CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO...

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CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR Name Row Period 1 If 7 , then xy dy xy e dx = = A) y x e B) x y e C) xy xy ye y x xe + D) y x E) xy xy ye y x xe + + 2 The volume of the solid that results when the area between the curve x y e = and the line 0 y = , from 1 to 2, x x = = is revolved around the axis is: x A) ( ) 4 2 2 e e π B) ( ) 4 2 2 e e π C) ( ) 2 2 e e π D) ( ) 2 2 e e π E) 2 2 e π 3 ( )( ) 18 3 4 x dx x x = + A) ( )( ) 5 3 4 dx x x + B) ( )( ) 3 4 dx x x + C) 2 3 4 dx dx x x + + D) 15 14 3 4 dx dx x x + E) 3 2 3 4 dx dx x x + 4 2 If 5 4 and ln then dy y x x x t dt = + = = A) 10 4 t + B) 10 ln 4 t t t + C) 10 ln 4 t t + D) 2 5 4 t t + E) 4 10 ln t t + 5 2 5 0 sin cos x xdx π = A) 1 6 B) 1 6 C) 0 D) 6 E) 6 6 ( ) 3 The tangent line to the curve 4 8 at the point 2,8 has an intercept at: y x x x = + A) ( ) 1, 0 B) ( ) 1, 0 C) ( ) 0, 8 D) ( ) 0,8 E) ( ) 8, 0 7 () () The graph in the plane represented by 3sin and 2 cos is: xy x t y t = = A) a circle B) an ellipse C) a hyperbola D) a parabola E) a line 8 2 4 9 dx x = A) 1 1 3 sin C 6 2 x + B) 1 1 3 sin C 2 2 x + C) 1 3 6sin C 2 x + D) 1 3 3sin C 2 x + E) 1 1 3 sin C 3 2 x + 9 1 lim 4 sin is: x x x →∞ A) 0 B) 2 C) 4 D) 4 π E) nonexistant 10 The position of a particle moving along the x axis at time t is given by xt () = e cos 2t () , 0 t π . For which of the following values of t will x ' t () = 0? I. t = 0 II. t = π 2 III. t = π A) I only B) II only C) I and III only D) I and II only E) I, II, and III 11 ( ) ( ) 0 sec sec lim h h h π π + = A) 1 B) 0 C) 1 2 D) 1 E) 2 12 Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm 3 ). A) 19.2 B) 15.36 C) 1.92 D) 0.01 E) 0.0001

Transcript of CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO...

CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR

Name Row Period 1 If 7 , then xy dyxy e

dx= − = A) yx e− B) xy e− C)

xy

xy

ye yx xe

+−

D) yx− E)

xy

xy

ye yx xe

++

2 The volume of the solid that results when the area between the curve xy e= and the line 0y = , from 1 to 2,x x= = is revolved around the axis is:x −

A) ( )4 22 e eπ − B) ( )4 2

2e eπ − C) ( )2

2e eπ − D) ( )22 e eπ − E) 22 eπ

3 ( )( )

183 4x dx

x x− =

+ −∫ A) ( )( )

53 4dx

x x+ −∫ B) ( )( )3 4

dxx x+ −∫ C) 2

3 4dx dxx x

++ −∫ ∫

D) 15 143 4dx dx

x x−

+ −∫ ∫ E) 3 23 4dx dxx x

−+ −∫ ∫

4 2If 5 4 and ln then dyy x x x tdt

= + = =

A) 10 4t+ B) 10 ln 4t t t+ C) 10 ln 4t

t+ D) 2

5 4t t+ E) 410 ln t

t+

5 25

0

sin cosx xdxπ

=∫ A) 16

B) 16− C) 0 D) ‒6 E) 6

6 ( )3The tangent line to the curve 4 8 at the point 2,8 has an intercept at:y x x x= − + −

A) ( )1,0− B) ( )1,0 C) ( )0, 8− D) ( )0,8 E) ( )8,0 7 ( ) ( )The graph in the plane represented by 3sin and 2cos is:xy x t y t− = =

A) a circle B) an ellipse C) a hyperbola D) a parabola E) a line 8

24 9dxx

=−∫ A) 11 3sin C

6 2x− ⎛ ⎞+⎜ ⎟⎝ ⎠

B) 11 3sin C2 2

x− ⎛ ⎞+⎜ ⎟⎝ ⎠ C) 1 36sin C

2x− ⎛ ⎞+⎜ ⎟⎝ ⎠

D) 1 33sin C2x− ⎛ ⎞+⎜ ⎟⎝ ⎠

E) 11 3sin C3 2

x− ⎛ ⎞+⎜ ⎟⎝ ⎠

9 1lim 4 sin is:x

xx→∞

⎛ ⎞⎜ ⎟⎝ ⎠

A) 0 B) 2 C) 4 D) 4π E) nonexistant

10

The position of a particle moving along the x − axis at time t is given by x t( )= ecos 2t( ), 0 ≤ t ≤ π .

