1997 AP Calculus BC Section I Part B 78 \u00b2 \u00b3 ln 1 lim h e h h o \u00b5 is A where ln

# 1997 ap calculus bc section i part b 78 ² ³ ln 1

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1997 AP Calculus BC: Section I, Part B 78. ²³0 ln 1 lim h e h h o µ ± is (A) ( ), where ( )lnfef xxc(B) ln( ), where ( )xfef xxc(C) (1), where ( )lnff xxc(D) ²³(1), where ( )lnffxxecµ(E) (0), where ( )lnff xxc 79. The position of an object attached to a spring is given by 11( )cos(5 )sin(5 )64y ttt±, where tis time in seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0? 80. Let f be the function given by ( ) cos(2 ) ln(3 ) f x x x µ . What is the least value of x at which the graph of f changes concavity? 81. Let fbe a continuous function on the closed interval >@3,6±. If ²³31f±±and ² ³63f, then the Intermediate Value Theorem guarantees that AP Calculus Multiple-Choice Question Collection 122 Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 1997 AP Calculus BC: Section I, Part B 82. If 04xdd, of the following, which is the greatest value ofx such that 202(2 )xxtt dttdt±t³³? (A) 1.35 (B) 1.38 (C) 1.41 (D) 1.48 (E) 1.59 83. If ²³1lndyxydxµand if y= 1 when x= 1, then y= 2 2 1 x x e ± 84. 2sinxxdx³ x x C ± µ 85. Let f be a twice differentiable function such that (1)2fand (3)7.fWhich of the following must be true for the function f on the interval 13xdd? I. The average rate of change of f is 52. II. The average value of f is 92. III. The average value of fcis 52. AP Calculus Multiple-Choice Question Collection 123 Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 1997 AP Calculus BC: Section I, Part B 86. (1)(3) dx x x ± µ ³ (A) 11ln43(B) 13ln41(C) ²³²³1ln132xxC±µµ(D) ²³²³(E) ²³²³ln13xxC±µµ x C x ± µ µ x C x µ µ ± 1 2 2 ln 2 1 3 x C x x µ µ ± µ 87. The base of a solid is the region in the first quadrant enclosed by the graph of 22yx±and the coordinate axes. If every cross section of the solid perpendicular to the y-axis is a square, the volume of the solid is given by   • • • 