Review for Third Exam

1. Page 410-411, problems 11, 12, 13, 14, 15, 16, 17, 18, 23, 24.
2. Page 416, problems 9-12, 13-20, 24.
3. Page 422, problems 4, 5, 6, 7, 10, 11, 12, 13, 16, 17.
4. Page 428, problems 11-21.
5. Page 429, problems 5-16.
6. Page 440, problems 1, 3, 4, 5, 7, 13, 31.
7. Page 445, problems 1-4, 5-11.
8. Page 451, problems 1-12.
9. The theory of relativity predicts that a moving object has greater mass. The relativistic mass, $m$ , of the object when it is moving at speed $v$ is given by the formula
   $$m = \frac{m_{0}}{\sqrt{1-v^{2}/c^{2}}}$$
   where $c$ is the speed of light and $m_{0}$ is the mass of the object when it is at rest.
   1. What values of $v$ are possible?
   2. Write the first three nonzero terms of the Taylor series for $m$ in terms of $v$ .

10. Estimate the value of $\int_{0}^{1} (\sin x/x) dx$ by approximating the function $\sin x/x$ with a Taylor polynomial of degree $4$ .
11. Estimate the value of $\int_{0}^{1} e^{-x^{2}} dx$ by approximating the function $e^{-x^{2}}$ with a Taylor polynomial of degree $6$ .