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1. (8 marks] Consider the following table of some values for a function f. Assume that f-1 exists. Compute as many table entries of f-1 as you can and indicate with 'un' that the value is unknown to you given the limited table of values. In addition, also indicate what you would need to know about f in order to determine f-1(5). 2 f(x) f-1(x) 0 1 ? 1 -1 ? 2 3 ? 3 2 ? 4 0 ?

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Beverley Smith
Beverley SmithLv2
9 Mar 2018
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3. (15 pts) MULTIPLE CHOICE !!! A table of values for f (x) and f'(x) is shown below. Suppose that fis a one-to-one function and f (x) is its inverse. Also, a graph of a function g (x) is given. x f (x) f'(x) y = g(x) CIRCLE THE CORRECT ANSWER IN EACH PART. g(x)) at x = 1. @ (c) 12 ; (d) 4; (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS. (11) f (g(x)) at x= 3. (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS. (111) 9 (f (x)) at 2= 3. (a) -1; (b) - 4; (a) 0; (e) DOES NOT EXIST ; (f) NONE OF THE PREVIOUS ANSWERS. (IV) f-1 (3) (a) 4; (b) 1; (b) 1 ; 0); (a) 2; (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS. (a) 1; (b) 4; (e) DOES NOT EXIST; (f) NONE OF THE PREVIOUS ANSWERS.

3. (20 pts) Let f be a differentiable one-to-one function on the interval (0,4) with the particular values of f and f' given in the table below, and let f-1 be the inverse function of f. Let g be the function given by the graph below. y y=g(x) 12 2 3 5 1 2 3 4 5 6 34-2 For (a), (b), and (c), circle the correct choice. lim 8(3+h) – g(3) h iii. 5 V. -2 vi. does not exist vii. none of the previous choices iv. O (b) dip [6^x +2)/(x) at x = 3 iii. 1 V. -1 vii. none of the previous choices iv. 0 vi. does not exist (0) [r_w) at x = 2 V. vii. none of the previous choices iv. I vi. does not exist (d) Consider the curve given by xey + y = f(x) - 1. Use implicit differentiation to computed at the point (2.0). Show your work.

1. (16 marks, 2 for each part.) The problem consists of 8 short-answer questions: V22 +12 - 1 (a) Evaluate lim - or determine that it does not exist. In the latter case, write DNE as answer. 1+2 -1 Answer (b) Find values of a that would make the following function continuous everywhere, or determine that no such value exists. In the latter case, write DNE as answer. g(x) = ( 22+2 2+1 ar if I 1. Answer (c) Find the derivative of y = r" lnr. Answ (d) Find the equation for the tangent line to the curve z-y + xy2 = 2 at (1,1). Answer (e) Use linear approximation to estimate (0.998) Answer if any exists. Write DNE if none r2 - 4 (f) Find the vertical, horizontal or slant asymptotes of f(x) = exists. Answer (g) Find any local maxima and minima of h(x) = r- in the interval (1,4). Give both r and h(2) values and state whether it is a local minimum or maximum. Answer (h) On which part of the interval [0,1] is f(x) = et sin x concave upward? Answer

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