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\flushright Class (circle one) ~~~~~~~~~~~~~~ 9:40 ~~~~~~ 10:45\\
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\begin{center}

Math 1210\\
Fall 2009\\
K. M. Golden
\vspace{5ex}

{\large {\bf EXAM I}}

\vspace{2ex}
Friday, September 18, 2009
\vspace {15ex}

\begin{tabular}{|l|l|l|l|l|l|l|}
%\hline
%\multicolumn{2}{|c|}{Dept. Use Only}\\
%\multicolumn{2}{|c|}{Exam Scores}\\
\hline
Problem &Points & Score~~~~~~\\
\hline
1.~~ & 10 & \\
\hline
2.~~ & 15 & \\
\hline
3.~~ & 20 & \\
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4.~~ & 30 &\\
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5.~~ & 10 &\\
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6.~~ & 15 &\\
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&TOTAL&\\
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\begin{enumerate}

\item[(10 points) ~~1.] 

\begin{enumerate}
\item[(a)] Find the equation of the line containing the two points
 $P=(-1,2)$ and $Q=(1,1)$ in the form $y=mx+b$.


\vspace{60ex}


\item[(b)] Find the derivative $\ds \frac{dy}{dx}$ 
           of the expression for $y(x)$ you found in (a). 
          


\end{enumerate}


\eject


\item[(15 points) ~~2.]  Find the following limits.


\begin{enumerate}
\item[(a)] $\ds \lim_{\Delta x \rightarrow 0} 
                (2 + 5\Delta x) $
\vspace{30ex}

\item[(b)] $\ds \lim_{h \rightarrow 0} 
        \frac{4xh+5h^3}{h}$
\vspace{35ex}
\item[(c)] $\ds \lim_{h \rightarrow 0}
       \frac{\sqrt{x+h}\;-\;\sqrt{x}}{h}$ 
%      \left({\frac{1}{x+h}}-{\frac{1}{x}}\right)
%       \left(\frac{1}{h}\right)$
\vfill

\end{enumerate}
\eject

\item[(20 points) ~~3. (a)]  Let $f(x) = x^2+5$.  Using the {\it
      definition} of the derivative, calculate $f'(x)$.
      Be sure to show all of your work.
      
\vspace{60ex}
\item[(b)]  Using your result from (a), find the equation of
      the line tangent to the graph of $f(x) = x^2+5$ at 
      $x = 2$. 

\eject



\item[(30 points) ~~4.]  Find the following.

\begin{enumerate}
\item[(a)] $\ds \frac{d}{dx} \left( 3x^5+x^4-2x^2+6 \right)$
\vspace{15ex}

\item[(b)]  $\ds \int{(3x+2)(x-1)\;dx}$
\vspace{20ex}

\item[(c)]  $v(t)$, $\;$ where $\;$ $x(t)=-16t^2+4t+10\;\;$ and $\;$
$\ds v(t)= \frac{dx}{dt}$

%\item[(d)]   $\ds \frac{d^{12}}{dx^{12}}(33x^{11}+18x^{10}-7x^9+4.5x^8-76x^6-2x^5
  %                     -6x^3+x^2-5x+\pi)$

\vspace{15ex}

\item[(d)] $\ds \int_0^2{ (x^2 + 1)  \;dx}$


\vspace{20ex}

\item[(e)] $x(t)$, where $\ds \frac{dx}{dt}=-32t+64$ 
           and $x(0)=50$.


\end{enumerate}
\eject

\item[(10 points) ~~5.] 
%On nearby planet $\Psi$,
%scientists have discovered how to vary their
%%planet's gravitational force with time so that
%the acceleration is $a(t)=-t$, which leads
%to the expression $x(t)=-t^3/6+v_0t+x_0$ for the position
%of a particle in one dimensional vertical motion, 
%where $x_0$ and $v_0$ are the initial position and velocity.
%Using this expression for $x(t)$, find how long it will 
%take for a ball, thrown upward from the ground on $\Psi$
%at $t=0$ with initial velocity 6$\;f/s$, to hit the ground. 
A pebble is dropped from a height of 32 feet. 
Its height above the ground at time $t$ 
is given by $x(t)=-16t^2+32.$ Find $t^*$, the 
time when the pebble hits the ground. 
%Is $t^*$ rational or irrational? 
Find the velocity of the pebble
$v(t^*)=x'(t^*)$ when it strikes the ground.

\vspace{35ex}

\item[(15 points) ~~6.]  
\begin{enumerate}
\item[(a)] Find the antiderivative of $3x^2-2x+2$ that has the 
         value 10 when $x=2$.
\vspace{25ex}

\item[(b)] Find the position $x(t)$ satisfying Newton's law $$\ds \frac{d^2 x}{dt^2}=-32$$
such that $x(0)=0$ and $x'(0)=v(0)=32$. Be sure to show all of your work.

\end{enumerate}

%\eject

%\item[(10 points) ~~7.] 
%Use the Intermediate Value Theorem to show that
%$x^3+3x-2=0$ has a real solution between 0 and 1.

\end{enumerate}

\end{document}
