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\begin{center} Pretest for Calculus II \end{center} 

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Answer the following  ten elementary questions from Calculus I and
algebra. Write your answer on a separate sheet of paper and show your
work.  You should not use a calculator to answer these questions.
Allow 15 minutes for this pretest.

If you are not able to answer 8 of these questions correctly, you may
have difficulty with Calculus II. Doing well on this quiz does not
guarantee success in Calculus II. 

\vskip 0.1in
\begin{enumerate}

\item Write as a single fraction and simplify. 
$$
\frac x { x-2} + \frac x { x+2}.
$$

\item Solve for $x$. Give exact answers.
$$
x^2+ x -3 = 0.
$$

\item Determine if the following limit exists and if the limit exists,
compute its value. 
$$
\lim_{h\rightarrow 1}  \frac   {h-1} { h^2-1}.
$$

\item Find the derivative, $f'(x)$ if 
$$
f(x) = (2 x+1)^5.
$$
\item Find the derivative $f'(x) $ if 
$$
f(x) = \cos(x^2+1).
$$

\item Find the derivative $ f'(x)$ if 
$$
f(x) = \frac { x+1} { x-1}.
$$
Simplify your answer. 

\item Evaluate the integral
$$
\int_0 ^1 x^{1/3}\,dx.
$$

\item Evaluate the integral 
$$
\int_ 0 ^ {\pi/2} \cos(2x) \, dx.
$$

\item Sketch the graph of $ f(t) = |t-1|$ and use your graph to
evaluate the integral  
$$
\int_0 ^ 1|t-1|\, dt.
$$

\item Suppose that we have 150 feet of fence which we use to make a
rectangular pen.  If we let $x$ be one side of the pen, write
a function $A(x)$ which gives the area of the pen as a function of
$x$. 

\end{enumerate}
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