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\begin{document}

\begin{center}
\bf{MATH 120\\Exam 1\\9-25-02}
\end{center}
\vskip.5in

1.  Let $f(x) = x + cos x$ and let $g$ be the inverse function of $f$. 
Find the value of $g'(1)$

\begin{tabbing}
(A) $0$ \hskip1in (B) ${\frac{1}{2}}$ \hskip 1in (C) $1$ \hskip1in (D)
${\frac{3}{2}}$\hskip1in (E) $2$
\end{tabbing} 

\newpage


2. Let $f(x) = e^{-x{^2}}$ Find the value of $f'(1)$.

\begin{tabbing}
(A) $2e^{-1}$ \hskip1in (B) $-2e^{-1}$ \hskip 1in (C) $-2e$ \hskip1in (D)
$-e$\hskip1in (E) $e$
\end{tabbing} 

\newpage

3.  Find the value of $log_21$.


\begin{tabbing}
(A) $-1$ \hskip1in (B) $-\frac{1}{2}$ \hskip1in (C) $0$ \hskip1in (D)
$10^2$\hskip1in (E) $1$
\end{tabbing} 


\newpage

4.  Solve the equation:  $e^{2x-2}=4$


\begin{tabbing}
(A) $\ln 2$ \hskip.75in (B) $1-\ln 2$ \hskip.75in (C) $1+\ln 2$ \hskip.75in (D)
$1-2\ln2$\hskip.75in (E) $1+2\ln 2$
\end{tabbing}

\newpage

5.  Let $f(x)=\ln(x^2)$.  Find the value of $f'(1)$.



\begin{tabbing}
(A) $2^e$ \hskip1in (B) $e^2$ \hskip1in (C) $\ln(\frac{1}{2})$ \hskip1in (D)
$2$\hskip1in (E) $e^{-\frac{1}{2}}$
\end{tabbing}


\newpage

6.  Find the value of the integral  $\int^e_1 \frac{dx}{x}$.


\begin{tabbing}
(A) $1$ \hskip1in (B) $e$ \hskip1in (C) $\frac{1}{2}$ \hskip1in (D)
$-1$\hskip1in (E) $-2$
\end{tabbing} 


\newpage

7.  Find the value of the integral $\int^1_0 \frac{xdx}{1+x^2}$.

\begin{tabbing}
(A) $1$ \hskip1in (B) $\frac{1}{2} \ln2$ \hskip1in (C) $2\ln 2$ \hskip1in (D)
$\frac{1}{\ln2}$\hskip1in (E) $\ln2$
\end{tabbing} 


\newpage

8.  Find the interval on which $f(x)=xe^{-x}$ is increasing.

\begin{tabbing}
(A) $(- \infty\ 1 \ ]$ \hskip.75in (B) $(-\infty, 2]$ \hskip.75in (C) $(-\infty, 3]$ \hskip.75in (D)
$[1,2]$\hskip.75
in (E) $[1,e]$
\end{tabbing} 


\newpage

9.  Find the value of $cos^{-1}(\frac{1}{2})$.

\begin{tabbing}
(A) $\frac{\pi}{8}$ \hskip1in (B) $\frac{\pi}{6}$ \hskip1in (C) $\frac{\pi}{2}$ \hskip1in (D)
$\frac{\pi}{12}$\hskip1in (E) $\frac{\pi}{3}$
\end{tabbing} 


\newpage

10.  Let $f(x) = \arctan x$.  Find the value of $f'(1)$.


\begin{tabbing}
(A) $-\frac{1}{2}$ \hskip1in (B) $\frac{1}{2}$ \hskip1in (C) $-\frac{1}{3}$ \hskip1in (D)
$1$\hskip1in (E) $\frac{1}{3}$
\end{tabbing} 


\end{document}

