14. (5 pts) For each function, find the limit as x approaches ∞ (positive infinity). a)

16. (3 pts) Explain why looking at the sign of the first derivative of a function can help us decide if a critical value is a maximum, a minimum, or neither. Include a drawing.

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

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

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