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\centerline
{
Answers to the Four Practice Exams for Exam II
}
\bigskip

{\bf First Practice Exam}

1. $7$ 

2. $-8$

3. ${{40960 \pi} \over {11}}$

4. ${{3} \over {2}}$

5. ${{32 \sqrt{2}} \over {5}}$ 

6. ${{\pi} \over {4}}(e^9-1)$

7. $3e^9$

8. ${{32} \over {45}}$

9. $3456$ 

10. $35$ .

\bigskip

{\bf Second Practice Exam}

1. $f=e^x+e^y+e^z+xyz$ .

2. $1- \cos(11\pi/26)$ (also $1-\sin(\pi/13)$).

3. $-6(u-v)(u-w)(v-w)$

4. ${{280} \over {3}}$

5. $-{{1} \over {3}}$ (corrected Nov. 13, 2009, 11:07am, thanks to Elazar Klein, who won \$10).

6. $ {{3^{12}} \over {8}}\pi$

7. ${{8} \over {15}}$

8. ${{16 \ln 2} \over {3}}$

9. $\int_{0}^{1} \int_{e}^{e^3} f(x,y) \, dx  \, dy$ +$\int_{1}^{3} \int_{e^y}^{e^3} f(x,y) \, dx  \, dy$

10. None ; ${{-17} \over {8}}$ at $(1/2,1/2)$ and $(-1/2,-1/2)$ ; $(0,0)$


\vfill\eject

{\bf Third Practice Exam}

1. ${{e^6-1} \over {2}}$ 

2. $7$

3. ${{2\pi(3^{21}-1)} \over {21}}$ 

4. Picture

5. $-4$

6. ${{162} \over {5}}$ 

7. ${{1} \over {6}}$

8. ${{16} \over {63}}$

9. None; None; $(3,-3)$ and $(-3,3)$.

10. ${{5} \over {8}}$


{\bf Fourth Practice Exam}

1. $8$ 

2. $136$

3. $54$

4. $e-1$

5. ${{\pi(e-1)} \over {8e}}$

6. ${{\pi(1-e^{-4})} \over {8}}$ (or  ${{\pi(e^4-1)} \over {8e^4}}$ )

7. ${{2\sqrt{2} -1} \over {10}}$

8. $1+ 5 \sqrt{13}$ ; $1- 5 \sqrt{13}$ 

9.${{8} \over {15}}$

10. $\int_0^8 \int_0^{\root 3 \of {y} } g(x,y) \, dx \, dy$

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