1988 AP Calculus BC: Section I
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1 988 AP Calculus BC: Sectio I 9 Miutes No Calculator Notes: () I this eamiatio, l deotes the atural logarithm of (that is, logarithm to the base e). () Uless otherwise specified, the domai of a fuctio f is assumed to be the set of all real umbers for which f () is a real umber.. The area of the regio i the first quadrat eclosed by the graph of y ad the -ais is 5. d ( ) l, the f ( ). If f. If u, v, ad w are ozero differetiable fuctios, the the derivative of uv w is uv uv w uvw uvw w uvwuvw uvw w uvw uvw uvw w uvw uvw uvw w AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
2 988 AP Calculus BC: Sectio I 5. Let f be the fuctio defied by the followig. si,, f( ),, For what values of is f NOT cotiuous? oly oly oly ad oly,, ad. If y y, the dy d y y y y y y y y y 7. d is l oeistet 8. If f ( ) e, the l f () e e e AP Calculus Multiple-Choice Questio Collectio 8 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
3 988 AP Calculus BC: Sectio I 9. Which of the followig pairs of graphs could represet the graph of a fuctio ad the graph of its derivative? I oly II oly III oly I ad III II ad III. si lim h h si h is si cos oeistet. If 7 y 9 is a equatio of the lie ormal to the graph of f at the poit,, the f () A particle travels i a straight lie with a costat acceleratio of meters per secod per secod. If the velocity of the particle is meters per secod at time secods, how far does the particle travel durig the time iterval whe its velocity icreases from meters per secod to meters per secod? m m 7 m m m AP Calculus Multiple-Choice Questio Collectio 9 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
4 988 AP Calculus BC: Sectio I. si 5 ( )! 5!! 5 ( ) ( ) ( ) ( )! 5!! ( ) ( ) ( ) ( )!!!!!!! 5 ( ) ( ) ( )! 5!!. If t dt the F( ) F( ), t t dt 5. For ay time t, if the positio of a particle i the y-plae is give by y l t, the the acceleratio vector is t ad, t ( t ), t ( t ), (t ), (t ), (t ) AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
5 988 AP Calculus BC: Sectio I. e d e e C e e C e e C e e C e C 7. ( )( ) d 9 5 l 8 l 5 l 5 8. If three equal subdivisios of, are used, what is the trapezoidal approimatio of e d? e e e e e e e e e e e e e e e e e e 9. A polyomial p( ) has a relative maimum at,, a relative miimum at,, a relative maimum at 5,7 ad o other critical poits. How may zeros does p( ) have? Oe Two Three Four Five. The statemet lim f ( ) L meas that for each, there eists a such that a if a, the f( ) L if f( ) L, the a if f( ) L, the a a ad f( ) L if a, the f( ) L AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
6 . The average value of o the closed iterval, is 988 AP Calculus BC: Sectio I l l l. If f ( ), the f ( ) l l l. Which of the followig gives the area of the regio eclosed by the loop of the graph of the polar curve r cos( ) show i the figure above? cos( ) d 8 cos( )d 8 cos ( )d cos ( ) d 8 cos ( )d AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
7 988 AP Calculus BC: Sectio I. If c is the umber that satisfies the coclusio of the Mea Value Theorem for the iterval, the c = f ( ) o 5. The base of a solid is the regio i the first quadrat eclosed by the parabola y, the lie, ad the -ais. Each plae sectio of the solid perpedicular to the -ais is a square. The volume of the solid is If f is a fuctio such that f ( ) eists for all ad f( ) for all, which of the followig is NOT ecessarily true? f( ) d f ( d ) f( d ) f ( d ) f( d ) f ( d ) f( d ) f ( d ) f( d ) f( d ) 7. If the graph of has a poit of iflectio at, y a b, what is the value of b? It caot be determied from the iformatio give. AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
8 988 AP Calculus BC: Sectio I d 8. l cos d is cos ta cos ta ta 9. The regio R i the first quadrat is eclosed by the lies ad y 5 ad the graph of y. The volume of the solid geerated whe R is revolved about the y -ais is i i. d 8. The geeral solutio of the differetial equatio y y is y = Ce Ce C e C Ce AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
9 988 AP Calculus BC: Sectio I. The legth of the curve y from = to = is give by d d 9 d 9 d 9 d. A curve i the plae is defied parametrically by the equatios A equatio of the lie taget to the curve at t is t t ad y t t. y y 8 y y 5 y 8 5. If k is a positive iteger, the lim e k is e k! oeistet. Let R be the regio betwee the graphs of y ad the solid obtaied by revolvig R about the -ais is give by y si from to. The volume of sid cosd si d si d si d 7. A perso meters tall walks directly away from a streetlight that is 8 meters above the groud. If the perso is walkig at a costat rate ad the perso s shadow is legtheig at the rate of 9 meter per secod, at what rate, i meters per secod, is the perso walkig? AP Calculus Multiple-Choice Questio Collectio 75 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
10 988 AP Calculus BC: Sectio I 8. What are all values of for which the series coverges? All real 9. If dy ysec ad y = 5 whe =, the y = d ta e ta e 5 5e ta ta 5 ta 5e. Let f ad g be fuctios that are differetiable everywhere. If g is the iverse fuctio of f ad if g( ) 5 ad f (5), the g( ) 5 5. lim d d d d d. If f( ) d, what is the value of f (5 d )? AP Calculus Multiple-Choice Questio Collectio 7 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
11 988 AP Calculus BC: Sectio I. Bacteria i a certai culture icrease at a rate proportioal to the umber preset. If the umber of bacteria doubles i three hours, i how may hours will the umber of bacteria triple? l l l l l l l 7 9 l. Which of the followig series coverge? I. ( ) II. III. l I oly II oly III oly I ad III oly I, II, ad III 5. What is the area of the largest rectagle that ca be iscribed i the ellipse 9y? AP Calculus Multiple-Choice Questio Collectio 77 Copyright 5 by College Board. All rights reserved. Available at apcetral.collegeboard.com.
(c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is
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