2008onlinemathuheduap Ab Version1 Questions 17

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29) If f is a differentiable function and f(0) = -3 and f(6) = 6, then which of the following must be true? I. There exists a c in [0,6] where f(c) = 0. II. There exists a c in [0,6] where f ' (c) = 0. III. There exists a c in [0,6] where f ' (c) = 3/2.

a) II only b) I only c) I and III only d) II and III only e) I, II and III 30) Which of the following function(s) is continuous and differentiable? I. II. III. a) I only b) II only c) III only d) I and II only e) I and III only 31) The area of the region in the first quadrant bounded by the graphs of y = 2cos(x) , y = 2sin(x), and the y-axis is a) b) c) d) e) 32) Air is pumped into a spherical balloon at a rate of 8cm3 per second. At what rate is the radius of the sphere changing when its volume is cm3? a)

cm/sec

b)

cm/sec

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c)

cm/sec

d)

cm/sec

e)

cm/sec

33) The graph of the derivative of f is shown below. Which of the following must be true?

a) f is increasing on [-5, 5]. b) f has a point of inflection at x = 10. c) f has a local maximum at x = 0. d) f is concave down on [0, 10]. e) f has a local minimum at x = -5. 34) A particle is moving along the x-axis and its position at time t > 0 is given by Which of the following is (are) true? I. The particle changes direction at x = 2 and x = 5. II. The particle is slowing down on [0, 2]. III. The particle is speeding up on [2, 5]. a) II only b) I only c) II and III only d) I and III only e) I, II and III 35) The region enclosed by the graphs of and the line

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for 0 < x < 1, is revolved about the y-axis. Which of the following integrals gives the volume generated? a)

b) c)

d)

e) 36) If then

is

a) b) c) d) e) 37) The sum of two positive integers x and y is 90. Find the value of x that minimizes a) b) c) d) e) 38) A particle moves along a straight line, and its velocity at time t is given by

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What is the total distance the particle travels from t = 1 to t = e? a) b) c) d) e) 39) The function f is defined as

x

7

Which of the following is false? a) f has a horizontal asymptote at y = 1. b) f has a vertical asymptote at x = 7. c) f is decreasing on [3, 7]. d) f has a local maximum at x = 3. e) f is concave up for x > 7. 40) The base of a solid is the region bounded by

the x-axis, and the line x = 7 Each cross-section of the solid perpendicular to the x-axis is a square, with one side on the xyplane. Which of the following expressions represents the volume of the solid? a) b) c) d) e) …uh.edu/…/Calc_AB_Section2_5.h…

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41) The rate at which a bacteria population grows is proportional to the number of bacteria present. Initially, there were 1000 bacteria present and the population doubled in 2 hours. Roughly how many hours does it take for the population to reach 10000? a) b) c) d) e) 42) Given that F'(x)= f(x), find

a) b) c) d) e) 43) The line normal to at x = m is parallel to the y-axis. What is m? a) b) c) d) e) 44) f and g are two differentiable functions such that f(1) = g(1) = 4 f'(1) = g'(1) = 7 f'(4) = 4 g'(4) = 7 If

, then h'(1) is

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e) 45) If

and y(0) = 7, then yln(2) =

a) b) c) d) e)

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