29) Find the average value of the function
over the interval [0, 4].
a)
b)
c)
d)
*e)
30) What is the y-intercept of the line tangent to the curve y = x2 + 7 at x = 3?
a)
b)
c)
*d)
e)
31) Which of the following function(s) is continuous and differentiable?
I.
II.
III.
a) I and III only
b) III only
*c) I and II only
d) I only
e) II only
32) Find m
a)
*b)
c)
d)
e)
33) The graph of the derivative of f is shown below. Which of the following must be true?

a) f is concave down on [0, 4].
b) f is increasing on [-2, 2].
c) f has a local maximum at x = 0.
d) f has a local minimum at x = -2.
*e) f has a point of inflection at x = 4.
34) The sum of two positive integers x and y is 60. 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) 7.1414
b) 6.7082
*c) 7.2801
d) 3.3166
e) 3.0000
36) The function f is defined as

x 6

Which of the following is false?
*a) f has a horizontal asymptote at y = 1.
b) f has a vertical asymptote at x = 6.
c) f is decreasing on [3, 6].
d) f has a local maximum at x = 3.
e) f is concave up for x > 6.
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 = 2 and x = 6.
II. The particle is slowing down on [0, 2].
III. The particle is speeding up on [2, 6].
a) II and III only
b) I only
*c) II only
d) I and III only
e) I, II and III
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 5 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
a)
*b)
c)
d)
e)
41)
for 0 < x < 3

The graph of g is shown above. Which of the following must be true?
I.
II.
III.
a) II and III only
b) II only
c) I and III only
*d) I and II only
e) I only
42) If the region bounded by y = tan-1(x), y = and the y-axis is rotated about the y-axis, the volume of the solid formed is
*a) 0.674
b) 0.215
c) 1.348
d) 0.430
e) 0.413
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) h < 1
e) -1 < h < 1
45) 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 xy-plane. Which of the following expressions represents the volume of the solid?
a)
*b)
c)
d)
e)