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{SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 19 "Homework Problem 60" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "restart:  #this is always a \+
good idea.  It clears the memory." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "f:= (x,y) -> x*exp(y);  #This defines the function f(
x,y) = xe^y." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6
\"6$%)operatorG%&arrowGF)*&9$\"\"\"-%$expG6#9%F/F)F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "d:=(u1,u2,h,x,y)-> (f(x+h*u1,y+h*u
2) - f(x,y))/(h*sqrt(u1^2+u2^2)); #I have set  up the difference quoti
ent as a function of the vector, h, and the point (x,y)." }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"dGf*6'%#u1G%#u2G%\"hG%\"xG%\"yG6\"6$%)operat
orG%&arrowGF,*(,&-%\"fG6$,&9'\"\"\"*&9&F79$F7F7,&9(F7*&F9F79%F7F7F7-F3
6$F6F<!\"\"F7F9FA-%%sqrtG6#,&*$)F:\"\"#F7F7*$)F>FHF7F7FAF,F,F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "d(1,2,0.01,1,1); # This is \+
the approximation to the directional derivative in the  u-direction (a
fter normalizing u) of  f  at  (1,1).  Here we used  h=0.01." }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$*($\"+++++?!\")\"\"\",&$\"+7n#4!G!\"*F(-%$
expG6#F(!\"\"F(\"\"&#F(\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 58 "evalf(%); # This forces Maple to give me a decimal answer." }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+s:*fp$!\"*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 76 "d(1,2,0.0001,1,1); #Setting h=0.001 should giv
e a much closer approximation." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(
$\"+++++?!\"'\"\"\",&$\"+Au4>F!\"*F(-%$expG6#F(!\"\"F(\"\"&#F(\"\"#F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+_sWZO!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "? limit" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "
# I was not sure of the calling sequence for limits, so I had Maple lo
ok it up for me." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "limit(d
(1,2,h,1,1), h=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"$\"\"&
\"\"\"*&-%$expG6#F(F(F'#F(\"\"#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+px&pk
$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Our approximatio
ns look good!" }}}}{MARK "12 0 0" 31 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }