{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 
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{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 0 688 "f:=y=exp(x)-c;\nA(0
,0) := 1/y;\nB(0,0) := implicitdiff(f,y,x)/y;\nfor i from 1 to 3 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
));\nif i = 3 then l := 0 fi; xprimeA := 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,&-%$expG6#%\"xG\"\"\"%\"cG!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!F'*$%\"yG!\"\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!F'*&-%$expG6#%\"xG\"\"\"%\"yG!\"\"" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"\"*&-%$expG6#%\"xGF(%\"yG!\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"\",$*(-%$expG6#%\"xG
F(,&F+!\"\"%\"yGF(F(F1!\"#F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"A
G6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xGF'\"\"\"-%$expG6#F+F,%\"yG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"\"*&,&*&)%\"xGF'F(-%
$expG6#F-F(F(*(F'F()F-,&F'F(!\"\"F(F(%\"yGF(F4F(F5!\"#" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"\",$*(-%$expG6#%\"xGF(,(*&)F.F'F
(F+F(!\"\"*&F1F(%\"yGF(F(*(F'F()F.,&F'F(F2F(F(F4F(F(F(F4!\"#F2" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"*(F&F'%\"yGF',
&*&-%$expG6#F&F'F&F'F'*&%\"lGF'F)F'!\"\"F1F1" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"*(F&F'%\"yGF',(*&-%$expG6#F&F'F
&F'!\"\"*&F&F'F)F'F'*&%\"lGF'F)F'F'F/F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"wG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"
\"#,$*(-%$expG6#%\"xG\"\"\",&F+!\"#%\"yGF/F/F2!\"$#!\"\"F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"#,$*(-%$expG6#%\"xG\"\"\",
(-F,6#,$F.F(F(*&%\"yGF/F+F/!\"$*$F5F(F/F/F5F6#F/F(" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xGF'\"\"\"-%$
expG6#F+F,%\"yG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG
\"\"#,$*&,,*&)%\"xGF'\"\"\"-%$expG6#,$F.F(F/F(*(F-F/-F16#F.F/%\"yGF/!
\"\"**F'F/)F.,&F'F/F8F/F/F7F/F5F/!\"#*(F'F()F.,&F'F/F<F/F/F7F(F/*(F'F/
F>F/F7F(F8F/F7!\"$#F/F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%
\"lG\"\"#,$*(-%$expG6#%\"xG\"\"\",0*&)F.F'F/-F,6#,$F.F(F/F(*(F2F/F+F/%
\"yGF/!\"$*&F2F/F7F(F/**F'F/)F.,&F'F/!\"\"F/F/F7F/F+F/!\"#*(F'F/F;F/F7
F(F(*(F'F()F.,&F'F/F>F/F/F7F(F/*(F'F/FAF/F7F(F=F/F7F8#F/F(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',&*&-%$
expG6#F&F'F&F'F'*&%\"lGF'F)F'!\"\"F',,*&-F-6#,$F&\"\"#F'F&F7!\"#*(F,F'
F)F'F&F7F'**F0F'F)F'F,F'F&F'F7*&F0F7F)F7F1*&F0F'F)F7F'F1F7" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',(*&-%$
expG6#F&F'F&F'!\"\"*&F&F'F)F'F'*&%\"lGF'F)F'F'F',0*&-F-6#,$F&\"\"#F'F&
F8F8*(F,F'F)F'F&F8!\"$*&F)F8F&F8F'**F2F'F)F'F,F'F&F'!\"#*(F2F'F)F8F&F'
F8*&F2F8F)F8F'*&F2F'F)F8F/F/F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
wG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$\"\"!\"\"$,$*(-%$e
xpG6#%\"xG\"\"\",(-F,6#,$F.\"\"#\"\"'*&%\"yGF/F+F/!\"'*$F7F4F/F/F7!\"%
#F/F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$\"\"!\"\"$,$*(-%$exp
G6#%\"xG\"\"\",*-F,6#,$F.F(!\"'*&%\"yGF/-F,6#,$F.\"\"#F/\"#7*&F6F:F+F/
!\"(*$F6F(F/F/F6!\"%#!\"\"\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%
\"AG6$%\"lG\"\"!*&)%\"xGF'\"\"\"%\"yG!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"!*()%\"xGF'\"\"\"-%$expG6#F+F,%\"yG!
