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 + 8 at x = 3?
a)
b)
c)
d)
e)
31) 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
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 has a point of inflection at x = 8.
b) f is increasing on [-4, 4].
c) f has a local maximum at x = 0.
d) f is concave down on [0, 8].
e) f has a local minimum at x = -4.
34) The sum of two positive integers x and y is 30. 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) 5.6569
b) 6.3246
c) 6.1644
d) 3.1623
e) 2.8284
36) The function f is defined as

x 7

Which of the following is false?
a) f is decreasing on [3, 7].
b) f has a vertical asymptote at x = 7.
c) f has a horizontal asymptote at y = 1.
d) f has a local maximum at x = 3.
e) f is concave up for x > 7.
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 = 6.
II. The particle is slowing down on [0, 3].
III. The particle is speeding up on [3, 6].
a) I, II and III
b) II and III only
c) I and III only
d) II only
e) I 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 6 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 < 9

The graph of g is shown above. Which of the following must be true?
I.
II.
III.
a) II only
b) I only
c) I and II only
d) I and III only
e) II and III 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) 0.413
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) -1 < h < 1
b) h > 1
c) h < 1
d) h > 1
e) h < 1
45) The base of a solid is the region bounded by

the x-axis, and

the line x = 5

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)