Author: Anonymous

10. (5 pts) A spherical softball is measured to have a radius of 9 cm, with a possible measurement error of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated surface area of the ball. Round your answer to 3 places after the decimal. (b) Using your answer from part a, estimate the maximum relative (percentage) error in the calculated surface area of the ball. Give your answer in percentage form. Formulas you may need: Sphere surface area: S = 4πr2 Sphere volume: V = (4/3)πr3

9. Let     a) (3 pts) Find a linear approximation L(x) for f(x) near x = 4. b) (1 pt) Use your linear approximation to estimate the value of   . c) (2 pts) Explain why your linear approximation from part a would NOT be a good way to estimate   . Include a drawing in your answer.

15. (4 pts) Use L’Hôpital’s Rule to find each limit. a)

3. (6 pts) Evaluate each limit. Do not use L’Hopital’s rule on these problems. a)

4. (4 pts) Let

12. (8 pts) Let

7. (4 pts) Given this equation, find dy/dx:

6. (8 pts) Find the derivative of each function. a)

8. (6 pts) Sand is being dumped from a conveyor belt at a rate of 35 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 feet high? Round your answer to four decimal places. Note that the volume of a cone is given by V = (1/3) πr2h where r is the radius of the base of the cone and h is the height of the cone.

11. (5 pts) Let