AP Calculus Multiple Choice Questions - Chapter 7

Transcription

1 Find the general solution to the eact differential equation dy/d = t cos(t ) a y = cos(6t) + b y = sin(6t) + c y = cos(t ) + d y = sin(t ) + Find the general solution to the eact differential equation dy/d = sec AP alculus Multiple hoice Questions - hapter 7 a y = 5 - tan + b y = 0 + tan + c y = 5 + tan + d y = 0 - tan + Find the general solution to the eact differential equation dy/d = sec tan - e a y = sec + e + b y = sec - e + c y = sin + e + d y = sin - e + 7.a 7.a 7.a 7.a The graph of f', the derivative of the function f, is shown above for 0 0. The areas of the regions between the graph of f' and the -ais are 0, 6, and 4, respectively. If f(0) =, what is the maimum value of f on the closed interval 0 0? a 6 b 0 c d 0 e Updated /4/08 Boyceville High School, Mr. Hamm Page of

2 Which of the following is the solution to the differential equation where y() = -? dy 4 d y a y = for > 0 b y = - 6 for is not equal to c for > (/) d y 4 y 4 for > (/) e for >.5 (/) y b If dy/d = y and y = when = 0, then y = a y b e ^ c y d y + e ( y / ) + dy/d = sin() and y = when = 0 a y = cos() + 5 b y = cos() - c y = cos() + d y = - cos() + 5 If f'() = / and f(e / ) = 5, then f(e) = a b ln 5 c 5 + (/e) - (/e ) d 6 e 5 7.b 7.b 7.b Updated /4/08 Boyceville High School, Mr. Hamm Page of

3 7.c The slope field for a certain differential equation is shown above. Which of the following could be a solution to the differential equation with the initial condition y(0) =? a y = cos() b - c y = e d e y = /( + ) y A slope field for the differential equaion dy/d = 4 - y will show a A line with slope - and y-intercept 4 b A vertical asymptote at = 4 c A horizontal asymptote at y = 4 d A family of parabolas opening downward e A family of parabolas opening to the left For which of the following differential equations will a slope field show nothing but negative slopes in the fourth quadrant? a dy/d = - / y b dy/d = y + 5 c dy/d = y - d dy/d = / e dy/d = y / - 7.c 7.c Updated /4/08 Boyceville High School, Mr. Hamm Page of

4 e sin( If f'() = and f(0) =, then f() = ) a -.89 b c d 0.57 e.57 Use Euler's Method with increments of Δ = 0. to approimate the value of y when =. dy/d = - y = when = a.0 b 4. c.0 d -.98 Use Euler's Method with increments of Δ = 0. to approimate the value of y when =. dy/d = y - y = when = a 5.55 b.66 c. d d 7.d 7.d Updated /4/08 Boyceville High School, Mr. Hamm Page 4 of

5 Evaluate: a (tan / ) + b ln cot() + c ln cos() + d -ln cos() + e -ln cot() + Evaluate: a sin() - + b sin() - + c cos() - + d cos() - + Evaluate: tan d (cos( ) ) d cos( 4 ) d a sin ( + 4) + b sin ( + 4) + c 0. sin (+4) + d 0. sin () + 7.a 7.a 7.a Updated /4/08 Boyceville High School, Mr. Hamm Page 5 of

6 Use differentiation to verify the antiderivative formula a True b False c an't Determine Use differentiation to verify the antiderivative formula a True b False c an't Determine Use differentiation to verify the antiderivative formula a True b False c an't Determine Evaluate: a - sin () + b -(/) sin () + c (/) sin () + d sin () + e sin () + Evaluate: csc udu cot u e 5 d 0.5e d ln( 5)5 cos() d d ( ) a / ( - ) + b / ( + ) + c / + d - / ( - ) + 7.b 7.b 7.b 7.b 7.b Updated /4/08 Boyceville High School, Mr. Hamm Page 6 of

7 Evaluate: 6 ln d a ( / 7) (ln ) 6 + b ( / 7) (ln ) 7 + c ( / 6) (ln ) 6 + d ( / 6) (ln ) 7 + AP alculus Multiple hoice Questions - hapter 7 7.b Updated /4/08 Boyceville High School, Mr. Hamm Page 7 of

8 Evaluate: a b c 6 ( + ) + d e Evaluate: a b c d e If then h()= a sin () + cos () + b sin () + c cos () - sin () + d 4 cos() - sin () + e ( - ) cos () - 4 sin () + 7.a 7.a 7.a d ) ( ) ( ) ( d ) ( / / / 5 / 5 / d h d sin ) ( cos Updated /4/08 Boyceville High School, Mr. Hamm Page 8 of

9 Evaluate: a ( )e - + b -( )e - + c ( )e + d -( )e + Evaluate: a -( )e + b ( )e + c -( )e - + d ( )e - + Evaluate: 4 e d ( 5) e d cos( ) d a ( /) sin() - ( /4)cos() - (/4)) sin() - (/8) cos() + b ( /) sin() - ( /4)cos() + (/4)) sin() + (/8) cos() + c ( /) sin() - ( /4)cos() + (/4)) sin() - (/8) cos() + d ( /) sin() + ( /4)cos() - (/4)) sin() - (/8) cos() + 7.b 7.b 7.b Updated /4/08 Boyceville High School, Mr. Hamm Page 9 of

10 Oil is leaking from a tanker at a rate of R(t) = 000 e -0.t gallons per hour, where t is measured in hours. How much oil leaks out of the tanker from time t = 0 to t = 0? a 54 gallons b 7 gallons c 865 gallons d 8647 gallons e 4778 gallons An apple pie comes out of the oven at 45 F and is placed on a counter in a 68 F room to cool. In 0 minutes it has cooled to 95 F. According to Newton's Law of ooling, how many additional minutes must pass before it cools to 00 F? a.4 b 5.4 c 5.0 d 5.0 e 40.0 A sample of e-4 (an isotope of cerium) loses 99% of its radioactive matter in 99 hours. What is the half-life of e-4? a 4 hours b 6 hours c 0 hours d 00.5 hours e 4 hours 7.4a 7.4a 7.4a Updated /4/08 Boyceville High School, Mr. Hamm Page 0 of

11 A bank account earning continuously compounded interest doubles in value in 7.0 years. At the same interest rate, how long would it take the value of the account to triple? a 4.4 years b 9.8 years c 0.5 years d. years e.0 years Suppose you deposit $800 in an account that pays 6.% annual interest. How much will you have 8 years later if the interest is compound continuously? a $998. b $58.45 c $4.6 d $48.9 e $5.0 Find the amount of time required for a $000 investment to double if the annual interest rate r is compounded continuously if the rate is 8.5% a 8.40 years b 7. years c 9.99 years d 6.58 years 7.4b 7.4b 7.4b Updated /4/08 Boyceville High School, Mr. Hamm Page of