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%TCIDATA{<META NAME="Title" CONTENT="Exercises">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 17:05:05 1997}
%TCIDATA{Language=American English}
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\input{tcilatex}
\begin{document}


\section{\ Exercises\label{Exercises}}

\begin{enumerate}
\item[1.]  \label{q1}Use \textsf{Implicit} under the \textsf{Plot 2D}
submenu to plot the conic sections $x^{2}+y^{2}=1$, $x^{2}-y^{2}=1$, and $%
x+y^{2}=0$ all on the same coordinate axes. \hfill \hyperref{\TCIIcon{%
BITMAPSETAnswer}{0.2171in}{0.2006in}{0in}}{}{}{a1}

\item[2.]  \label{q2}Use \textsf{Implicit} under the \textsf{Plot 2D}
submenu to plot the conic sections $(x-1)^{2}+(y+2)^{2}=1$, $%
(x-1)^{2}-(y+2)^{2}=1$, and $(x-1)+(y+2)^{2}=0$\ on one pair of coordinate
axes. With the hand symbol visible over the view, translate the view so that
the curves match the curves in Exercise 1. In which direction did the axes
move?\hfill \hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in}{0.2006in}{0in}}{}{%
}{a2}

\item[3.]  \label{q3}Plot $x^{2}+y^{2}=4$ and $x^{2}-y^{2}=1$ together. How
many intersection points are there? Zoom in on the one in the first quadrant
to estimate where the curves cross each other. Verify your estimate by
typing the formulas into a matrix and choosing \textsf{Numeric} from the 
\textsf{Solve} submenu.\hfill \hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in}{%
0.2006in}{0in}}{}{}{a3}

\item[4.]  \label{q4}Plot the astroid $x^{2/3}+y^{2/3}=1$.\hfill \hyperref{%
\TCIIcon{BITMAPSETAnswer}{0.2171in}{0.2006in}{0in}}{}{}{a4}

\item[5.]  \label{q5}Plot the folium of Descartes $x^{3}+y^{3}=6xy$.\hfill 
\hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in}{0.2006in}{0in}}{}{}{a5}

\item[6.]  \label{q6}Plot the surface $z=\sin xy$, with $-4\leq x\leq 4$ and 
$-4\leq y\leq 4$. Compare the location of the ridges with the implicit plot
of the three curves $xy=\frac{\pi }{2}$, $xy=\frac{3\pi }{2}$, and $xy=\frac{%
5\pi }{2}$.\hfill \hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in}{0.2006in}{0in%
}}{}{}{a6}

\item[7.]  \label{q7}A standard calculus problem involves finding the
intersection of two right circular cylinders of radius 1. View this problem
by choosing \textsf{Rectangular} from the \textsf{Plot 3D} submenu to plot
the two parametric surfaces $\left[ s,\cos t,\sin t\right] $ and $\left[
\cos t,s,\sin t\right] $.\hfill \hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in%
}{0.2006in}{0in}}{}{}{a7}

\item[8.]  \label{q8}Do the two space curves 
\[
\left[ (2+\sin t)10\cos t,\ (2+\cos t)10\sin t,3\sin 3t\right] 
\]
and$\,$%
\[
\left[ 20\cos t,20\sin t,-3\sin 3t\right] 
\]
intersect? Use \textsf{Tube} from the \textsf{Plot 3D} submenu and rotate
the curves to find out.\hfill \hyperref{\TCIIcon{BITMAPSETAnswer}{0.2171in}{%
0.2006in}{0in}}{}{}{a8}

\item[9.]  \label{q9}View the intersection of the sphere $%
x^{2}+y^{2}+z^{2}=1 $ and the plane $x+y+z=\frac{1}{2}$ by solving for $z$
and choosing \textsf{Rectangular }from the \textsf{Plot 3D} submenu. Verify
that the points of intersection lie on an ellipse (it is actually a circle)
by solving $x+y+z=\frac{1}{2}$ for $z$, substituting this value into the
equation $x^{2}+y^{2}+z^{2}=1$, and calculating the \hyperref{discriminant}{%
}{}{DM3-6.tex#Discriminant} of the resulting equation.\hfill \hyperref{%
\TCIIcon{BITMAPSETAnswer}{0.2171in}{0.2006in}{0in}}{}{}{a9}

