1. The domain of f (x) = 1 V7+ex-x A. (-1, 7) B. [-1, 7] C. x >-1orx 7} E. (-60, -1] U [7,) 2. If f (x) = x + 2 and g(x) = x2 - 4 then which of the following will have a domain of (x: x # 12]? A. (e/ f)(x) B. (f/g)(x) C. (g-f)(x) D. g(f(x)) E. fle(x)) 3. If f(xx) = then f-' (x) = A. 3 B. *+3 C. D. I . No inverse exists 4. In which of the following is y a function of x? yz = 9 - x] II. lyl = x III. y = 3V x2 A. I only B. II only C. Ill only D. I and Ill only E. I, II, and ill5. lim V9+h-3 S A. 6 B. 1/6 C. O D. 3 1/3 6. lim 4x--3r+1 2x2+1 A. -2 B. -1 C. 0 D. 1 E. 7. Given that: X 4.8 4.9 4.99 5.01 5.1 5.2 g(x) 9.44 10.75 10.99 11.01 11.25 12.56 It would appear that lim g (x) A. 0 B. 7 11 D. Does not exist E. x+48. If g(x) is continuous for all real numbers and g(0) =-2, g(1) =3, which of the following are necessarily true? I. g(x) = 1 at least once lim g(x) = g(0.5) Ill. lim g(x) = lim g(x) x-1 x-1+ A. I only B. II only C. | and II only D. I, II, and Ill E. None of these. X4-2x+1 9. Let f be defined as follows, f (x) = x#1 X-1 3 *=1 lim f (x) exists I+1 Il. f(1) exists Ill. f (x) is continuous at x = 1 A. I, II, and Ill B. I only C. II only D. I and II only E. None10. Given the picture of f(x) find lim f(x), lim f(x), lim f(x) *+1" *++1+ A. 1, 1, 1 B. -2, 1, 1 C. -2, 1, Does Not Exist D. 1, -2, Does Not Exist E. None of them exist 11. If f(x) = 3x* + 5x - 4sinx, find the value of the derivative at (0, 0). A. -1 B. 0 1 D. 2 E. Undefined 12. What is the value of g'(0) if y = g (x) has a graph given by: A. 0 B. 1 1 C. -2 D. 3 4 -3 -2 2 E. -4 -1 13. Find the derivative of f (x) = Sing+1 COST A. f'(x) = -csc'x - csexcotx B. f'(x) = secr+tonx C. f'(x) = sink D. f'(x) = 2sec x E. None of the above14. Suppose the functions f and g and their derivatives have the following values at x = 1 and x = 2. Let h(x) = f(g(x)). Evaluate h'(1). X )g(x) f'(x) g'(x) N 1/3 -3 ( 00 NO -4 5 A. B. C. -6IL D. n E. 24 15. The inflection point of the curve y = 2x* - 12x- is: A. (-1, -14) B. (0, 0) C. (1, -10) D. (2, -32) E. There is no point of inflection.16. Which points on the curve of x? - y? = 5 have vertical tangent lines? A. (V5, 0) and (-V5, 0) B. (3, 2) C. (3, -2) and (3, 2) D. There are no vertical tangents to this curve. E. None of the above. 17. Find as f (x) for f (x) = cosx - 3x*. A. f" (x) = sinx - 72x B. f"(x) = cosx - 72x C. f"(x) = -sinx - 72x D. f"(x) = -cosx - 72x E. None of the above 18. A particle's position (in meters) is given by the equation s(t) = 5t sin(2t), on the interval [-1, 4] minutes. What is its instantaneous velocity at t = n? A. B. -1 CO D. n E. -10n19. The altitude of a kite is graphed here (the y-axis is in increments of ten feet, the t-axis is in minutes). Over which intervals is the kite accelerating upward (where the acceleration is positive)? Note, this is the graph of the POSITION function. A. [0, 1.5) U (4.5, 7.75) B. (3, 6.3) C. [0, 10] D. (0, 3) U (6.3, 10) E. Cannot be determined. 20. The volume of an open-topped box with a square base is 245 cubic centimeters. Find the height, in centimeters, of the box that uses the least amount of material. A. 7.883 centimeters B. 6 centimeters C. 3.942 centimeters D. 3 centimeters E. 2 centimeters