MATH 112 Midterm: MATH 112 BYU KeyF2008A

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turquoisegnu128

15 Feb 2019

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Fill in the answer to each problem on your scantron. Make sure your name, section and instructor is on your scantron: simplify sin(tan 1 5. Solution: d: find lim x 1 x2 + x + 2. 2x2 + x 3: does not exist d) 4: if f (x) = ax2 + bx + c, nd lim h 0, ax2 + bx d) Solution: b) f (x + h) f (x) h b) 2ax2 + bx + c: does not exist, the derivative of h(x) = x2x is a) 2x2x: x2x ln x, the equation of the tangent line to y = sin2 x at ( ) is a) y = d) y = ) sin x cos x b) y = 4: none of the above, for the function f (x) = x2, for which value of c is f (c) equal to the average rate of change of f on [0, 3]? a)

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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.

4. (16 pts) MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART. (I) ( 4 pts) Complete the statement of the Intermediate Value Theorem: Suppose f is continuous on the interval [a, b] and L is a number between f (a) and f (b). Then there is at least one number c in (a, b) such that (a) C = L; (b) f(c) = 0; (c) f(c) = L; (a) f' (c) = L; (e) C = 0; (f) f (a) < c < f (b); (g) NONE OF THE PREVIOUS ANSWERS. (II) (4 pts) The figure shows the graph of a function f. At what point (points) c does the conclusion of the Intermediate Value Theorem hold for f (x) on the interval [1, 5] and L = 2. --- - - - -1 - - - 2 - - I- - - (a) c = 1; (b) C = 0; (c) C = 2; (a) c = 3; (e) C = 4; (f) C = 5; (g) c= -1. (III) (4 pts) Given that cos x s f (x) s et, for all x > 0 evaluate lim f (x) x+0+ (a) lim f (x) = 0; (b) lim f (x) = 1; (c) lim f (x) = e; x0+ X0+ (d) lim f(x) DOES NOT EXIST. WE DON'T HAVE ENOUGH INFORMATION TO ANSWER THE QUESTION *40+ (IV) (4 pts) Given the function 1 f (x) = , find its inverse, f+(x) x -2 (a) f (x) = x -2; (b) f«+ (x) = x+2 ; (c) fº+ (x) = -2; (f) f-+ (x) -2; (e) f (x) DOES NOT EXIST.

MATH 112 Midterm: MATH 112 BYU KeyF2008A

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