\item[10.]  \label{q10}Explore the meaning of contours by plotting the
surface $z=xy$. Choose \textsf{Patch \& Contour} as a \textsf{Style} in the 
\textsf{Rectangular} dialog box. Rotate the surface until only the top face
of the cube is visible, and interpret the meaning of the curves that you
see. Rotate the cube until the top face just disappears, and interpret the
meaning of the contours that appear.\hfill \hyperref{\TCIIcon{BITMAPSETAnswer%
}{0.2171in}{0.2006in}{0in}}{}{}{a10}
\end{enumerate}

\section{\ Solutions\label{Solutions}}

\begin{enumerate}
\item[1.]  \label{a1}\textsf{Plot 2D + Implicit}: $%
x^{2}+y^{2}=1,x^{2}-y^{2}=1,x+y^{2}=0$

(Take $-2\leq x\leq 2$ and $-2\leq y\leq 2$. Choose \textsf{Equal Scaling
Along Each Axis})\hfill \hfill \hyperref{\TCIIcon{BITMAPSETProbSolvHint}{%
0.2006in}{0.243in}{0in}}{}{}{q1}\FRAME{dtbpF}{3.9998in}{2.7492in}{0pt}{}{}{%
Figure }{\special{language "Scientific Word";type "MAPLEPLOT";width
3.9998in;height 2.7492in;depth 0pt;display "PICT";function
\TEXUX{$x^{2}+y^{2}=1$};linecolor "red";linestyle 1;linethickness
1;pointstyle "point";function \TEXUX{$x^{2}-y^{2}=1$};linecolor
"blue";linestyle 1;linethickness 1;pointstyle "point";function
\TEXUX{$x+y^{2}=0$};linecolor "black";linestyle 1;linethickness 1;pointstyle
"point";xmin "-2";xmax "2";ymin "-2";ymax "2";xviewmin "-2.08";xviewmax
"2.082";yviewmin "-1.799";yviewmax "1.801";rangeset"XY";phi 45;theta
45;plottype 12;constrained TRUE;num-x-gridlines 25;num-y-gridlines
25;plotstyle "wireframe";axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

\item[2.]  \label{a2}\textsf{Plot 2D + Implicit}: $\left( x-1\right)
^{2}+\left( y+2\right) ^{2}=1,\left( x-1\right) ^{2}-\left( y+2\right)
^{2}=1,\left( x-1\right) +\left( y+2\right) ^{2}=0$

(Take $-1\leq x\leq 3$ and $-4\leq y\leq 0$. Choose \textsf{Equal Scaling
Along Each Axis}) \hfill \hyperref{\TCIIcon{BITMAPSETProbSolvHint}{0.2006in}{%
0.243in}{0in}}{}{}{q2}\FRAME{dtbpF}{3.7559in}{2.4811in}{0pt}{}{}{Figure }{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3.7559in;height
2.4811in;depth 0pt;display "PICT";plot-snapshots TRUE;function
\TEXUX{$\left( x-1\right) ^{2}+\left( y+2\right) ^{2}=1$};linecolor
"red";linestyle 1;linethickness 1;pointstyle "point";function \TEXUX{$\left(
x-1\right) ^{2}-\left( y+2\right) ^{2}=1$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";function \TEXUX{$\left( x-1\right)
+\left( y+2\right) ^{2}=0$};linecolor "green";linestyle 1;linethickness
1;pointstyle "point";xmin "-1";xmax "3";ymin "-4";ymax "0";xviewmin
"-1.08";xviewmax "3.082";yviewmin "-3.799";yviewmax
"-0.1993";rangeset"XY";phi 45;theta 45;plottype 12;constrained
TRUE;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"normal";xis \TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name
\TEXUX{$y$};}}

\item[3.]  \label{a3}\textsf{Plot 2D + Implicit}: $%
x^{2}+y^{2}=4,x^{2}-y^{2}=1$

