Unformatted text preview: y =
(A) 5. xe x ( x + 2 ) {x : (C) {x : (E) {x : x2 − 4
?
x−3 x ≤ 2} x ≥ 2} x ≥ 2 and x ≠ 3} A particle with velocity at any time t given by v(t ) = et moves in a straight line. How far does the
particle move from t = 0 to t = 2 ?
(A) 4. (C) 2x + e (A) 3. ) ∫ sec x<0
2 (B) e −1 (C) 2e (D) e2 (E) e3
3 (E) x>2 (C) cos 2 x + C −5
is concave downward for all values of x such that
x−2
(B) x<2 (C) x<5 (D) x>0 x dx = (A) tan x + C (B) csc 2 x + C (D) sec3 x
+C
3 (E) 2sec2 x tan x + C AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 57 1988 AP Calculus AB: Section I 7. If y = ln x
dy
, then
=
x
dx (A) 6. 1
x (B) x dx ∫ 3x 2 + 5 (C) ln x − 1
x (D) 2 ) 3
2 +C (B) 1
3x 2 + 5
4 ) 1
2 +C (E) 3
3x 2 + 5
2 (
(A) (D) 8. x 2 1 − ln x
x 2 1 + ln x (E) x2 = 1
3x 2 + 5
9
1
3x 2 + 5
3 ( 1 (
( ) 3
2 +C ) 1
2 +C ( 1
3x 2 + 5
(C)
12 ) 1
2 +C The graph of y = f ( x) is shown in the figure above. On which of the following intervals are
dy
d2y
> 0 and
<0?
dx
dx 2
I.
II.
III. a< x<b
b<x<c
c<x<d (A) I only (B) II only (C) III only AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) I and II (E) II and III 58 1988 AP Calculus AB: Section I
9. If x + 2 xy − y 2 = 2, then at the point (1,1) ,
3
2 (A) 10. If k ∫0 (B) 1
2 dy
is
dx − (C) 0 (D) (C) 3 3
2 (D) 9 (E) nonexistent ( 2kx − x2 ) dx = 18, then k = (A) –9 (B) –3 (E) 18 11. An equation of the line tangent to the graph of f ( x) = x(1 − 2 x)3 at the point (1, − 1) is
(A) y = −7 x + 6 (B) y = −6 x + 5 (D) y = 2x − 3 (E) y = 7x − 8 (C) 2
2 (C) y = −2 x + 1 (E) 3 ⎛π⎞
12. If f ( x) = sin x , then f ′ ⎜ ⎟ =
⎝3⎠
(A) − 1
2 (B) 1
2 (D) 13. If the function f has a continuous derivative on [ 0, c ] , then
(A) f (c) − f (0) 14. ∫ π
2
0 (B) f (c) − f (0) (C) f (c ) c ∫0 3
2 f ′( x) dx = (D) f ( x) + c (E) f ′′(c) − f ′′(0) cos θ
dθ =
1 + sin θ (A) −2
(D) 2 ( ( ) 2 −1 ) 2 −1 (B) −2 2
(E) 2 ( (C) 2 2 ) 2 +1 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 59 1988 AP Calculus AB: Section I
15. If f ( x) = 2 x , then f ′(2) = (A) 1
4 (B) 1
2 (C) 2
2 (D) 1 2 (E) 16. A particle moves along the xaxis so that at any time t ≥ 0 its position is given by
x(t ) = t 3 − 3t 2 − 9t + 1 . For what values of t is the particle at rest? (A) No values
17. 1 ∫ 0 ( 3x − 2 )
(A) − 2 (B) 1 only (C) 3 only (D) 5 only (E) 1 and 3 dx = 7
3 (B) − 7
9 1
9 (D) 1 (E) 3 ⎛ x⎞
(C) − sin ⎜ ⎟
⎝2⎠ ⎛x⎞
(D) − cos ⎜ ⎟
⎝2⎠ 1
⎛ x⎞
(E) − cos ⎜ ⎟
2
⎝2⎠ (C) ln 2 (D) 2 ln 2 (E) (C) d2y
⎛x⎞
18. If y = 2 cos ⎜ ⎟ , then
=
dx 2
⎝2⎠ ⎛ x⎞
(A) −8 cos ⎜ ⎟
⎝2⎠
19. 3 ∫2 (A) x
2 x +1 ⎛ x⎞
(B) −2 cos ⎜ ⎟
⎝2⎠ dx = 13
ln
22 (B) 1
ln 2
2 1
ln 5
2 20. Let f be a polynomial function with degree greater than 2. If a ≠ b and f (a) = f (b) = 1 , which
of the following must be true for at least one value of x between a and b?
I.
II.
III. f ( x) = 0
f ′( x) = 0
f ′′( x) = 0 (A) None (B) I only (C) II only (D) I and II only AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) I, II, and III 60 1988 AP Calculus AB: Section I
21. The area of the region enclosed by the graphs of y = x and y = x 2 − 3 x + 3 is
(A) 2
3 (C) 4
3 (C) (B) 1 e (E) 14
3 (E) (D) 2 e2 ⎛1⎞
22. If ln x − ln ⎜ ⎟ = 2, then x =
⎝ x⎠
(A) 1
e 1
e (B) 2 (D) 2e f ( x)
is
x→0 g ( x ) 23. If f ′( x) = cos x and g ′( x) = 1 for all x, and if f (0) = g (0) = 0 , then lim (A) 24. π
2 (B) 1 (D) −1 (E) nonexistent () d ln x
x
=
dx
(A) x ln x (B) ( ln x ) x 25. For all x > 1, if f ( x) = ∫
(A) 1 26. (C) 0 ∫ π
2
0 (A) (B) (C) x
1 () 2
( ln x ) xln x
x (D) ( ln x ) ( xln x−1 ) () (E) 2 ( ln x ) x ln x 1
dt , then f ′( x) =
t 1
x (C) ln x − 1 (D) ln x (E) ex (D) 1 (E) π
−1
2 x cos x dx = − π
2 (B) –1 (C) 1 − π
2 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 61 1988 AP Calculus AB: Section I
⎧ x2 , x < 3
⎪
27. At x = 3 , the function given by f ( x ) = ⎨
is
⎪6 x − 9, x ≥ 3
⎩
(A)
(B)
(C)
(D)
(E)
28. 4 ∫1 (A) undefined.
continuous but not differentiable.
differentiable but not continuous.
neither continuous nor differentiable.
both continuous and differentiable.
x − 3 dx = − 3
2 (B) 3
2 (C) 5
2 (D) 9
2 (E) 5 tan 3( x + h ) − tan 3x
is
h →0
h 29. The lim
(A) 0 (B) 3sec 2 (3x) (C) sec2 (3 x) (D) 3cot(3x) (E) nonexistent 30. A region in the first quadrant is enclosed by the graphs of y = e 2 x , x = 1, and the coordinate axes.
If the region is rotated about the y axis , the volume of the solid that is...
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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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