Name:, - 4. For which of the following does lim, f(x) exist? L II Graph of f Graph off Graph of f a. I only d. I and II only b. II only e. I and III only C. Ill only me: - 5. Complete the table of values (to five decimal places) and use the table to estimate the value of the limit. lim √x-6 x-36 x-36 x f(x) 35.9 35.99 35.999 36.001 36.01 36.1 The limit does not exist. a. 12 b. 1 C. 36 d. 6. Use a table of values to estimate the value of the limit. lim x+7 x-7x+9x+14 a. b. 151217 C. d. The limit does not exist. Name: 7. Use a table of values to estimate the value of the limit. lim √√x+16-4 X x0 018 a. b. c. 4 The limit does not exist. <-100 d. -16 8. For the function f whose graph is given, state the value of the given quantity, if it exists. lim x→ 3* f(x) 1.5 a. b. 2 c. 3 Name: ID: A 9. Use a graphing device to determine whether the limit exists. If the limit exists, estimate its value to two decimal places. If the limit does not exist so indicate. lim x0 cos a. -1 1 b. C. d. Does not exist. 0 10. Graph the piecewise-defined function and use your graph to find the value of the limit, if it exists. If the limit does not exist so indicate. if x <9 f(x)=. if x ≥9 lim f(x). 618 Does not exist. a. 7 b. C. 10 d. 9 BE Name: - 11. Given that lim x→3 f(x)=-5. Find the limit: lim (Ax))². - * 3 a. 9 b. 25 c. -25 12. Evaluate the limit: lim (4x²+8x+4). a. 68 *→4 b. 96 C. 100 13. Evaluate the limit: lim (x+5)-125 018 a. x The limit does not exist. b. 24 C. 75 d. 25 14. Evaluate the limit: lim 4 1 x+4 a. 114 b. 16 C. 16 d. The limit does not exist. Name: - Derivatives 15. The function f given by f(x) = x² + 12x-24 is a. increasing for x <-2, decreasing for -2<x<2, increasing for x > 2 d. decreasing for all x b. decreasing for x < 0, increasing for x > 0 e. C. increasing for all x decreasing for x < -2, increasing for -2<x<2, decreasing for x > 2 16. Iff is a differentiable function, then f' (a) is given by which of the following? 1. lim,→ fla+h)-f(a) h f(x)-f(a) II. lima x-a f(x+h)-f(x) III. lim,a h - a. I only b. II only c. I and II only 17. If f(x)=-x+x+, then f'(-1)= a. 319 b. 1 C. -1 d. I and III only e. I, II, and III d. -3 e. 35