2008onlinemathuheduap Bc Version1 Answers 17

7/3/2009

http://online.math.uh.edu/apcalcu…

29) Find the average value of the function over the interval [0, 2]. a) b) *c) d) e) 30) What is the y-intercept of the line tangent to the curve y = x 2 + 6 at x = 3? *a) b) c) d) e) 31) Which of the following function(s) is continuous and differentiable? I. II. III. a) II only *b) I only c) III only d) I and II only e) I and III only 32) Find m

*a) b) c) d) e) …uh.edu/…/Calc_BC_Section2_5k…

1/6

7/3/2009

http://online.math.uh.edu/apcalcu…

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) The sum of two positive integers x and y is 120. Find the value of x that minimizes *a) b) c) d) e) 35) A particle moves on the curve find the speed of the particle at time t = a) 5.1962 b) 4.5826 *c) 5.3852 d) 3.0000 e) 2.6458 36) The function f is defined as

.

x

…uh.edu/…/Calc_BC_Section2_5k…

6

2/6

7/3/2009

http://online.math.uh.edu/apcalcu…

Which of the following is false? a) f has a local maximum at x = 4. b) f has a vertical asymptote at x = 6. c) f is decreasing on [4, 6]. d) f is concave up for x > 6. *e) f has a horizontal asymptote at y = 1. 37) 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 = 3 and x = 5. II. The particle is slowing down on [0, 3]. III. The particle is speeding up on [3, 5]. a) I and III only b) I only c) II and III only d) I, II and III *e) II only 38) f (x) is a differentiable function and it is decreasing on ( If

,

).

then g has a local maximum at a) *b) c) d) e) 39) 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) 40) Find the radius of convergence of the series

…uh.edu/…/Calc_BC_Section2_5k…

3/6

7/3/2009

http://online.math.uh.edu/apcalcu…

a) b) c) *d) e)

41)

for 0 < x < 6 The graph of g is shown above. Which of the following must be true? I. II. III. a) I only *b) I and II only c) II only d) I and III only e) II and III only 42) If the region bounded by y = tan-1(x), y = …uh.edu/…/Calc_BC_Section2_5k…

and the y-axis is rotated about the y-axis, the 4/6

7/3/2009

http://online.math.uh.edu/apcalcu…

volume of the solid formed is a) 0.413 b) 1.348 c) 0.430 *d) 0.674 e) 0.215 43) f (x) is represented by the Maclaurin series

What is the slope of the line normal to the graph of f at x =

?

a) b) c) d) *e) 44) What are all values of h for which

converge? a) h < 1 b) h < 1 c) h > 1 d) -1 < h < 1 *e) h > 1 45) The base of a solid is the region bounded by

the x-axis, and the line x = 6 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?

…uh.edu/…/Calc_BC_Section2_5k…

5/6

7/3/2009

http://online.math.uh.edu/apcalcu…

a) b) c) *d) e)

…uh.edu/…/Calc_BC_Section2_5k…

6/6