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\begin{flushleft} Recitation 1\hfill \course\\
27 August 1998 \hfill \semester \\
\medskip

Below are a selection of problems over section 1.1 and section 1.3 on
graphing calculators. You should form groups of 3 to 5 and begin work
on these problems.  The teaching assistant will be available to answer
questions as they arise.  You should finish all of these
problems. This will probably require time outside of class. 

These problems will not be collected or graded. 

\begin{enumerate}

\item Work problems 1, 2, 5, 7, 21, 23, 43, 45, 49, 51 from section
1.1 of Stewart. 

\item Using your graphing calculator, graph the functions 
\begin{eqnarray*}
f(x) & = & x^2 \\
g(x) & = & (x-1) ^ 2 + 2 
\end{eqnarray*}
in the same window. 
How are the graphs the same? How are they different?
\item Using your graphing calculator,
graph the functions
\begin{eqnarray*}
f(x)&  =& \sin(x) \\
f(x) & =& \sin(2x)\\
h(x)& = &2 \sin (x) 
\end{eqnarray*}
in the same window.
How are the graphs the same? How are they different?

\item Graph the function 
$$
f(x) = \sin(75 x) 
$$
for $ -2 \leq x \leq 2$.  Now make a small change in the window, say
$-1.9 \leq x \leq 2$. What happens to the graph?  Do you think the
graphs are right? Why does the TI-82 have problems with this function?

\item For the following exercises, you are to graph a  parametric curve.
 To do this on the TI-82, touch the {\tt mode} key, push the
down 
arrow three times until you reach the line with {\tt Func Par Pol
Seq},
touch the left or right arrows to select {\tt Par} and touch the {\tt
Enter } and then {\tt 2nd, Quit}.
Now to graph a parametric curve, touch the {\tt Y= } key, and enter
the expressions below for $x(t)$ and $y(t)$. Finally, touch the {\tt
Window } key to adjust the interval for $t$ and the {\tt Graph } key to draw the
curve.

\begin{enumerate} \item Graph circle of radius 2. 
$$
x(t) = 2 \cos t , \qquad y(t) = 2 \sin (t) , \qquad 0 \leq t \leq 2
\pi.
$$
Does the circle  look round?  How can you adjust the window to make the
circle look like a circle?

\item Graph the parametric curve
$$
x(t ) = 2 \cos(-t), \qquad y ( t) = 2 \sin (-t).
$$
How does this compare with the curve in the previous question?

\item Graph the curve 
$$
x(t) = 2\cos( t) , \qquad \sin( 2t), \qquad 0 \leq t \leq \pi
$$
What happens if you increase the interval for $t$?

\end{enumerate}

\item Stewart, section 1.3 \#17 and \#23. For \#17, you might graph
the left hand side of the equation and then use the 
{\tt root }  entry on the {\tt 2nd Calc } menu.

\end{enumerate}
\end{flushleft}
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