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Unformatted text preview: ver x − 2 < δ ?
(A) π4 ε
4 ∫0 π
−1
4 ε
2 (C) ε
ε +1 (D) (C) 1
3 ε +1
ε (D) (E) 3ε (E) π
+1
4 tan 2 x dx = (A) 25. (B) (B) 1 − π
4 2 −1 26. Which of the following is true about the graph of y = ln x 2 − 1 in the interval ( −1,1) ?
(A)
(B)
(C)
(D)
(E) It is increasing.
It attains a relative minimum at ( 0, 0 ) .
It has a range of all real numbers.
It is concave down.
It has an asymptote of x = 0 . 13
x − 4 x 2 + 12 x − 5 and the domain is the set of all x such that 0 ≤ x ≤ 9 , then the
3
absolute maximum value of the function f occurs when x is 27. If f ( x) = (A) 0 (B) 2 (C) 4 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 6 (E) 9
33 1973 AP Calculus BC: Section I
x = sin y is made in the integrand of 28. If the substitution
12 (A) ∫0 (D) ∫0 π4 12 sin y dy (B) 2∫ 0 sin 2 y dy (E) 2∫ 0 2 π6 x 12 ∫0 sin 2 y
dy
cos y 1− x dx , the resulting integral is 2∫ (C) π4
0 sin 2 y dy sin 2 y dy 29. If y′′ = 2 y′ and if y = y′ = e when x = 0, then when x = 1, y =
(A) ( ∫1 x−4 (A) 30. ) e2
e +1
2 − 2 ( e3 − e ) (B) e (C) e3
2 (B) ln 2 − 2 (C) ln 2 (D) 2 (E) ln 2 + 2 (C) ln x
x (D) (E) 1
x ln x (D) e
2 (E) 2 dx x2 1
2 31. If f ( x) = ln ( ln x ) , then f ′( x) =
(A) 1
x (B) 1
ln x x 32. If y = x ln x , then y′ is
(A) x ln x ln x
x2 (B) x1 x ln x (C) 2 x ln x ln x
x (D) x ln x ln x
x (E) None of the above AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 34 1973 AP Calculus BC: Section I
33. Suppose that f is an odd function; i.e., f (− x) = − f ( x) for all x. Suppose that f ′ ( x0 ) exists.
Which of the following must necessarily be equal to f ′ ( − x0 ) ? (A) f ′ ( x0 ) (B) − f ′ ( x0 ) (C) 1
f ′ ( x0 ) (D) − (E) None of the above 1
f ′ ( x0 ) x over the interval 0 ≤ x ≤ 2 is 34. The average (mean) value of
1
2
3 (A) (B) 1
2
2 (C) 2
2
3 (D) 1 35. The region in the first quadrant bounded by the graph of y = sec x, x = (E) 4
2
3 π
, and the axes is rotated
4 about the xaxis. What is the volume of the solid generated?
π2
4 (A) (B) x +1 1 37. ∫0 x2 + 2 x − 3 (A) 36. (B) − ln 3 lim x2 (A) –2
38. If − (D) 2π (E) 8π
3 (D) ln 3 (E) divergent (D) 2 (C) π (E) 4 (E) –5 dx is 1 − cos 2 (2 x) x →0 π −1 ln 3
2 (C) 1 − ln 3
2 = (B) 0 (C) 1
2−c 2 ∫ 1 f ( x − c ) dx = 5 where c is a constant, then ∫ 1−c f ( x ) dx = (A) 5+c (B) 5 (C) 5−c AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) c − 5 35 1973 AP Calculus BC: Section I
39. Let f and g be differentiable functions such that
f (1) = 2 , f ′(1) = 3 , f ′(2) = −4 , g (1) = 2 , g ′(1) = −3 , g ′(2) = 5. If h( x) = f ( g ( x) ) , then h′(1) =
(A) –9 (B) –4 (C) 0 (D) 12 (E) 15 40. The area of the region enclosed by the polar curve r = 1 − cos θ is
(A) 3
π
4 (B) π (C) ⎧ x + 1 for x < 0,
41. Given f ( x) = ⎨
⎩cos π x for x ≥ 0,
(A) 11
+
2π (B) − 1
2 3
π
2 (D) 2π (E) 3π (D) 1
2 (E) 1
− +π
2 1 ∫ −1 f ( x) dx =
(C) 11
−
2π 42. Calculate the approximate area of the shaded region in the figure by the trapezoidal rule, using
4
5
divisions at x = and x = .
3
3
(A) 50
27 (B) 251
108 (C) 7
3 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 127
54 (E) 77
27 36 1973 AP Calculus BC: Section I
43. ∫ arcsin x dx =
x dx (A) sin x − ∫ (B) ( arcsin x )2 + C (C) arcsin x + ∫ (D) x arccos x − ∫ (E) x arcsin x − ∫ 1 − x2 2 dx
1 − x2
x dx
1 − x2
x dx
1 − x2 () 44. If f is the solution of x f ′( x) − f ( x) = x such that f (−1) = 1, then f e −1 =
(A) −2e −1 (B) 0 e −1 C) (D) −e−1 (E) 2e −2 x 45. Suppose g ′( x) < 0 for all x ≥ 0 and F ( x) = ∫ t g ′(t ) dt for all x ≥ 0 . Which of the following
0 statements is FALSE?
(A) F takes on negative values. (B) F is continuous for all x > 0. (C) F ( x) = x g ( x) − ∫ (D) F ′( x) exists for all x > 0. (E) F is an increasing function. x
0 g (t ) dt AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 37 1985 AP Calculus AB: Section I
90 Minutes—No Calculator Notes: (1) In this examination, ln x denotes the natural logarithm of x (that is, logarithm to the base e).
(2) Unless otherwise specified, the domain of a function f is assumed to be the set of all real
numbers x for which f (x) is a real number.
1. 2 ∫1 x −3 dx = − (A) 2. 7
8 (C) 15
64 (D) If y = If (B) 24
3 4+ x 2 (E) 15
16 ( 4 + x2 ) 2 48 (D) 240 (E) 384 dy
=
dx , then −6 x (C) (B) 3x ( 4 + x2 ) 2 (C) 6x ( 4 + x2 ) 2 (D) −3 ( 4 + x2 ) 2 (E) 3
2x dy
= cos ( 2 x ) , the...
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