\def\wsn{34}
\input worksheet.tex

\centerline{\bf a.k.a. Practice Exam 3}

\bigskip\bigskip
\item{1.} {\bf(warm-up)} Compute the following antiderivatives:
$$
\pt a \int{e^{2x}+e^x\over e^x}\,dx\hskip.5in
\pt b \int{x^5+x+1\over x}\,dx\hskip.5in
\pt c \int(2\cos x+\sec^2x)\,dx\hskip.5in
\pt d \int{1+\sqrt x\over\sqrt x}\,dx
$$

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\item{2.}  Compute the following indefinite intrgrals:
$$
\pt a \int{x\over\sqrt{1+x}}\,dx\hskip1in
\pt b \int{1\over\sin^2 x\sec x}\,dx\hskip1in
\pt c \int{x\sqrt{1-x^2}}\,dx
$$

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\item{3.}  Compute the following definite integrals:
$$
\displaylines{
\pt a \int_0^{\pi/4}2\sec x\tan x\,dx\hskip1in
\pt b \int_1^{e^2}{1\over x(1-\ln x)}\,dx\hskip1in
\pt c \int_0^1x\sqrt{e^{x^2}}\,dx\cr\cr
\pt d \int_0^1{1\over\sqrt{e^x}}\,dx\hskip1in
\pt e \int_0^4{e^{\sqrt x}\over\sqrt x}\,dx\cr}
$$

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\item{4.}  Let $f(x)=x(\ln x)^2$ on the interval $[e^{-4},e^1]$.

\medskip
\itemitem{a)}  Differentiate and simplify.

\medskip
\itemitem{b)}  Find all points $c$ where $f'(c)=0$ or $f'(c)$ does not exist. 

\medskip
\itemitem{c)}  Use the first derivative test to classify the above points.

\medskip
\itemitem{d)}  Find all local and global extremes

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\item{5.}  Let $f(x)=xe^{-x^2}$ on the interval $[-1,1]$.

\medskip
\itemitem{a)}  Differentiate and simplify.

\medskip
\itemitem{b)}  Find all points $c$ where $f'(c)=0$ or $f'(c)$ does not exist. 

\medskip
\itemitem{c)}  Use the first derivative test to classify the above points.

\medskip
\itemitem{d)}  Find all local and global extremes


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\item{6.}  Integrate:
$$
\pt a \int x(x+1)^5\,dx\hskip.7in
\pt b \int_1^e{\sqrt{\ln x}\over x} \,dx\hskip.7in
\pt c \int e^x\sqrt{e^x}\,dx\hskip.7in
\pt d \int{\sec^2x\over\tan x}\,dx
$$




\bye