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Unformatted text preview: base of a solid is the region in the first quadrant enclosed by the parabola y = 4 x 2 , the line
x = 1 , and the xaxis. Each plane section of the solid perpendicular to the xaxis is a square. The
volume of the solid is
(A) 4π
3 16π
5 (B) 4
3 (C) (D) 16
5 (E) 64
5 26. If f is a function such that f ′( x) exists for all x and f ( x) > 0 for all x, which of the following is
NOT necessarily true?
1 (A) ∫ −1 f ( x) dx > 0 (B) ∫ −1 2 f ( x) dx = 2∫ −1 f ( x) dx (C) ∫ −1 f ( x) dx = 2∫ 0 f ( x) dx (D) ∫ −1 f ( x) dx = − ∫ 1 (E) ∫ −1 f ( x) dx = ∫ −1 f ( x) dx + ∫ 0 f ( x) dx 1 1 1 1 1 −1 1 f ( x) dx 0 1 27. If the graph of y = x3 + ax 2 + bx − 4 has a point of inflection at (1, − 6 ) , what is the value of b?
(A) –3
(E) (B) 0 (C) 1 (D) 3 It cannot be determined from the information given. AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 73 1988 AP Calculus BC: Section I
28. d
⎛π⎞
ln cos ⎜ ⎟ is
dx
⎝x⎠ (A) (D) −π
⎛π⎞
x 2 cos ⎜ ⎟
⎝ x⎠ (B) π
⎛π⎞
tan ⎜ ⎟
x
⎝x⎠ ⎛π⎞
− tan ⎜ ⎟
⎝x⎠ (C) 1
⎛π⎞
cos ⎜ ⎟
⎝x⎠ π ⎛π⎞
tan ⎜ ⎟
x2
⎝ x⎠ (E) 29. The region R in the first quadrant is enclosed by the lines x = 0 and y = 5 and the graph of
y = x 2 + 1 . The volume of the solid generated when R is revolved about the y axis is (A) ∞ 30. 6π 3 ⎡ ⎛1⎞
⎢1 − ⎜ ⎟
2 ⎢ ⎝3⎠
⎣ (E) 2⎛1⎞
⎜⎟
3⎝3⎠ (C) π (E) 544π
15 (C) (D) 16π 3⎛1⎞
⎜⎟
2⎝3⎠ (E) 4π ⎛1⎞
∑ ⎜3⎟ =
i=n ⎝ ⎠ (A) 3 ⎛1⎞
−⎜ ⎟
2 ⎝3⎠ (D) 2⎛1⎞
⎜⎟
3⎝3⎠ 2 n n ∫0 8
3 n⎤ ⎥
⎥
⎦ n n +1 4 − x 2 dx = (A) 31. 34π
3 (B) 8π (C) i (B) (B) 16
3 (D) 2π 32. The general solution of the differential equation y′ = y + x 2 is y =
(A) Ce x (B) Ce x + x 2 (D) e x − x2 − 2 x − 2 + C (E) Ce x − x 2 − 2 x − 2 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (C) − x 2 − 2 x − 2 + C 74 1988 AP Calculus BC: Section I
33. The length of the curve y = x3 from x = 0 to x = 2 is given by
2 (A) ∫0 1 + x 6 dx (D) 2π ∫ 2 ∫0 1 + 3x 2 dx (E) 1 + 9 x 4 dx 0 2 (B) ∫0 2 (C) π ∫ 2 1 + 9 x 4 dx 0 1 + 9 x 4 dx 34. A curve in the plane is defined parametrically by the equations x = t 3 + t and y = t 4 + 2t 2 .
An equation of the line tangent to the curve at t = 1 is
(A) y = 2x (B) y = 8x (D) y = 4x − 5 (E) y = 8 x + 13 35. If k is a positive integer, then lim x→+∞ (A) 0 (B) 1 xk
ex (C) y = 2x −1 is
(D) k ! (C) e (E) nonexistent 36. Let R be the region between the graphs of y = 1 and y = sin x from x = 0 to x = π
. The volume of
2 the solid obtained by revolving R about the xaxis is given by
(A) 2π ∫
(D) π ∫ π
2
0 π
2
0 (B) 2π ∫ x sin x dx (E) π ∫ sin 2 x dx π
2
0 π
2
0 (C) π ∫ x cos x dx π
2
0 (1 − sin x )2 dx (1 − sin 2 x ) dx 37. A person 2 meters tall walks directly away from a streetlight that is 8 meters above the ground. If
4
the person is walking at a constant rate and the person’s shadow is lengthening at the rate of
9
meter per second, at what rate, in meters per second, is the person walking?
(A) 4
27 (B) 4
9 (C) 3
4 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 4
3 (E) 16
9 75 1988 AP Calculus BC: Section I
∞ xn
∑ n converges?
n =1 38. What are all values of x for which the series
(A) −1 ≤ x ≤ 1 (B) (D) −1 < x < 1 (E) All real x 39. If −1 < x ≤ 1 (C) −1 ≤ x < 1 (C) 5e tan x dy
= y sec 2 x and y = 5 when x = 0, then y =
dx (A) e tan x + 4 (B) e tan x + 5 (D) tan x + 5 (E) tan x + 5e x 40. Let f and g be functions that are differentiable everywhere. If g is the inverse function of f and
1
if g (−2) = 5 and f ′(5) = − , then g ′(−2) =
2
(A) 2 41. lim n→∞ 1
2 (D) ∫ 1 x dx 2 ∫1 ∫0 (E) 1 11
dx
2 ∫0 x 4 1
5 1
5 2 ∫ x x dx − (E) −2 (C) (D) ∫ 0 x dx (E) −6 1⎡ 1
2
n⎤
+
+… +
⎢
⎥=
n⎣ n
n
n⎦ (A) 42. If (C) (B) (B) f ( x) dx = 6, what is the value of (A) 6 (B) 3 4 ∫1 1 x dx 1 2 1 f (5 − x) dx ? (C) 0 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) −1 76 1988 AP Calculus BC: Section I
43. Bacteria in a certain culture increase at a rate proportional to the number present. If the number of
bacteria doubles in three hours, in how many hours will the number of bacteria triple?
(A) 3 ln 3
ln 2 (B) 2 ln 3
ln 2 (C) ln 3
ln 2 ⎛ 27 ⎞
(D) ln ⎜ ⎟
⎝2⎠ (E) ⎛9⎞
ln ⎜ ⎟
⎝2⎠ 44. Which of the following series converge?
I. ∞ 1 ∑ (−1)n+1 2n + 1
n =1 ∞ II. ∑ 1⎛3⎞
⎜⎟
n⎝2⎠ ∞ 1
n ln n n =1 III. ∑ n=2 (A)
(B)
(C)
(D)
(E) n I only
II only
III only
I and III only
I, II, and III 45. What is the area of the largest rectangle that can be inscribed in the ellipse 4 x 2 + 9 y 2 = 36 ?
(A) 62 (B) 12 (C) 24 AP Calculus MultipleChoice Que...
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This note was uploaded on 12/29/2010 for the course MATH 214 taught by Professor Smith during the Fall '10 term at Oregon Tech.
 Fall '10
 smith
 Calculus

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