(Take $-5\leq x\leq 5$ and $-5\leq y\leq 5$. Choose \textsf{Equal Scaling
Along Each Axis})\FRAME{dtbpF}{3.813in}{2.5253in}{0pt}{}{}{Figure }{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3.813in;height
2.5253in;depth 0pt;display "PICT";plot-snapshots TRUE;function
\TEXUX{$x^{2}+y^{2}=4$};linecolor "red";linestyle 1;linethickness
1;pointstyle "point";function \TEXUX{$x^{2}-y^{2}=1$};linecolor
"blue";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";ymin "-5";ymax "5";xviewmin "-5.2";xviewmax "5.204";yviewmin
"-5.091";yviewmax "5.095";rangeset"XY";phi 45;theta 45;plottype
12;constrained TRUE;num-x-gridlines 25;num-y-gridlines 25;plotstyle
"wireframe";axesstyle "normal";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}}

\hfill \hyperref{\TCIIcon{BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{%
}{q3}

\textsf{Solve + Numeric}: $
\begin{array}{c}
x^{2}+y^{2}=4 \\ 
x^{2}-y^{2}=1 \\ 
x\in \left( 1,2\right) \\ 
y\in \left( 1,2\right)
\end{array}
$, Solution is : $\left\{ x=1.58113883,y=1.224744871\right\} $

\item[4.]  \label{a4}\textsf{Plot 2D + Implicit}: $\left| x\right|
^{2/3}+\left| y\right| ^{2/3}=1$

(Take $-1\leq x\leq 1$ and $-1\leq y\leq 1$.)\FRAME{dtbpF}{3.9998in}{2.6446in%
}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3.9998in;height 2.6446in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$\left| x\right| ^{2/3}+\left|
y\right| ^{2/3}=1$};linecolor "magenta";linestyle 1;linethickness
1;pointstyle "point";xmin "-1";xmax "1";ymin "-1";ymax "1";xviewmin
"-1.04";xviewmax "1.041";yviewmin "-1.04";yviewmax "1.041";rangeset"XY";phi
45;theta 45;plottype 12;constrained TRUE;num-x-gridlines 25;num-y-gridlines
25;plotstyle "wireframe";axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

Without the absolute values, \textsl{Scientific Notebook} returns only the
first quadrant portion of the graph.\hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q4}

\item[5.]  \label{a5}\textsf{Plot 2D + Implicit}: $x^{3}+y^{3}=6xy$

(Take $-5\leq x\leq 5$ and $-5\leq y\leq 5$ and set the grid to 50 by 50.)%
\FRAME{dtbpF}{2.6507in}{2.6507in}{0pt}{}{}{Figure }{\special{language
"Scientific Word";type "MAPLEPLOT";width 2.6507in;height 2.6507in;depth
0pt;display "PICT";plot-snapshots TRUE;function
\TEXUX{$x^{3}+y^{3}=6xy$};linecolor "navy";linestyle 1;linethickness
1;pointstyle "point";xmin "-5";xmax "5";ymin "-5";ymax "5";xviewmin
"-5.163";xviewmax "3.34";yviewmin "-5.163";yviewmax "3.34";rangeset"XY";phi
45;theta 45;plottype 12;constrained TRUE;num-x-gridlines 50;num-y-gridlines
50;plotstyle "wireframe";axesstyle "normal";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

Notice how the folium of Descartes shows up as a level curve on the surface $%
z=x^{3}+y^{3}-6xy$.\vspace{6pt}

\textsf{Plot 3D + Rectangular:} $x^{3}+y^{3}-6xy$

(Use \textsf{Patch \& Contour} and take $-5\leq x\leq 5$, $-5\leq y\leq 5$, 
\textsf{Turn} 16, and \textsf{Tilt} 34.)\hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q5}\FRAME{dtbpF}{3in}{%
2.0003in}{0pt}{}{}{}{\special{language "Scientific Word";type
"MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$x^{3}+y^{3}-6xy$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-5";xmax
"5";ymin "-5";ymax "5";xviewmin "-5.2";xviewmax "5.204";yviewmin
"-5.2";yviewmax "5.204";zviewmin "-411.8";zviewmax "200";rangeset"X";phi
34;theta 16;plottype 5;num-x-gridlines 25;num-y-gridlines 25;plotstyle
"patchcontour";axesstyle "none";plotshading "Z";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