\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"AG6$%\"lG\"\"$,$*&,6*&)%
\"xGF'\"\"\"-%$expG6#,$F.F(F/!\"'*(F-F/-F16#,$F.\"\"#F/%\"yGF/\"\"'*(F
-F/-F16#F.F/F:F9!\"\"**F'F/)F.,&F'F/F?F/F/F:F/F6F/F;**F'F/FAF/F:F9F=F/
!\"$**F'F9)F.,&F'F/!\"#F/F/F:F9F=F/FD**F'F/FFF/F:F9F=F/F(*(F'F()F.,&F'
F/FDF/F/F:F(F/*(F'F9FKF/F:F(FD*(F'F/FKF/F:F(F9F/F:!\"%#F?F;" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>-%\"BG6$%\"lG\"\"$,$*(-%$expG6#%\"xG\"\"\",
>*&)F.F'F/-F,6#,$F.F(F/!\"'*(F2F/-F,6#,$F.\"\"#F/%\"yGF/\"#7*(F2F/F+F/
F<F;!\"(*&F2F/F<F(F/**F'F/)F.,&F'F/!\"\"F/F/F<F/F8F/\"\"'**F'F/FBF/F<F
;F+F/!\"**(F'F/FBF/F<F(F(**F'F;)F.,&F'F/!\"#F/F/F<F;F+F/!\"$*(F'F;FJF/
F<F(F(**F'F/FJF/F<F;F+F/F(*(F'F/FJF/F<F(FM*(F'F()F.,&F'F/FMF/F/F<F(F/*
(F'F;FRF/F<F(FM*(F'F/FRF/F<F(F;F/F<!\"%#FDFE" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%(xprimeAG,&%\"xG\"\"\"**%\"yGF'F&F',,*&-%$expG6#,$F&
\"\"#F'F&F0!\"#*(-F-6#F&F'F)F'F&F0F'**%\"lGF'F)F'F3F'F&F'F0*&F6F0F)F0!
\"\"*&F6F'F)F0F'F',6*&-F-6#,$F&\"\"$F'F&F?\"\"'*(F,F'F)F'F&F?!\"'*(F3F
'F)F0F&F?F'**F6F'F)F'F,F'F&F0FB**F6F'F)F0F3F'F&F0F?**F6F0F)F0F3F'F&F'F
?**F6F'F)F0F3F'F&F'!\"$*&F6F?F)F?F8*&F6F0F)F?F?*&F6F'F)F?F1F8F?" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xprimeBG,&%\"xG\"\"\"**%\"yGF'F&F',
0*&-%$expG6#,$F&\"\"#F'F&F0F0*(-F-6#F&F'F)F'F&F0!\"$*&F)F0F&F0F'**%\"l
GF'F)F'F2F'F&F'!\"#*(F7F'F)F0F&F'F0*&F7F0F)F0F'*&F7F'F)F0!\"\"F',>*&-F
-6#,$F&\"\"$F'F&FB!\"'*(F,F'F)F'F&FB\"#7*(F2F'F)F0F&FB!\"(*&F)FBF&FBF'
**F7F'F)F'F,F'F&F0\"\"'**F7F'F)F0F2F'F&F0!\"**(F7F'F)FBF&F0FB**F7F0F)F
0F2F'F&F'F4*(F7F0F)FBF&F'FB**F7F'F)F0F2F'F&F'FB*(F7F'F)FBF&F'F4*&F7FBF
)FBF'*&F7F0F)FBF4*&F7F'F)FBF0F<FB" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 593 }{VIEWOPTS 1 1 0 1 1 1803 }