For which of the following values of t will x ' t( )= 0?

I. t = 0 II. t = π2

III. t = π

A) I only B) II only C) I and III only D) I and II only E) I, II, and III 11 ( ) ( )

0

sec seclim h

hh

π π→

+ −= A) −1 B) 0 C) 1

2 D) 1 E) 2

12 Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm3). A) ‒19.2 B) ‒15.36 C) ‒1.92 D) ‒0.01 E) ‒0.0001

CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR

13 A particle which is at position ( )1,3 with velocity ( )0, 1− when 0t = , moves with acceleration

( )211,

1 t

⎛ ⎞⎜ ⎟⎜ ⎟+⎝ ⎠

. Where is the object when 2t = .

A) ( )3,3 ln3− B) ( )2, ln3 C) ( )2,3 ln3− D) ( )3, ln3− E) ( )3,3 ln3+ 14

( )1

1

0

sin x dx− =∫ A) 0 B) 22

π + C) 22

π − D) 2π E)

2π−

15 The equation of the line normal to

2

2

55xyx

−=+

at x = 2 is

A)81 60 142x y− = B) 81 60 182x y+ = C) 20 27 49x y+ = D) 20 27 31x y+ = E) 81 60 182x y− = 16 If c satisfies the conclusion of the Mean Value Theorem for derivatives for ( ) 2sinf x x= on the interval

[0, ]π , then c could be A)0 B) 4π C)

2π D) π E) There is no value of c on[0, ]π

17 The average value of ( ) lnf x x x= on the interval [1, ]e is

A) 2 14

e + B) 2 1

4( 1)ee++

C) 14e + D)

2 14( 1)ee+−

E) 23 1

4( 1)ee+−

18 A 17−foot ladder is sliding down a wall at a rate of 5 feet/second. When the top of the ladder is 8 feet from the ground, how fast is the foot of the ladder sliding away from the wall ( )in feet/second .

A) 758

B) 83

C) 38

D) −16 E) 753

19 If 3 cosdy y xdx

= , and y = 8 when x = 0 , then y = ?

A) 3sin8 xe B) 3cos8 xe C) 3sin8 3xe + D) 2

3 cos 82y x+ E)

2

3 sin 82y x+

20

The length of the curve determined by 23 and 2 from 0 to 9 is:x t y t t t= = = =

A) 9

2 4

0

9 4t t dt+∫ B) 162

2

0

9 16t dt−∫ C) 162

2

0

9 16t dt+∫ D) 3

2

0

9 16t dt−∫ E) 9

2

0

9 16t dt+∫

21 If a particle moves in the xy‒plane so that at time t > 0, its position vector is ( )2 3

, ,t te e− then its velocity

vector at time 3t = is: A) ( )( )ln 6, ln 27− B) ( )( )ln 9, ln 27− C) ( )9 27,e e−

D) ( )9 276 , 27e e−− E) ( )9 279 , 27e e−− 22 The graph of ( ) 211f x x= + has a point of inflection at:

A) ( )0, 11 B) ( )11,0− C) ( )0, 11− D) 11 33,2 2

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

E) There is no point of inflection

******* PROBLEMS 23 – 28 ARE ON THE NEXT PAGE *****

CALCULUS BC -- PRACTICE EXAM #3 – DAY 1 -- NO CALCULATOR

23 What is the volume of the solid generated by rotating about the y −axis the region enclosed by

siny x= and the x −axis, from 0x = to x π= ? A) 2π B) 22π C) 24π D) 2 E) 4 24 ( )

2 2

sin 1/ tdt

∞=∫ A) 1 B) 0 C) 1− D) 2 E) Undefinded

25

A rectangle is to be inscribed between the parabola 24y x= − and the x −axis. A value of x that

maximizes the area of the rectangle is A) 0 B) 23

C) 23

D) 43

E) 32

26 29

dxx

=−∫ A) 1sin 3x C− + B) 2ln 9x x C+ − + C) 11 sin

3x C− +

D) 1sin3x C− + E) 21 ln 9

3x x C+ − +

27 Find

1

lim xxx

→∞ A) 0 B) 1 C) ∞ D) 1− E) −∞

28 What is the sum of the Maclaurin series ( ) ( )

3 5 7 2 1

... 1 ...?3! 5! 7! 2 1 !

nn

nπ π π ππ

+

− + − + + − ++

A) 1 B) 0 C) ‒1 D) e E) There is no sum. JJJJJ END OF PART A JJJJJ