\item[6.]  \label{a6}\textsf{Plot 3D + Rectangular}: $\sin xy$

(Choose \textsf{Patch and Contour} and take $-4\leq x\leq 4$, $-4\leq y\leq
4 $, \textsf{Turn} 108, and \textsf{Tilt} 17.)\ \FRAME{dtbpF}{3.8484in}{%
2.5694in}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3.8484in;height 2.5694in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$\sin xy$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";xmin "-4";xmax
"4";ymin "-4";ymax "4";xviewmin "-4.16";xviewmax "4.163";yviewmin
"-4.16";yviewmax "4.163";zviewmin "-1.04";zviewmax "1.041";phi 18;theta
109;plottype 5;num-x-gridlines 25;num-y-gridlines 25;plotstyle
"patchcontour";axesstyle "none";plotshading "Z";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

\textsf{Plot 2D + Implicit}: $xy=\pi /2,xy=5\pi /2,xy=3\pi /2$

(Take $-4\leq x\leq 4$ and $-4\leq y\leq 4$.)\hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q6}\FRAME{dtbpF}{4.0482in%
}{2.6991in}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 4.0482in;height 2.6991in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$xy=3\pi /2$};linecolor
"black";linestyle 1;linethickness 1;pointstyle "point";function
\TEXUX{$xy=\pi /2$};linecolor "red";linestyle 1;linethickness 1;pointstyle
"point";function \TEXUX{$xy=5\pi /2$};linecolor "blue";linestyle
1;linethickness 1;pointstyle "point";xmin "-4";xmax "4";ymin "-4";ymax
"4";xviewmin "-4.16";xviewmax "4.163";yviewmin "-4.16";yviewmax
"4.163";rangeset"XY";phi 45;theta 45;plottype 12;num-x-gridlines
25;num-y-gridlines 25;plotstyle "wireframe";axesstyle "normal";xis
\TEXUX{x};yis \TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

\item[7.]  \label{a7}\textsf{Plot 3D + Rectangular}: $[s,\cos t,\sin
t],[\cos t,s,\sin t]$

(Take $-2\leq s\leq 2$ and $0\leq t\leq 2\pi $.)\ \hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q7}\FRAME{dtbpF}{3.4489in%
}{2.2987in}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3.4489in;height 2.2987in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$[s,\cos t,\sin t],[\cos t,s,\sin
t]$};linecolor "black";linestyle 1;linethickness 1;pointstyle "point";xmin
"-2";xmax "2";ymin "0";ymax "6.28";xviewmin "-2.08";xviewmax
"2.082";yviewmin "-2.08";yviewmax "2.082";zviewmin "-1.04";zviewmax
"1.041";phi 45;theta 45;plottype 5;num-x-gridlines 25;num-y-gridlines
25;plotstyle "hidden";axesstyle "none";plotshading "Z";xis \TEXUX{s};yis
\TEXUX{t};var1name \TEXUX{$s$};var2name \TEXUX{$t$};}}

