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 = x2 + 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) 
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
6
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
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 = 
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) 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 xy-plane. Which of the following expressions represents the volume of the solid?
a) 
b) 
c) 
*d) 
e) 