AP Calculus AB
Fall Semester Final Exam Review
Name
Per
Date
sin 12θ
θ →0
3θ
1.) lim
[b] 4
[c] 3
[d]
1
4
[e] does not exist
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[a] 12
2.) Let h( x) = f (g (2x)). Find the value of hʹ′(3) given the following information about f and g :
x
f (x)
f ʹ′(x )
g (x)
g ʹ′(x)
1
−3
3
6
−1
3
1
6
2
3
−2
6
[a] − 12
k
3.) If
[b]
∫1 (4x + 2)dx = 8 ,
[e] − 1
[d] 3
k=
[b] 3
[c] 4
[d] –2
[e] –4
sh
Th
[a] 2
[c] − 3
1
2
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12
4.) Which of the following integral expressions is equivalent to
∫x
2
x − 3 dx
4
12
∫ (u
[a]
4
12
∫ (u
[c]
5
2
3
2
3
1
9
)
[b]
+ 6u 2 + 9u 2 du
1
9
)
1
2
[d]
+ 3u du
4
∫ (u
∫ (u
5
2
3
2
3
1
)
+ 6u 2 + 9u 2 du
1
)
+ 3u 2 du
1
[e] None of the above
(2 + h)4 − 24
=
h →0
h
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7.) lim
[a] 16
[b] 32
[c] 256
[d] –16
[e] does not exist
8.) Given the function
⎧ x 2 − 9
, x ≠ −3
⎪
f ( x) = ⎨ x + 3
⎪6,
x = −3
⎩
Which of the following statements is true?
[a] f (−3) = −6
[b] f (x ) is continuous at x = −3
[c] lim f ( x) exists
x→−3
[d] f (x ) has a vertical asymptote at x = −3
[e] lim+ 6
Th
x→−3
2
If
∫ f (x)dx = 4, and
−1
[a]
4
sh
9.)
2
−1
∫ g(x)dx = -3, find
∫2 [f (x) + 3g(x)]dx
−1
[b] − 4
[c] 5
[d] − 5
[e] 13
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10
( )
10.) Given that g (x ) = ∫ sin 2 t 3 dt , which of the following is g ʹ′(x)?
x
( )
( )
( )
[b] − sin 2 x 3
[d] − 3x 2 sin 2 x 3
[e] cos 2 x 3
[a] sin 2 x 3
( )
[c] 3x 2 sin 2 x 3
( )
sin x
when x = π .
2x
[a] x − 2πy = π
[b] x + 2πy = π
[c] x + 2πy = −π
[d] − x + 2πy = π
[e] None of these
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11.) Find the equation of the line tangent to g (x ) =
12.) Which of the following functions appears to be differentiable for all values of x?
[a]
[b]
[c]
5
4
3
2
1
5
y
y
5
4
4
3
3
2
2
1
1
x
x
-5
-4
-3
-2
-1
1
-1
-2
-3
-4
-5
2
3
4
-5
5
-4
-3
-2
-1
1
[d]
2
3
4
Th
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
y
5
4
4
3
3
2
2
1
y
1
x
-3
-2
-1
sh
-4
x
5
[e]
5
-5
y
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
2
3
4
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5
2
3
4
5
15.) The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 3 feet per
minute. When the top of the ladder is 7 feet from the ground, what is the rate of change of the
distance between the bottom of the ladder and the wall?
[a] −
7
ft/min
8
[d]
[b] −
7
ft/min
8
7
ft/min
24
[e]
[c]
21
ft/min
25
16.) Given x 2 − 2 y 2 = 9 , which of the following is
x
2y
1
2
d2y
?
dx 2
y−x
2 y2
x2 − 2 y 2
4 y3
−9
4 y3
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[a]
7
ft/min
24
[b]
[c]
[d]
[e]
17.) Which of the following functions has a horizontal asymptote of y = 2 and a vertical
asymptote of x = −1 ?
2 x 2 + 5x + 3
2x 2 + x − 3
2 x 2 + 5x + 3
[a] f ( x) =
[b] f ( x) =
[c] f ( x) =
1− x2
1− x2
x2 −1
2x 2 + x − 3
[d] f ( x) =
[e] None of these
x2 −1
20.) The table below gives the values of f (x) for several values of x . Which of the following
limit expressions does the table seem to indicate is true?
0
-11.03
0.3
-11.5
Th
x
f (x)
[a] lim f ( x) = 0
0.49
-11.95
[b] lim f ( x) = −12
x→−11
sh
0.4
-11.9
x→0.5
[d] lim+ f ( x) = −11
x→0
0.499
-11.98
[c] lim− f ( x) = −11
x→0.5
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x→0
[e] lim− f ( x) = −12