\item[8.]  \label{a8}\textsf{Plot 3D + Tube}: $\left[ 
\begin{array}{c}
(2+\sin t)10\cos t \\ 
(2+\cos t)10\sin t \\ 
3\sin 3t
\end{array}
\right] ;$ drag $\left[ 
\begin{array}{c}
20\cos t \\ 
20\sin t \\ 
-3\sin 3t
\end{array}
\right] $ onto the plot, set $0\leq t\leq 2\pi $, and set the radius for
both items to 1.\hfill \hyperref{\TCIIcon{BITMAPSETProbSolvHint}{0.2006in}{%
0.243in}{0in}}{}{}{q8}\FRAME{dtbpF}{3.4489in}{2.2987in}{0pt}{}{}{Figure }{%
\special{language "Scientific Word";type "MAPLEPLOT";width 3.4489in;height
2.2987in;depth 0pt;display "PICT";plot-snapshots TRUE;function
\TEXUX{$\MATRIX{1,3}{c}\VR{,,c,,,}{,,,,,}\HR{,,,}\CELL{20\cos t}\CELL{20\sin
t}\CELL{-3\sin 3t}$};linecolor "black";linestyle 1;linethickness
1;pointstyle "point";radius \TEXUX{$1$};function
\TEXUX{$\MATRIX{1,3}{c}\VR{,,c,,,}{,,,,,}\HR{,,,}\CELL{(2+\sin t)10\cos
t}\CELL{(2+\cos t)10\sin t}\CELL{3\sin 3t}$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";radius \TEXUX{$1$};xmin "0";xmax
"6.28";xviewmin "-23.86";xviewmax "23.95";yviewmin "-23.91";yviewmax
"23.91";zviewmin "-4.156";zviewmax "4.162";rangeset"X";phi 45;theta
45;plottype 13;num-x-gridlines 50;num-y-gridlines 10;plotstyle
"patch";axesstyle "none";plotshading "Z";xis \TEXUX{t};}}

\textsf{Solve + Exact}:

$
\begin{array}{c}
(2+\sin t)10\cos t=20\cos s \\ 
(2+\cos t)10\sin t=20\sin s \\ 
3\sin 3t=-3\sin 3s
\end{array}
$, Solution is : $\left\{ t=0,s=0\right\} ,\left\{ t=\pi ,s=\pi \right\} $

\item[9.]  \label{a9}\textsf{Plot 3D + Rectangular}: $\sqrt{\left(
-x^{2}-y^{2}+1\right) },-\sqrt{\left( -x^{2}-y^{2}+1\right) },\frac{1}{2}%
-\left( x+y\right) $

(Take $-1\leq x\leq 1$, $-1\leq y\leq 1$, $-1\leq z\leq 1$, and style 
\textsf{Patch \& Contour}.)

\FRAME{dtbpF}{3in}{2.0003in}{0pt}{}{}{}{\special{language "Scientific
Word";type "MAPLEPLOT";width 3in;height 2.0003in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$\sqrt{\left(
-x^{2}-y^{2}+1\right) },-\sqrt{\left( -x^{2}-y^{2}+1\right)
},\frac{1}{2}-\left( x+y\right) $};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-1";xmax "1";ymin "-1";ymax
"1";xviewmin "-1.04";xviewmax "1.041";yviewmin "-1.04";yviewmax
"1.041";zviewmin "-1.04";zviewmax "1.041";viewset"XYZ";rangeset"XYZ";phi
66;theta 45;plottype 5;num-x-gridlines 25;num-y-gridlines 25;plotstyle
"patchcontour";axesstyle "boxed";plotshading "Z";xis \TEXUX{x};yis
\TEXUX{y};var1name \TEXUX{$x$};var2name \TEXUX{$y$};}}

\textsf{Simplify:} $x^{2}+y^{2}+\left( \frac{1}{2}-\left( x+y\right) \right)
^{2}=\allowbreak 2x^{2}+2xy+2y^{2}-x-y+\frac{1}{4}=1$

$\bigtriangleup \,=B^{2}-4AC=2^{2}-4\times 2\times 2=\allowbreak -12<0$,
implying the curve is an ellipse or circle.\hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q9}

\item[10.]  \label{a10}\textsf{Plot 3D + Rectangular}: $xy$

(This is the default plot with settings $-5\leq x\leq 5$, $-5\leq y\leq 5$,
and style \textsf{WireFrame}.) \hfill \hyperref{\TCIIcon{%
BITMAPSETProbSolvHint}{0.2006in}{0.243in}{0in}}{}{}{q10}\FRAME{dtbpF}{%
4.0482in}{2.6991in}{0pt}{}{}{Figure }{\special{language "Scientific
Word";type "MAPLEPLOT";width 4.0482in;height 2.6991in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$xy$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-5";xmax "5";ymin "-5";ymax
"5";xviewmin "-5.2";xviewmax "5.204";yviewmin "-5.2";yviewmax
"5.204";zviewmin "-26";zviewmax "26.02";phi 45;theta 45;plottype
5;num-x-gridlines 25;num-y-gridlines 25;plotstyle "wireframe";axesstyle
"none";plotshading "Z";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}}

