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{\bf Math 120. - Exam 2 - October 30, 2002}

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1. Let $f(x) = sinhx$.  Find the value of $f'(0)$.\\

A)  $ \sqrt{2}$ \hskip1in  B)  $\frac{1}{2}$\hskip1in  C)
$2$\hskip1in  D)  $\frac{1}{3}$ \hskip1in E)  $1$\\


2.  Find the value of the limit  $\lim_{x \to 0^+}$$ \frac{x}{\sin x
+ \tan x}$.\\


A)  $-2$ \hskip1in  B)  $0$\hskip1in  C)  $-\frac{1}{2}$\hskip1in  D)
$\frac{1}{4}$ \hskip1in E)  $\frac{1}{2}$\\


3.  Find the value of the integral  $\int_{0}^{1}xe^x dx$\\

A)  $2$ \hskip1in  B)  $e^2-e$\hskip1in  C)  $1$\hskip1in  D)  $e^2$
\hskip1in E)  $e$\\

4.  Find the value of the integral $\int^{\pi}_{0}x \sin x dx$\\

A)  $4\pi-2$ \hskip.8in  B)  $2\pi-2$\hskip.9in  C)
$\frac{\pi}{2}$\hskip.9in  D)  $4\pi-4$ \hskip.9in E)  $\pi$\\

5.  Evaluate the following integral $\int\frac{ln(2x) dx}{x}$\\

A)  $ln(2lnx)+C$ \hskip1in  B)  $ln(2lnx)+\frac{1}{2} (\ln x)^2
+ C$ \hskip1in  C)
$(ln2)(lnx)+\frac{1}{2}(lnx)^2+C$\hskip1in

D)  $(ln2)(lnx)+(lnx)^2+C$ \hskip1in E)
$\frac{1}{2}(lnx)^2+C$\\

6.  Find the value of the integral $\int^{\pi}_{0} \sin^2 x dx$\\

A)  $2\pi-4$ \hskip.9in  B)  $\pi-2$\hskip.9in  C) $ \pi-1$\hskip.9in
D)  $\pi$ \hskip.9in E)  $\frac{\pi}{2}$\\


7.  Find the value of the integral $\int^{\pi}_{0} \sin^2 x \cos x dx$\\

A)  $\frac{4}{3}$ \hskip1in  B)  $1$\hskip1in  C)  $0$\hskip1in  D)
$\frac{2}{3}$ \hskip1in E)  $4\frac{\pi}{3}$\\

8.  Find the integral $\int\frac{\tan^2x}{\cos^2x}dx$\\

A)  $\frac{1}{3}\tan^3x+C$ \hskip.4in  B)  $\cos x \tan^{2}x
+C$\hskip.4in  C)  $\ln \tan x +C$\hskip.4in  D)  $\cos^3 + C$ \hskip.4in
E)
$\ln |\cos x| + C$\\


9.  Find the value of the integral $I=\int^{1}_{0} \frac{dx}{\sqrt{x^2+1}}$\\


A)  $1$ \hskip.7in  B)  $\ln(\sqrt{2}-1)$\hskip.7in  C)$
\ln(\sqrt{3}+1)$ \hskip.7in   D) \  $\ln2$ \hskip.7in E)
$\ln(\sqrt{2}+1)$\\


10.  Find the value of the integral $\int^{\frac{1}{2}}_{0}
\frac{x^2}{x^2-1} dx$\\

A)  $\frac{1}{2}(1-\ln 3)$ \hskip.6in  B)  $\ln3$\hskip.6in
C)$1-\ln\frac{3}{4}$ \hskip.6in   D) $1 + \ln(\frac{3}{4})$ \hskip.6in  E)
$1 + \ln 3$
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