1997 AP Calculus BC:
Section I, Part B
78. ²³0
ln
1
lim
h
e
h
h
o
µ
±
is
(A) ( ), where ( )lnfef xxc(B) ln( ), where ( )xfef xxc(C) (1), where ( )lnff xxc(D) ²³(1), where ( )lnffxxecµ(E) (0), where ( )lnff xxc
79. The position of an object attached to a spring is given by 11( )cos(5 )sin(5 )64y ttt±, where tis time in seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0?
80.
Let
f
be the function given by
( )
cos(2 )
ln(3 )
f x
x
x
µ
. What is the least value of
x
at which the
graph of
f
changes concavity?
81. Let fbe a continuous function on the closed interval >@3,6±. If ²³31f±±and ² ³63f, then the Intermediate Value Theorem guarantees that

AP Calculus Multiple-Choice Question Collection
122
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1997 AP Calculus BC:
Section I, Part B
82. If 04xdd, of the following, which is the greatest value ofx such that 202(2 )xxtt dttdt±t³³?
(A) 1.35 (B) 1.38 (C) 1.41 (D) 1.48 (E) 1.59
83. If ²³1lndyxydxµand if y= 1 when x= 1, then y=
2
2
1
x
x
e
±
84. 2sinxxdx³
x
x
C
±
µ
85. Let f be a twice differentiable function such that (1)2fand (3)7.fWhich of the following must be true for the function f on the interval 13xdd? I. The average rate of change of f is 52. II. The average value of f is 92. III. The average value of fcis 52.

AP Calculus Multiple-Choice Question Collection
123
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1997 AP Calculus BC:
Section I, Part B
86. (1)(3)
dx
x
x
±
µ
³
(A) 11ln43(B) 13ln41(C) ²³²³1ln132xxC±µµ(D) ²³²³(E) ²³²³ln13xxC±µµ
x
C
x
±
µ
µ
x
C
x
µ
µ
±
1
2
2
ln
2
1
3
x
C
x
x
µ
µ
±
µ
87. The base of a solid is the region in the first quadrant enclosed by the graph of 22yx±and the coordinate axes. If every cross section of the solid perpendicular to the y-axis is a square, the volume of the solid is given by

AP Calculus Multiple-Choice Question Collection
124
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