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10. (5 pts) A spherical golf ball is measured to have a radius of 5 cm, with a possible measurement error of 0.1 cm. (a) Use differentials to estimate the maximum error in the calculated volume of the golf 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 volume of the golf ball. Give your answer in percentage form. Formulas you may need: Sphere surface area: S = 4πr2 Sphere volume: V = (4/3)πr3

17. (6 pts) Find the antiderivative F(x) of each function. a)   b)

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

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.

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

4. (4 pts) Let

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

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

12. (8 pts) Let

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