(Take $-1\leq x\leq 1$, $-1\leq y\leq 1$, \textsf{Turn} $90$, \textsf{Tilt} $%
0$, and choose the style \textsf{Patch \& Contour}.)\FRAME{dtbpF}{3.9885in}{%
2.6576in}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3.9885in;height 2.6576in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$xy$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-1";xmax "1";ymin "-1";ymax
"1";xviewmin "-1";xviewmax "1";yviewmin "-1";yviewmax "1";zviewmin
"-1";zviewmax "1";viewset"XYZ";rangeset"XYZ";phi 0;theta 90;plottype
5;num-x-gridlines 25;num-y-gridlines 25;plotstyle "patchcontour";axesstyle
"none";plotshading "Z";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}}

(Take $-1\leq x\leq 1$, $-1\leq y\leq 1$, \textsf{Turn} $90$, \textsf{Tilt} $%
90$, and choose the style \textsf{Patch \& Contour}.)\FRAME{dtbpF}{3.9885in}{%
2.6576in}{0pt}{}{}{Figure }{\special{language "Scientific Word";type
"MAPLEPLOT";width 3.9885in;height 2.6576in;depth 0pt;display
"PICT";plot-snapshots TRUE;function \TEXUX{$xy$};linecolor "black";linestyle
1;linethickness 1;pointstyle "point";xmin "-1";xmax "1";ymin "-1";ymax
"1";xviewmin "-1";xviewmax "1";yviewmin "-1";yviewmax "1";zviewmin
"-1";zviewmax "1";viewset"XYZ";rangeset"XYZ";phi 90;theta 90;plottype
5;num-x-gridlines 25;num-y-gridlines 25;plotstyle "patchcontour";axesstyle
"none";plotshading "Z";xis \TEXUX{x};yis \TEXUX{y};var1name
\TEXUX{$x$};var2name \TEXUX{$y$};}}
\end{enumerate}

\subsection{\ Related topics}

\begin{itemize}
\item  \hyperref{Plotting Curves and Surfaces}{}{}{DM6-1.tex#Plotting}

\item  \hyperref{Frame Properties}{}{}{DM6-2.tex#Frame Properties}

\item  \hyperref{The View for 2D Plots}{}{}{DM6-3.tex#View intervals}

\item  \hyperref{2D Plots of Functions and Expressions}{}{}{DM6-4.tex#Plot
expression}

\item  \hyperref{The View Box for 3D Plots}{}{}{DM6-5.tex#Plot 3D, view}

\item  \hyperref{3D Plots of Functions and Expressions}{}{}{DM6-6.tex#3D
Plots}
\end{itemize}

\rule{0.67in}{0.01in}

\hyperref{\FRAME{itbpF}{38.875pt}{24.5pt}{6pt}{}{}{index.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "PICT";valid-file "F";width 38.875pt;height 24.5pt;depth
6pt;original-width 36.125pt;original-height 22.5625pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'index.wmf';file-properties
"XNPEU";}}}{}{}{DMIndex.tex#Math Index}\quad {\small Index entries: 
\hyperref{Curves in space}{}{}{DMIndex.tex#Curves in space}, \hyperref{%
Cylindrical coordinates}{}{}{DMIndex.tex#Cylindrical coordinates}, \hyperref{%
Plot properties}{}{}{DMIndex.tex#Plot properties}, \hyperref{Plotting tools}{%
}{}{DMIndex.tex#Plotting tools}, \hyperref{Surfaces of revolution}{}{}{%
DMIndex.tex#Surfaces of revolution}, \hyperref{Tube plots}{}{}{%
DMIndex.tex#Tube plots}}

\end{document}
