1969, 1973, 1985, 1993, 1997, 1998 AP Multiple Choice Sections, AB and BC, Solutions (620)

At x 0 which of the following is true of the function

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Unformatted text preview: ity at time t ( t > 0 ) is given by v = ln t . t At what value of t does v attain its maximum? (A) 1 (E) (B) 1 e2 (C) e (D) 3 e2 There is no maximum value for v. 20. An equation for a tangent to the graph of y = arcsin x at the origin is 2 (A) x − 2y = 0 (B) x− y =0 (D) y=0 (E) π x − 2y = 0 (C) x=0 21. At x = 0 , which of the following is true of the function f defined by f ( x) = x 2 + e −2 x ? (A) f is increasing. (B) f is decreasing. (C) f is discontinuous. (D) f has a relative minimum. (E) f has a relative maximum. 22. If f ( x) = ∫ x 1 0 3 t +2 dt , which of the following is FALSE? (A) f (0) = 0 (B) f is continuous at x for all x ≥ 0 . (C) f (1) > 0 (D) f ′(1) = (E) 1 3 f (−1) > 0 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 14 1969 AP Calculus BC: Section I 23. If the graph of y = f ( x) contains the point ( 0, 2 ) , (A) 3+e − x 2 3+e − x (D) (B) − tan x (B) 3 + e− x (E) 2 24. If sin x = e y , 0 < x < π, what is (A) dy −x = and f ( x) > 0 for all x, then f ( x) = dx ye x 2 3+e x (C) 1 + e− x 2 dy in terms of x ? dx − cot x (C) cot x 25. A region in the plane is bounded by the graph of y = x = 2m , m > 0 . The area of this region (D) tan x (E) csc x 1 , the x-axis, the line x = m , and the line x (A) is independent of m . (B) increases as m increases. (C) decreases as m increases. 1 1 ; increases as m increases when m > . 2 2 1 1 increases as m increases when m < ; decreases as m increases when m > . 2 2 (D) decreases as m increases when m < (E) 26. 1 ∫0 x 2 − 2 x + 1 dx is (A) −1 (B) − 1 2 1 2 (D) 1 (E) none of the above (C) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 15 1969 AP Calculus BC: Section I dy = tan x , then y = dx 27. If (A) 1 tan 2 x + C 2 (B) sec 2 x + C (D) ln cos x + C (E) sec x tan x + C (C) ln sec x + C e2 x − 1 ? x→0 tan x 28. What is lim (A) –1 29. ∫0 ( 1 (A) 30. (B) 0 3 2 −2 4− x ) 2− 3 3 (C) 1 (D) 2 (E) The limit does not exist. dx = (B) 2 3 −3 4 (C) 3 12 (D) 3 3 (E) 3 2 ∞ (−1) n x n ∑ n ! is the Taylor series about zero for which of the following functions? n =0 (A) sin x (B) cos x (C) ex (D) e− x (E) ln(1 + x) e1− x (D) e− x (E) −e x 31. If f ′( x) = − f ( x) and f (1) = 1, then f ( x) = (A) 1 −2 x + 2 e 2 (B) e − x −1 (C) 32. For what values of x does the series 1 + 2 x + 3x + 4 x + (B) x < −1 (A) No values of x + nx + (C) x ≥ −1 converge? (D) x > −1 (E) All values of x 33. What is the average (mean) value of 3t 3 − t 2 over the interval −1 ≤ t ≤ 2 ? (A) 11 4 (B) 7 2 (C) 8 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 33 4 (E) 16 16 1969 AP Calculus BC: Section I 34. Which of the following is an equation of a curve that intersects at right angles every curve of the 1 family y = + k (where k takes all real values)? x 1 1 (A) y = − x (B) y = − x 2 (C) y = − x3 (D) y = x3 (E) y = ln x 3 3 35. At t = 0 a particle starts at rest and moves along a line in such a way that at time t its acceleration is 24t 2 feet per second per second. Through how many feet does the particle move during the first 2 seconds? (A) 32 (B) 48 (C) 64 (D) 96 (E) 192 36. The approximate value of y = 4 + sin x at x = 0.12 , obtained from the tangent to the graph at x = 0, is (A) 2.00 (B) 2.03 (C) 2.06 (D) 2.12 (E) 2.24 37. Of the following choices of δ , which is the largest that could be used successfully with an arbitrary ε in an epsilon-delta proof of lim (1 − 3x ) = −5? x →2 (A) δ = 3ε ( ) 38. If f ( x) = x 2 + 1 (A) 1 − ln(8e) 2 δ=ε (B) (2−3 x ) (C) δ= ε 2 (D) δ= (C) 3 − ln(2) 2 (D) − ε 4 (E) δ= (E) ε 5 1 8 , then f ′(1) = (B) − ln(8e) 1 2 1 dy at x = e ? 39. If y = tan u , u = v − , and v = ln x , what is the value of v dx (A) 0 (B) 1 e (C) 1 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 2 e (E) sec 2 e 17 1969 AP Calculus BC: Section I 40. If n is a non-negative integer, then (A) no n (D) nonzero n, only 1 ∫0 x n 42. If ∫x 2 (B) 1 0 (1 − x )n dx (B) n even, only (E) all n ⎧ f ( x) = 8 − x 2 for − 2 ≤ x ≤ 2, ⎪ then 41. If ⎨ 2 elsewhere , ⎪ f ( x) = x ⎩ (A) 0 and 8 dx = ∫ 8 and 16 for (C) n odd, only 3 ∫ −1 f ( x) dx is a number between (C) 16 and 24 (D) 24 and 32 (E) 32 and 40 cos x dx = f ( x) − ∫ 2 x sin x dx, then f ( x) = (A) 2 sin x + 2 x cos x + C (B) x 2 sin x + C (C) 2 x cos x − x 2 sin x + C (D) 4 cos x − 2 x sin x + C (E) ( 2 − x2 ) cos x − 4sin x + C 43. Which of the following integrals gives the length of the graph of y = tan x between x = a and π x = b , where 0 < a < b < ? 2 b (A) ∫a (B) ∫a (C) ∫a...
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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.

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