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\noindent
{\Large {\bf Mathematics 1210  \hspace{3ex} PRACTICE EXAM I 
\hspace{6ex}Fall 2004}}
%\vspace{2ex}\\
\begin{center}
{\Large {\bf ANSWER KEY}}
\end{center}
\vspace{2ex}

\begin{enumerate}

\item[1.]  
%(a) 6 \hspace{3ex} (b) DNE, $\longrightarrow \pm \infty$

\begin{enumerate}
 \item[(a)] 6
 \hspace{4ex}
% \item[(b)] 
(b) DNE; $\longrightarrow \pm \infty$
\hspace{4ex}
% \item[(c)] 
(c)  DNE; $\longrightarrow \pm \infty$
\hspace{4ex}
% \item[(d)] 
(d) 0
 \item[(e)] 0 
\hspace{4ex}
(f) 0
\hspace{4ex}
(g) DNE; LHL $\neq$ RHL
\hspace{4ex}
(h) 0
\hspace{4ex}
(i) 2

\end{enumerate}



\item[2.] 
\begin{enumerate}
\item[(a)] $\ds f'(x) = \frac{1}{2\sqrt{x}}\;,\;\;\;\;\;
g'(x) = \frac{-1}{x^2}\;\;\;\;\;$  (see pp. 108-109) 
\item[(b)]  $\ds y=\frac{1}{2}x  + \frac{1}{2}\;, \;\;\;\;\;\;\;
         y = -x + 2$
\end{enumerate}


\item[3.] See attached page.

\begin{enumerate}
\item[(a)]  all points except $x=1$
%\vfill
\item[(b)]  all points except $x=-1,1$
%\vfill
\item[(c)] all points except $x=-1,0,1,3$
\end{enumerate}


\item[4.] See attached page.


\item[5.] 
\begin{enumerate}
\item[(a)] $\ds f'(x) = 60x^4+20x^3+2x+2, \;\;\;\; 
            \int{f(x)dx}=2x^6+x^5+\frac{1}{3}x^3+x^2+x+C$  
\item[(b)]  $\ds f'(x) = 3(x+1)^2, \;\;\;\;
            \int{f(x)dx}=\frac{1}{4}(x+1)^4+C$
\item[(c)]  $\ds f'(x) = 9x^2-10x+3, \;\;\;\; 
            \int{f(x)dx}=\frac{3}{4}x^4-\frac{5}{3}x^3+\frac{3}{2}x^2-x+C$ 
\end{enumerate}





\item[6.] $v(t)=6t-2;\;\;\;v=0$ when $\ds t=\frac{1}{3},\;\; x=\frac{2}{3}$



%(a) $\ds \frac{-2}{(x-1)^2} $ \hspace{2ex}
%(b) $\ds \frac{3}{2} \sqrt{x}$ \hspace{2ex}
%(c) $\ds \frac{-(3x^2+6x+2)}{(x^3+3x^2+2x+1)^2}$  \hspace{2ex}
%(d) $\ds 2x\cos{x}-(x^2+1)\sin{x}$



\item[7.] $x(t)=-16t^2+22$. Setting $x(t^*)=6$ yields $t^*=1$ second; 
        $v(t)=-32t,$ so that $v(1)=-32$ feet/second

\item[8.] $\ds x(t)=-\frac{t^3}{6}+v_0 t +x_0; \;\;\; x(t^*)=0$ with $v_0=6$ and $x_0=0$  
            $\Longrightarrow t^*=6$
           seconds


\end{enumerate}

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