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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra
ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "f:=x^3+y^3+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
fG,(*$)%\"xG\"\"$\"\"\"F**$)%\"yGF)F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 "Df:=[diff(f,x),diff(f,y)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#DfG7$,$*$)%\"xG\"\"#\"\"\"\"\"$,$*$)%\"yGF*F+F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(\{x=0,y=1\},Df);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"!\"\"$" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 61 "also l\344\337t sich f in Umgebung von [0,1] lokal nach
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(g(x))^3+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,(*$)%\"xG\"\"$
\"\"\"F**$)-%\"gG6#F(F)F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "diff(F,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#
\"\"\"\"\"$*(F)F()-%\"gG6#F&F'F(-%%diffG6$F,F&F(F(" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 22 "solve(%,diff(g(x),x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&*$)%\"xG\"\"#\"\"\"F)*$)-%\"gG6#F'F(F)!\"\"F/" }}}
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{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "diff(F,x$2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"
xG\"\"'*(F%\"\"\"-%\"gG6#F$F')-%%diffG6$F(F$\"\"#F'F'*(\"\"$F')F(F/F'-
F-6$F(-%\"$G6$F$F/F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "s
olve(%,diff(g(x),x$2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&%\"xG
\"\"\"*&-%\"gG6#F&F')-%%diffG6$F)F&\"\"#F'F'F'*$)F)F0F'!\"\"!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "subs(\{diff(g(x),x)=0,g(x)=1
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0 "> " 0 "" {MPLTEXT 1 0 12 "diff(F,x$3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,*\"\"'\"\"\"*&F$F%)-%%diffG6$-%\"gG6#%\"xGF.\"\"$F%F%*
*\"#=F%F+F%F(F%-F)6$F+-%\"$G6$F.\"\"#F%F%*(F/F%)F+F7F%-F)6$F+-F56$F.F/
F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(%,diff(g(x),x
$3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,(\"\"\"F&*$)-%%diffG6$-%
\"gG6#%\"xGF/\"\"$F&F&**F0F&F,F&F)F&-F*6$F,-%\"$G6$F/\"\"#F&F&F&*$)F,F
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{XPPMATH 20 "6#!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "also ist d
as Taylorpolynom von g vom Grad 3 im Punkt x=0:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "T3g:=1-2/3!*x^3;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$T3gG,&\"\"\"F&*&#F&\"\"$F&*$)%\"xGF)F&F&!\"\"" }}}{EXCHG 
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