BarronsCalculus-Set12 MCQ

*

-

Chapter 1 1

Miscellaneous Multiple Choice Practice Questions

These questions provide further practice for Parts A and B of Section I of the examination. Answers begin on page 395.

Part A. Directions: Answer these questions without using your calculator.

l. Which of the following functions is continuous at x = O?I

(A) f (x){ = sinx; for x * 0

= 0 for x = Ox= - for x 0

(B) f (x) = [x) (greatest-integer function)

= x sin .!:_ for x ;t O

(x) {= 0 for x = 0

(D) !( x ){ x

(C) f

(E) f (x) = x +

1

x

= 0 for x = O

x2 + I

2. Which of the following statements about the graph of y = , is not true?(A) The graph is symmetric to the y-axis. x- - 1

(B) The graph has two vertical asymptotes.(C) There is no y-intercept.(D) The graph has one horizontal asymptote.(E) There is no x-intercept.

3. lim ([x) - lxl) =X-)1-

(A) -1 (B) 0 (C) I (D) 2 (E) none of these

4. The x-coordinate of the point on the curve y = x2 - 2x + 3 at which the tangent is perpendicular to the line x + 3y + 3 = 0 is

(A) 5 I 7(B) - - (C)

- 5(D)-

(E) none of these2 2 6 2

379

1 I

1-

--

80 Chapter 11: Miscellaneous Multiple-Choice Practice Questions

3- - 3x

5. Jim .-isX -:) l X - 1(A) -3 (B) -1 (C) I (D) 3 (E) nonexistent

6. In (3ex + 2) - In ( 3ex ) =

(A) 2 (B) e2 (C) 2 ln 3 (D) In 3 + 2 (E) 2 ln 3 + 2

7. J 6

Jx - 4J dx =0

(A) 6 (B) 8 (C) 10 (D) 11 (E) 12

]' 3 + x - 2x2 .

S. x '.1! 4x2 + 9 IS

(A) l (B) ! (C) 1 (D) 32 2 (E) nonexistent

9. The maximum value of the function!(x) = x4 - 4x3 + 6 on the closed interval [1, 4)

IS

(A) 1 (B) 0 (C) 3 (D) 6 (E) none of these

f (x) = Vx+4 - 3if x f. 5,

:1.0. Letl/

(5)

= c,

·x - 5

and letf be continuous at x = 5. Then c =

(A) -6 (B) 0 (C) 6 (D) 1 (E) 6

(rr/211. Jo cos

2 x sin x dx =

(A) -I (B) -3 (C) 0 (D)1

3(E) 1

12. If sin x = In y and 0 < x < 'IT, then, in terms of x, equals

(A) e''"" cos x (B) e-sin x COS X

esin x(C) -

cos x(])) eoosx (E) e''" x

13. If f (x) = x cos;. then f '( ) equals

(A)'IT- (B)

2(C) -1 (

D)(E) 1

2 'IT 2

14. The equation of the tangent to the curve y = ex In x, where x = 1, is

(A) y = ex (B) y = e' + 1 (C) y = e( x - !) (D) y = ex + 1(E) y =x - 1

0

-

{ 2

2-

5

5 3

Miscellaneous Multiple-Choice Practice Questions 381

15. If the displacement from the origin of a particle on a line is given by s = 3 + ( t - 2)•, then the number of times the particle reverses direction is(A) 0 (B) 1 (C) 2 (D) 3 (E) none of these

16. f_ e

1

-x dx equals1 - e

(A) 1 - e

(IB) -e

(C) e - 1

(D) I - 1

e(IE) e + 1

17. If

4f (x) =

x' for x 24x - x for x > 2 ,

then J_ / (x) dx equals

(A) 7 (B) 3 (C) 253

(D) 9 (E)65

3

18. If the position of a particle on a line at time t is given by s = i3 + 3t, then the speed of the particle is decreasing when(A) -1< t < 1 (B) -1< t < 0 (C) t < 0 (D) t > 0(E) l t l > I

Jl 9. A rectangle with one side on the x-axis is inscribed in the triangle formed by the lines

y = x, y = 0, and 2x + y = 12. The area of the largest such rectangle is

(A) 6 (B) 3 (C) 2 (D) 5 (E) 7

20. The abscissa of the first-quadrant point that is on the curve of x2 - y2 = 1 and closest to the point (3, 0) is

3(A) 1 (B) - (C) 2 (D) 3 (E) none of these

2

21. If y = 1x' +16 then'\/ '

1

d'y- isdx 2

(A) (B) 4(3x2 + 16) (C 16

(D)

4(x2 + 16)312

2x2 + 16

(x2 + 16)312

16(E) (x2 + 16)3/2

) Vx2 + 16

22. The region bounded by the parabolas y = x' and y = 6x - x2 is rotated about thex-axis so that a vertical line segment cut off by the curves generates a ring. The value of x for which the ring of largest area is obtained is

