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Unformatted text preview: −1 g ( x) dx + ∫ b (C) ∫ −1( f ( x) − g ( x) ) dx (D) ∫ −1( f ( x) − g ( x) ) dx (E) 6. ∫ 0 ( f ( x) − g ( x) ) dx + ∫ −1 ( f ( x) + g ( x) ) dx ∫ −1( b c f ( x) dx c a a If f ( x) = (A) 2 f ( x) − g ( x) ) dx x
⎛π⎞
, then f ′ ⎜ ⎟ =
tan x
⎝4⎠
(B) 1
2 (C) 1 + π
2 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) π
−1
2 (E) 1− π
2 48 1985 AP Calculus BC: Section I
1 Which of the following is equal to ∫ x
(A) arcsin + C
5 7. (B) arcsin x + C (E) 2 25 − x 2 + C (D)
8. 25 − x 2 + C If f is a function such that lim x →2 25 − x 2 dx ?
(C) 1
x
arcsin + C
5
5 f ( x) − f (2)
= 0 , which of the following must be true?
x−2 (A) The limit of f ( x) as x approaches 2 does not exist.
(B)
(C) f is not defined at x = 2 .
The derivative of f at x = 2 is 0. (D)
(E)
9. f is continuous at x = 0 .
f (2) = 0 If xy 2 + 2 xy = 8, then, at the point ( 1, 2 ) , y′ is
(A) − 5
2 − (B) 4
3 (C) –1 (D) − 1
2 (E) 0 (−1)n +1 x 2 n−1
, then f ′( x) =
2n − 1
n =1
∞ 10. For −1 < x < 1 if f ( x) = ∑
∞ (A) ∑ (−1)n+1 x 2n−2 n =1 (B) ∞ ∑ (−1)n x 2n−2 n =1 (C) ∞ ∑ (−1)2n x 2n
n =1
∞ (D) ∑ (−1)n x2n n =1 (E) ∞ ∑ (−1)n+1 x 2n
n =1 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 49 1985 AP Calculus BC: Section I
11. d ⎛1⎞
ln ⎜
⎟=
dx ⎝ 1 − x ⎠
(A) 12. 1
1− x 1
x −1 (B) (C) 1 − x (D) x −1 (E) (1 − x )2 dx ∫ ( x − 1)( x + 2) =
(A) 1
x −1
ln
+C
3
x+2 (B) 1
x+2
ln
+C
3
x −1 (D) ( ln (E) ln ( x − 1)( x + 2) 2 + C x −1 ) ( ln x+2 )+C (C) 1
ln ( x − 1)( x + 2) + C
3 13. Let f be the function given by f ( x) = x3 − 3 x 2 . What are all values of c that satisfy the conclusion
of the Mean Value Theorem of differential calculus on the closed interval [ 0,3] ?
(A) 0 only (B) 2 only (C) 3 only (D) 0 and 3 (E) 2 and 3 14. Which of the following series are convergent?
I.
II.
III. 1+ 1
2 2 + 1
2 3 +… + 1 n2 +… 11
1
1+ + +… + +…
23
n
11
(−1) n +1
1 − + 2 − … + n −1 + …
33
3 (A) I only (B) III only (C) I and III only (D) II and III only (E) I, II, and III 15. If the velocity of a particle moving along the xaxis is v(t ) = 2t − 4 and if at t = 0 its position is 4,
then at any time t its position x(t ) is
(A) t 2 − 4t (B) t 2 − 4t − 4 (C) t 2 − 4t + 4 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 2t 2 − 4t (E) 2t 2 − 4t + 4 50 1985 AP Calculus BC: Section I
16. Which of the following functions shows that the statement “If a function is continuous at x = 0 ,
then it is differentiable at x = 0 ” is false?
(A) f ( x) = x − 4
3 (B) 1
3 (C) f ( x) = ln x 2 + 2 (C) ln x 2 + f ( x) = x − 1
x3 (D) f ( x) = 4
x3 f ( x) = x3 (E) () 17. If f ( x) = x ln x 2 , then f ′( x) =
(A)
18. () ln x 2 + 1 (B) () () 1
x (D) 1 x (E) 2 1
x ∫ sin ( 2 x + 3) dx =
(A) −2 cos ( 2 x + 3) + C
(D) 1
cos ( 2 x + 3) + C
2 (B) − cos ( 2 x + 3) + C (E) 1
(C) − cos ( 2 x + 3) + C
2 cos ( 2 x + 3) + C 19. If f and g are twice differentiable functions such that g ( x) = e f ( x ) and g ′′( x) = h( x)e f ( x ) ,
then h( x) =
(A) f ′( x) + f ′′( x)
(D) (B) ( f ′( x) )2 + f ′′( x) f ′( x) + ( f ′′( x) ) 2 (C) ( f ′( x) + f ′′( x) )2 (E) 2 f ′( x) + f ′′( x) 20. The graph of y = f ( x) on the closed interval [ 2, 7 ] is shown above. How many points of
inflection does this graph have on this interval?
(A) One (B) Two (C) Three AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) Four (E) Five
51 1985 AP Calculus BC: Section I
21. If ∫ (A) f ( x) sin x dx = − f ( x) cos x + ∫ 3 x 2 cos x dx , then f ( x) could be 3x 2 (B) x3 (C) − x3 (D) sin x (E) cos x 22. The area of a circular region is increasing at a rate of 96π square meters per second. When the area
of the region is 64π square meters, how fast, in meters per second, is the radius of the region
increasing?
(A) 6
1+ h 23. lim ∫1 (B) 8 (D) 43 (E) 12 3 (C) 3 (D) 22 (E) nonexistent (E) π
4 x5 + 8 dx
h h →0 (C) 16 (A) 0 is
(B) 1 24. The area of the region enclosed by the polar curve r = sin ( 2θ ) for 0 ≤ θ ≤
(A) 0 (B) 1
2 (C) 1 (D) π
8 π
is
2 25. A particle moves along the xaxis so that at any time t its position is given by x(t ) = te−2t . For what
values of t is the particle at rest?
(A) No values 26. For 0 < x <
(A)
(D) (B) 0 only (C) 1
only
2 (D) 1 only (E) 0 and 1
2 π
dy
x
, if y = ( sin x ) , then
is
2
dx x ln ( sin x ) ( sin x ) x ( x cos x + sin x ) (B) ( sin x ) x cot x (E) AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Av...
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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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