CALCULUS BC -- PRACTICE EXAM #3 – DAY 2 -- CALCULATOR NAME________________________________________________________PER_________R−S__________ 76

The first three non-zero terms in the Taylor series about 0x = for ( ) cosf x x=

A)3 5

3! 5!x xx + + B)

3 5

3! 5!x xx − + C)

2 4

12! 4!x x− + D)

2 4

12! 4!x x− − E)

2 4

12! 4!x x+ +

77 3cos xdx =∫ A)

4cos C4x + B)

4sin C4x + C)

3sinsin C3xx − +

D) 3sinsin C3xx + + E) 3sin Cx +

78 If ( ) ( )( )33 xf x x= then ( )f x′ = A) ( )( ) ( )( )33 3ln 3 3xx x + B) ( )( ) ( )( )33 3ln 3 3xx x x+

C) ( )( ) ( )( )39 ln 3 1xx x + D) ( )( ) ( )3 13 3xx x− E) ( )( ) ( )3 13 9xx x− 79

To what limit does the sequence 33nn+⎧ ⎫

⎨ ⎬⎩ ⎭

converge as n approaches infinity?

A) 1 B) 13

C) 0 D) ∞ E) 3

80 ( )( )18 17

2 3 1x dx

x x− =

− +∫ A) 8ln 2 3 7 ln 1 Cx x− + + + B) 2ln 2 3 7 ln 1 Cx x− + + +

C) 4ln 2 3 7 ln 1 Cx x− + + + D) 7 ln 2 3 2ln 1 Cx x− + + + E) 7 ln 2 3 4ln 1 C2

x x− + + +

81 A particle moves along a path described by 3cosx t= and 3siny t= . The distance that the particle

travels along the path from 0t = to 2

t π= is A) 0.75 B) 1.50 C) 0 D) 3.50− E) 0.75−

82 A man 5 feet tall is walking away from a street-light hung 20 feet from the ground at the rate of 6

ft/sec. Find how fast his shadow (in ft/sec) lengthening? A) 2 B) C) 3 D) E) 4

83 The area enclosed by the polar equation 4 cosr θ= + for 0 2θ π≤ ≤ , is

A) 0 B) 92π C) 18π D) 33

2π E) 33

4π

84 Use the trapezoid rule with n = 4 to approximate the area between the curve 3 2y x x= − and the axisx − from 3x = to 4x = .

A) 35.266 B) 27.766 C) 63.031 D) 31.516 E) 25.125 85

If ( ) ( )2

0cos

k

kf x x

∞

=

=∑ , then 4f π⎛ ⎞ =⎜ ⎟⎝ ⎠

A) −2 B) −1 C) 0 D) 1 E) 2

CALCULUS BC -- PRACTICE EXAM #3 – DAY 2 -- CALCULATOR 86 The volume of the solid that results when the area between the graph of 2 2y x= + and the graph of

210y x= − from 0x = to 2x = is rotated around the axisx − is:

A) ( ) ( )2 2

0 0

2 2 2 10y y dy y y dyπ π− + −∫ ∫ B) ( ) ( )6 10

2 6

2 2 2 10y y dy y y dyπ π− + −∫ ∫

C) ( ) ( )6 10

2 6

2 2 2 10y y dy y y dyπ π− − −∫ ∫ D) ( ) ( )2 2

0 0

2 2 2 10y y dy y y dyπ π− − −∫ ∫

E) ( ) ( )2 2

0 0

2 10 2 2y y dy y y dyπ π− − −∫ ∫

87 4

20 9

dxx

=+∫ A) ln 3 B) ln4 C) ln 2− D) ln4− E) Undefined

88 The rate that an object cools is directly proportional to the difference between its temperature (in

Kelvins) at that time and the surrounding temperature (in Kelvins). If an object is initially at 35K, and the surrounding temperature remains constant at 10K, it takes 5 minutes for the object to cool to 25K. How long will it take for the object to cool to 20K?

A) 6.66 min B) 7.50 min C) 7.52 min D) 8.97 min E) 10.00 min 89

cosxe xdx∫ = A) ( )sin cos C2

xe x x+ + B) ( )sin cos C2

xe x x− + C) ( )cos sin C2

xe x x− +

D) ( )2 sin cos Cxe x x+ + E) ( )sin cos Cxe x x+ + 90 Two particles leave the origin at the same time and move along the y −axis with their respective

positions determined by the functions 1 cos 2y t= and 2 4siny t= for 0 6.t< < For how many values of t do the particles have the same acceleration? A)0 B)1 C) 2 D)3 E)4

91 The minimum value of the function 3 7 11,y x x= − + 0,x ≥ is approximately A) 18.128 B) 9.283 C) 6.698 D) 5.513 E) 3.872

92 Use Euler’s Method with 0.2xΔ = to estimate ( )1 ,y if y y′ = and ( )0 1.y = A)1.200 B) 2.075 C) 2.488 D)4.838 E)9.677

JJJJJ END OF PART B JJJJJ