MATH 127 Quiz # 5 (Practice Version) Bubble your answer(s) for each question 1 - 6 on the last page of the exam. 1] 1. The table shows values of f(x). x -0.1 -0.01 -0.001 0 0.001 |0.01 0.1 f(x) 3.97 3.98 3.99 6 4.01 4.02 4.03 This tells us that (a) lim f(z) = 6 (b) lim f (z) = 4 (c) lim f(x) does not exist (d) There is not enough information to determine if lim f(x) exists. [1] 2. Assume lim g(x) = 5. Select all of the statements that must be true. (a) g(x) is continuous at x = 2 (b) lim g(x) = lim g(x). (c) lim 9(2) = 1. (d) lim g(x) = 10. (1] 3. The graph of a piecewise defined function h(x) is given below. Select all of the true statements. (a) lim h(x) = 1.5. (b) lim h(x) = 3. (c) lim h(x) does not exist.Bubble your answer(s) for each question 1 - 6 on the last page of the exam. 1] 4. The function f is continuous on [0, 2] and has the values that are given in the table. 1) 1 k 2 The equation f(x) = - must have at least two solutions in the interval [0, 2] if (a) k = 0. (b) k = 1/2. (c) k = 1. (d) k = 2. (e) k = 3. (1] 5. Assume that lim g(x) = 0 and g(x) # 0 for all x. Then, im g(x) (a) does not exist. (b) = 0. (c) = 1. (d) there is not enough information to determine if the limit exists or not. (e) exists, but there is not enough information to determine the value of the limit. 1 6. If a number very close to zero is divided by another number very close (but not equal) to zero, the result (a) must be a number very close to zero. (b) must be a number close to 1. (c) could be any number. (d) might not be a number at all.9. Compute the following limits using any method (including L'Hospital's Rule if you know it). If a limit does not exist, prove it. 2 (a) lim (2 + 4)(2 -6) 2-+00 3x2 + 2 122 + x - 21 [3] (b) lim 22 - 1 (2] 10. Suppose you leave for Montreal from Waterloo at 10 a.m. on Friday morning and arrive in Montreal at 6 p.m. The following Monday, you begin your return trip at 10 a.m. and arrive back in Waterloo at 6 p.m. Show that at some point on the trip, there is a time where you will be at the exact same point on the road on both Monday and Friday.3 7. Find all the vertical and horizontal asymptotes of f (x) = 72_ 1- (3] 8. Find the value of c that makes the function f (x) = cx2 + 2x if x