29) Find the average value of the function
over the interval [0, 4].
a) ![](images/Calc_BC_Section2_69.gif)
b) ![](images/Calc_BC_Section2_70.gif)
*c) ![](images/Calc_BC_Section2_71.gif)
d) ![](images/Calc_BC_Section2_72.gif)
e) ![](images/Calc_BC_Section2_73.gif)
30) What is the y-intercept of the line tangent to the curve y = x2 + 4 at x = 3?
a) ![](images/Calc_BC_Section2_74.gif)
b) ![](images/Calc_BC_Section2_75.gif)
*c) ![](images/Calc_BC_Section2_76.gif)
d) ![](images/Calc_BC_Section2_77.gif)
e) ![](images/Calc_BC_Section2_78.gif)
31) Which of the following function(s) is continuous and differentiable?
I. ![](images/Calc_BC_Section2_79.gif)
II. ![](images/Calc_BC_Section2_80.gif)
III. ![](images/Calc_BC_Section2_81.gif)
a) I and III only
b) III only
*c) I and II only
d) I only
e) II only
32) Find m
a) ![](images/Calc_BC_Section2_83.gif)
b) ![](images/Calc_BC_Section2_84.gif)
c) ![](images/Calc_BC_Section2_85.gif)
*d) ![](images/Calc_BC_Section2_86.gif)
e) ![](images/Calc_BC_Section2_87.gif)
33) The graph of the derivative of f is shown below. Which of the following must be true?
![](images/image_33_6.gif)
a) f has a local maximum at x = 0.
b) f is increasing on [-6, 6].
*c) f has a point of inflection at x = 12.
d) f is concave down on [0, 12].
e) f has a local minimum at x = -6.
34) The sum of two positive integers x and y is 90. Find the value of x that minimizes
a) ![](images/Calc_BC_Section2_89.gif)
*b) ![](images/Calc_BC_Section2_90.gif)
c) ![](images/Calc_BC_Section2_91.gif)
d) ![](images/Calc_BC_Section2_92.gif)
e) ![](images/Calc_BC_Section2_93.gif)
35) A particle moves on the curve
find the speed of the particle at time t =
.
*a) 4.4721
b) 3.4641
c) 4.2426
d) 2.8284
e) 2.4495
36) The function f is defined as![](images/Calc_BC_Section2_96.gif)
x
7
Which of the following is false?
a) f has a vertical asymptote at x = 7.
*b) f has a horizontal asymptote at y = 1.
c) f is decreasing on [2, 7].
d) f has a local maximum at x = 2.
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 = 2 and x = 5.
II. The particle is slowing down on [0, 2].
III. The particle is speeding up on [2, 5].
a) I only
*b) II only
c) II and III 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) ![](images/Calc_BC_Section2_101.gif)
b) ![](images/Calc_BC_Section2_102.gif)
*c) ![](images/Calc_BC_Section2_103.gif)
d) ![](images/Calc_BC_Section2_104.gif)
e) ![](images/Calc_BC_Section2_105.gif)
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 3 hours. Roughly how many hours does it take for the population to reach 10000?
*a) ![](images/Calc_BC_Section2_106.gif)
b) ![](images/Calc_BC_Section2_107.gif)
c) ![](images/Calc_BC_Section2_108.gif)
d) ![](images/Calc_BC_Section2_109.gif)
e) ![](images/Calc_BC_Section2_110.gif)
40) Find the radius of convergence of the series
a) ![](images/Calc_BC_Section2_112.gif)
b) ![](images/Calc_BC_Section2_113.gif)
*c) ![](images/Calc_BC_Section2_114.gif)
d) ![](images/Calc_BC_Section2_115.gif)
e) ![](images/Calc_BC_Section2_116.gif)
41) ![](images/image_41_3.gif)
for 0 < x < 9
The graph of g is shown above. Which of the following must be true?
I. ![](images/Calc_BC_Section2_118.gif)
II. ![](images/Calc_BC_Section2_119.gif)
III. ![](images/Calc_BC_Section2_120.gif)
*a) I and II only
b) I 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) 0.430
b) 0.215
c) 1.348
d) 0.413
*e) 0.674
43) f (x) is represented by the Maclaurin series
![](images/image_43.gif)
What is the slope of the line normal to the graph of f at x =
?
a) ![](images/Calc_BC_Section2_123.gif)
b) ![](images/Calc_BC_Section2_124.gif)
c) ![](images/Calc_BC_Section2_125.gif)
*d) ![](images/Calc_BC_Section2_126.gif)
e) ![](images/Calc_BC_Section2_127.gif)
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 ![](images/Calc_BC_Section2_129.gif)
the x-axis, and
the line x = 2
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) ![](images/Calc_BC_Section2_130.gif)
b) ![](images/Calc_BC_Section2_131.gif)
c) ![](images/Calc_BC_Section2_132.gif)
d) ![](images/Calc_BC_Section2_133.gif)
e) ![](images/Calc_BC_Section2_134.gif)