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\begin{document}


   
\begin{center}
{\bf  Math 180 - 8 AM   \hfill Hour Exam 1 \hfill  2/20/2004}
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{Name:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\hfill SSN:\_\_\_\_\_\_\_\_--\_\_\_\_\_\_--\_\_\_\_\_\_\_\_\_\_}\\
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 \begin{center}
{\bf  Section (circle one) :  \hfill 8 AM (Xu) \hfill 9 AM (Brydges)  \hfill  10 AM (Brydges)}
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\centerline{Show {\bf all} of your work. {\bf No work means no credit!}}
\centerline{All work and solutions should be put on the paper provided.}

 
 \bigskip
  


 {\bf Problem 1:}  (10 pts)  Give a formula for a function which has the following graph.

 
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{\bf Problem 2:}  (20 pts) 
 A differentiable function $f(x)$ 
 has the following values given by the table 
$$\matrix{ x  & -2    &  0   &  2  &   4 &  6  &  8 \cr
         f(x) & 2   & 10   &  16  & 20  & 22  & 21    \cr}$$

a) Using the data from this table, make a table of the approximate  values of the derivative function $f'(x)$ for the same values of $x$.

\medskip

b) Is $f(x)$ increasing or decreasing on the interval $-2 \leq x \leq 8$? Explain your answer.
 
 \medskip
 
 c) Using the data from your answer to part a), make a table of the approximate values of the second derivative function $f''(x)$ for the same values of $x$.
 
 \medskip
 
 d)   Is $f(x)$  linear,  concave up, or   concave down on the interval $-2 \leq x \leq 8$?
Explain your answer.

\bigskip


{\bf Problem 3:}  (20 pts)  Let $f(x) = x^3 + x$. Calculate $f'(2)$ \underline{using the limit definition of the derivative}.

\bigskip


{\bf Problem 4:}  (20 pts)
Given the function 
$$
f(x) = \left\{ \begin{array}{ll}
                x^2+x+1    & \mbox{if $x \geq 1$} \\
                3 -x   & \mbox{if $x < 1$}
               \end{array} \right.
$$


(a) State the domain of the function.
\medskip

(b) Determine $\lim_{x \rightarrow 1^-} f(x)$.
\medskip

(c) Determine $\lim_{x \rightarrow 1^+} f(x)$.
\medskip

(d) Is $f(x)$ continuous on its domain? Explain your answer.


\bigskip


{\bf Problem 5:}  (20 pts) Let $\displaystyle f(x) = \frac{3x^2 -3}{x^2 - 4}$.

a) What are the zeros of $f(x)$?

\medskip

b) Find all asymptotes for $f(x)$.
\medskip

c) Made a careful graph of $y = f(x)$. Be sure to label the axes, label the zeros and indicate all asymptotes.

\bigskip

{\bf Problem 6:}  (10 pts)  Suppose that  $f(2)=-5$ and $f'(2) = 3$.
 Write the formula for the tangent line   to $f$ at $x= 2$.

\bigskip

\centerline{\bf Return this copy of the exam with your solutions.}

 
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