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{SECT 0 {PARA 256 "" 0 "" {MPLTEXT 0 21 0 "" }}{PARA 257 "" 0 "" 
{TEXT 256 15 "Calculus Lab 3\n" }{TEXT -1 25 " Implicit Differentiatio
n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
334 "Calling sequence for implicit differentiation:\nimplicitdiff(f, y
, x). The call implicitdiff(f, y, x) computes dy/dx, the partial deriv
ative of the function y with respect to x. The input f defines y as a \+
function of x implicitly. It must be an equation in x and y or an alge
braic expression which is understood to be equated to zero. " }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "implicitdiff(x^(2/3)+y^(2/3)
=4,y,x);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 257 46 "Work out the impli
cit derivative of x^3+y^3=1:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
1 "?" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 134 "Calling sequences for \+
implicitplot:\nwith(plots):\nimplicitplot(expr,x=a..b,y=c..d,<options>
),\nimplicitplot(f,a..b,c..d,<options>)\nPlot " }{XPPEDIT 18 0 "x^(2/3
)+y^(2/3)=4" "/,&)%\"xG*&\"\"#\"\"\"\"\"$!\"\"F()%\"yG*&\"\"#F(\"\"$F*
F(\"\"%" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "w
ith(plots):\nimplicitplot(x^(2/3)+y^(2/3)=4,x=-8..8,y=-8..8,\ngrid=[10
0,100]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Plot  x^3+y^3=1:" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "" 0 
"" {TEXT -1 28 "Work out the derivative at (" }{XPPEDIT 18 0 "(3*sqrt(
3),1)" "6$*&\"\"$\"\"\"-%%sqrtG6#\"\"$F%\"\"\"" }{TEXT -1 2 ")." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "imp:=implicitdiff(x^(2/3)+y^
(2/3)=4,y,x):\nm:=subs(y=1,x=3*sqrt(3),imp):\nm;" }}}}{SECT 0 {PARA 3 
"" 0 "" {TEXT 259 47 "Work out the derivative of  x^2+y^3=2 at (1,1):
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{SECT 0 {PARA 3 "
" 0 "" {TEXT -1 50 "Plot the graph and the tangent line at the point (
" }{XPPEDIT 18 0 "(3*sqrt(3),1)" "6$*&\"\"$\"\"\"-%%sqrtG6#\"\"$F%\"\"
\"" }{TEXT -1 2 ")." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "a:=i
mplicitplot(x^(2/3)+y^(2/3)=4,x=-8..8,y=-8..8):\nb:=plot(1-(sqrt(3)/3)
*(x-3*sqrt(3)),x=-8..8):\ndisplay(\{a,b\});" }}}}{SECT 0 {PARA 3 "" 0 
"" {TEXT -1 58 "Plot the graph of x^2+y^3=2 and the tangent line at (1
,1):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "?" }}}}{PARA 3 "" 0 "
" {TEXT -1 0 "" }}}{MARK "10 0 0" 28 }{VIEWOPTS 1 1 0 3 2 1804 }