.*(F,F'F)F'F/F. F2*(F,F'F)F'F/F'!\"#*&F,F'F)F'F2*&F)F')F&,&F&F'F'F'F'F2**F4F'FAF'F)F'F /F'F>*(F4F'FAF'F)F'F>*&F4F.F)F.F'*&F4F'F)F.F2F2F." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',4*()*$F&\"\"#F&F' -%#lnG6#F&F.F&F'F'*(F,F'F/F'F&F'F.*&F,F'F&F'F'*(F)F')F&,&F&F'F'F'F'F/F .!\"\"*(F)F'F5F'F/F'!\"#*&F)F'F5F'F7*&F)F')F&F&F'F7**%\"lGF'FF'FF'F)F'F,F'F/F.F&F'F.*,F>F'F)F'F,F'F/F'F&F'\"\"%**F>F'F)F'F,F'F&F'F .**F>F'FF.FF'F5F'F)F.F/F'!\"%**F,F'F/F'F)F'F&F'FD*(F)F'F,F'F&F'FD**F>F'F5F'F)F. F/F.F9*&F)F.FF'FF.FF'F5F'F)F.F9F7F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"$" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\" \"$,$*(,D*(-%#lnG6#%\"xGF()*$F0F(F0\"\"\"F0F3!\"'*(F-\"\"#F1F3F0F3!#=* (F-F3F1F3F0F3F7**)*$F0F6F0F3F-F(%\"yGF3F0F3\"\"'**F:F3F-F6F-%\"BG6$\"\"!\"\"$,$ *(,`o*(%\"yGF()%\"xG,&F/\"\"\"F1F1F1-%#lnG6#F/F1!#7*(F-F(F.F1F2\"\"#! \"'*(F-F()F/,&F/F1F7F1F1F2F1!\"%*(F-F(F:F1F2F7F8*(F-F(F:F1F2F(F<*(F-F( )F/F/F1F2F1\"\"%*&F-F()F/,&F/F1!\"\"F1F1!\"#*&F-F(F:F1FE*&F-F(F.F1F8*& F-F(F@F1F1*(F-F(F:F1F2FAFE*(F-F7)*$F/F7F/F1F/F1\"#=*(F-F1F/F1)*$F/F(F/ F1F5*&F/F7)*$F/FAF/F1\"\"'**FLF1F2F1F-F7F/F1\"#O**FLF1F2F7F-F7F/F1FN** FLF1F2F(F-F7F/F7\"#G**FLF1F2F7F-F7F/F7\"#U**FLF1F2F1F-F7F/F7FZ**FLF1F2 FAF-F7F/F7\"\"(**F2F7F-F1F/F7FPF1!#s**F2F1F-F1F/F7FPF1!#[**F2FAF-F1F/F 7FPF1F5**F2F(F-F1F/F7FPF1F]o*(F-F7FLF1F/F7Fin*(F-F1F/F7FPF1F5*(F2F1F/F 7FSF1\"#C*(F2F7F/F7FSF1FW*(F2FAF/F7FSF1FU*(F2F(F/F7FSF1Fco**F2F7F-F1F/ F1FPF1F5*(FLF1F2F1F-F7F<*&F-F7FLF1FE**F2F1F-F1F/F1FPF1!#CF1F/FFF-F<#F1 FU" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\" \"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!* ()%\"xG,&F'\"\"\"F+F-F-,&-%#lnG6#F+F-F-F-F-%\"yG!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"$,$*(,fn**)%\"xG,&F'\"\"\"F0F0F0 )*$F.\"\"#F.F0-%#lnG6#F.F0%\"yGF0\"#=*(F-F0F7F0F1F0\"\"'*(F-F0F4F()*$F .F(F.F0!\"'**F'F0)F.F'F0F7F0F1F0F:*()F.,(F'F0F.F0F0F0F0F7F3F4F(!\"\"*, F'F0F@F0F7F0F1F0F4F0\"#7*(F'F0)F.,&F'F0F.F0F0F7F3!\"$*,F'F0F@F0F7F0F1F 0F4F3F:**F'F0)F.,(F'F0F.F0FDF0F0F7F3F4F0F(*(F'F3)F.,&F'F0!\"#F0F0F7F(F J*(F'F0FPF0F7F(F3*(F'F3FMF0F7F3FJ*&FMF0F7F3F0*&FBF0F7F3FD**F@F0F1F0F4F 0F7F0F:*(F@F0F7F0F1F0F:*(F'F(FPF0F7F(F0*&F-F0F*&FHF0F7F3FJ**F-F0F 1F0F4F(F7F0F:*(F-F0F4F0F **F'F0FHF0F7F3F4F3FJ**F'F3FMF0F7F3F4F0FJ*(FBF0F7F3F4F0FJ*(FHF0F7F3F4F0 FJ*(F-F0F4F3F-%\"BG6$%\"lG\"\"$,$*(,jr*,F'\"\"\")%\"xG,&F'F-F-F- F-%\"yG\"\"#)*$F/F2F/F--%#lnG6#F/F-!#F**F'F-)F/,(F'F-F/F-F-F-F-F1F(F5F (F(**F'F-)F/F'F-F1F2F3F-!\"'*()F/,(F'F-F/F-F2F-F-F1F(F5F-\"\"%*(F:F-F1 F(F5F2\"\"'**F'F-)F/,(F'F-F/F-!\"\"F-F-F1F(F5F-F2*,F'F-F.F-F1F-F5F2)*$ F/F(F/F-\"#=**F'F2F=F-F1F2F3F-!\"$**)F/,&F'F-F2F-F-F5F2F1F-FJF-\"#s*&) F/,&F'F-F/F-F-F1F(FH**F.F-F5F2F1F-FJF-\"#7*(F'F2FTF-F1F(F(*,F'F-F.F-F1 F-F5F-FJF-FL*&F:F-F1F(FD*(F=F-F1F2F3F-F-**F'F-F.F-F1F-FJF-FD**F.F-F3F- F5F2F1F2!#=*(FPF-F1F-FJF-FW*(FPF-F5F-)*$F/FBF/F-!#C*&FFF-F1F(F2**F=F-F 3F-F5F-F1F2FB**F'F-F:F-F1F(F5F-\"\"***F'F(FFF-F1F(F5F-F-*(F'F(FFF-F1F( F-*&F@F-F1F(F-*(FPF-F5F2F[oF-!#O**FPF-F3F-F5F-F1F2!#G**F.F-F3F-F5F-F1F 2Ffo*(FPF-F5F(F[oF-F]o*(F@F-F1F(F5F(FB**FPF-F5F(F1F-FJF-\"#[**F'F2FTF- F1F(F5F-FD**F.F-F5F-F1F-FJF-\"#C**F'F2FFF-F1F(F5F-FN**F'F2FTF-F1F(F5F2 F(*(FTF-F1F(F5F-!\"%*,F'F-F=F-F1F2F3F-F5F2F(*(F:F-F1F(F5F-FW*(F'F-F:F- F1F(F(*(F@F-F1F(F5FBF-*(F.F-F1F2F3F-Fhn*(F@F-F1F(F5F2FD*,F'F-F=F-F1F2F 3F-F5F-FN*(F'F-FFF-F1F(Fdp*(FPF-F5FBF[oF-F>*(F'F-FTF-F1F(FD**F'F-FTF-F 1F(F5F-F(*,F'F2F=F-F1F2F3F-F5F2FN*,F'F2F=F-F1F2F3F-F5F-F>*,F'F-F.F-F1F 2F3F-F5F2F8*,F'F-F.F-F1F2F3F-F5F(!\"***F'F-F:F-F1F(F5F2Fao*,F'F-F.F-F1 F-F5F(FJF-FD**F'F-F.F-F1F2F3F-Fdq*&FPF-F[oF-F>**F'F-FTF-F1F(F5F2FN**FP F-F5FBF1F-FJF-FW**FPF-F3F-F5F2F1F2!#U**FPF-F3F-F5FBF1F2!\"(**FPF-F5F-F 1F-FJF-F]p*(F.F-F1F-FJF-FW*(FPF-F1F2F3F-F^r**FPF-F3F-F5F(F1F2FhoF-F/! \"#F1Fdp#FHFD" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\" \"\"**%\"yGF'F&F',8*()*$F&\"\"#F&F'-%#lnG6#F&F.F&F.F.*(F,F'F/F'F&F.\" \"%*&F,F'F&F.F.*()F&,&F&F'F.F'F'F)F'F/F.!\"\"*(F6F'F)F'F/F'!\"#*&F6F'F )F'F8*&F)F')F&,&F&F'F'F'F'F8**%\"lGF'F=F'F)F'F/F'F:*(F@F'F=F'F)F'F:*&F @F.F)F.F'*&F@F'F)F.F8F',fn*()F&,&F&F'\"\"$F'F'F)F.F/F'!\"$**F@F'F6F'F) F.F/F'!\"'*(FFF'F)F.F/F.FI*(FFF'F)F.F/FHF8*(F@F'F6F'F)F.FI**F@F'F6F'F) F.F/F.FI*&FFF'F)F.F8*&F@F'F)FHF.*&F@F.F)FHFI*&F@FHF)FHF'*(F@F.F=F'F)F. 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