W 4 ) 3 :Z 2 OO :z

J23. _:I!!_ equalsx n x

(A) In (Inx) + C (B) -

-

1+

C(C) (In x) ' + C

(D) In x + C

(E) none of theseln2 x 2

L

4

1m , 1

>82 Chapter 11: Miscellaneous Multiple-Choice Practice Questions

24. The volume obtained by rotating the region bounded by x = y2 and x = 2 - y2

about the y-axis is equal to161T 321T

(A) - (B) -3 3

321T(C) -

15(D) 64TI

15(E) 8TI

3

25. The general so1ut1·0n of the d"1ff erentl·a1equati·on dy = 1 - 2x i·s a farm·ly of

dx y(A) straight lines(E) ellipses

(B) circles (C) hyperbolas (.D) parabolas

26. Estimate f 4

Y25 - x2 dx using the left rectangular rule and two subintervals.0

(A) 3 + \121 (B) 5 + \121 (C) 6 + 2V21 (D) 8 + 2V21(E) 10 + 2\121

7

27. sin 1T7 dx =

2 1 2(A) -2 (B) (C) 0 (D) - (E) -

1T 1T 1Tr tan 3x1m --=

x->0 2x 1 2 3(A) 0 (B) - (C) - (D) - (E) oo

2 3 2

29. lim tan ('TT /4 + h) - 1 =

h--7 0 h

(A) 01

(B) -2

(C) 1 (D)2 (E) oo

30. The number of values of k for which / (x) = e' and g(x) = k sin x have a common point of tangency is(A) 0 (B) 1 (C) 2 (D) large but finite (E) infinite

31. The curve 2x2 y + y2 = 2x + 13 passes through (3, 1). Use the local linearization of the curve to find the approximate value of y at x = 2.8.(A) 0.5 (B) 0.9 (C) 0.95 (D) 1.1 (E) 1.4

32. f cos3

x dx =

cos4 x sin4 x(A) - + C (B) -+ C

4 4sin3 x

sin3 x(C) sin x --- + C

3cos3 x

(D) sin x + -

- + C

3

(E) cos x--- + C3

1T33. The region bounded by y = tan x, y = 0, and x = is rotated about the x-axis. The

volume generated equals1T2

(A) 1T - -

4(E) none of these

(B) TI(Yl - 1)

(C)31T-4

34•1. ah - 1 " f a > 0, equaIsh->O h(A) 1 (B) a (C) In a (E) aIn a

*2s.

*An asterisk denotes a topic covered only in Calculus BC.

-, - - - I

I / -

lim- -- dx

' \

0 123456


35. Solutions of the differential equation whose slope field is shown here are most likelyto be

, / - - - -I , / - - - -I , / - - - -I , / - - - -

/ - - - -,

I , /

I , /

- - - --

I , / - - - -/

I , / - - - -I , / - - - -, - - -I , / - - - -I , / - -

(A) quadratic (B) cubic (C) sinusoidal (][)) exponential(E) logarithmic

36. l if+h sinxh---tO h f X

(A) 0 (B) 1 (C) J2 (D) 2J2 (E) 2J2(rr - 4) 2 rr rr'

37. The graph of g, shown below, consists of the arcs of two quarter-circles and two straight-line segments. The value of J ' g( x) dx is

y

5

4 g (x)

3

2

x7 8 9 10 11 12

-]

-2

-3

-4

(A) rr +

2

(B)7n

+ 9

(C) 7n + 8 (D)

- --+ 7rr + 9 25rr 21

4 2 4 2 4 2

1

I I I

II

//// / / ////

, , , , , , , , , ,

I /I /I /I I I I III I

,///////////

, ,// -- --- - - -

/

/ /

-- -/

/ /

-/

I /

,,//////

/ /

/ /

/ - -/

- --/

/

-- -/

/ /

/

/ - - -/

/

-/

II

/ / ,_,,/

-/

/ / ,_,, /

4 Chapter 11 : Miscellaneous Multi ple-Choice Practice Questions

38. Which of these could be a particular solution of the differential equation whose slope field is shown here?

I

/ /

, ,

(A)1

y =

x

(B) y =In x (C) y = ex (JE) Y = e"

39. The slope field shown here is for the differential equation

, 1 ,(A) y = - (B) y = ln

x xy ' = ex (D) y' = y

E) y ' = -y2

(C)(

'40. A particle moves along the parabola x = 3y - y2 so that dy = 3 at all time t. Thedt

speed of the particle when it is at position (2, 1) is equal to

(A) 0 (B) 3 (C)\/:i3 (D) 3\12. (E) none of these

'41. If x = 2 sin u and y = cos 2u, then a single equation in x and y is (A) x2 + y2 = 1 (B) x2 + 4y2 = 4 (C) x2 + 2y = 2 (D) x2 + y2 = 4 (E) x2

- 2y = 2

'42. The area bounded by the lemniscate with polar equation r2 = 2 cos 20 is equal to

(A) 4 (B) 1 (C) 2 (D) 2 (E) none of these

(A) 0'1T

(B) -2

(C) '1T (D) 2'1T (E) none of these

* An asterisk denotes a topic covered only in Calculus BC.

()x

L

-


'44f. The first four terms of the Maclaurin series (the Taylor series about x = O) forI

f (x) = _ 1

x are2

(A) 1 + 2x + 4.x2 + 8x3

(R) 1 - 2x + 4x2 - 8x3

(C) - 1 - 2x - 4x-?-.

(E) 1 + x + x2 + x3

,.45. J x2 e -x dx =

8x3(J[)J) 1 - x + x2

- x3

(A)1

x 3 e - . + C

- x3

'4.

L-rr/2

sin2 x dx is equal to

1 1T 1 1T 1T 1 1T

(A) 3 (B) 4 - 4

(C) -2

(][JI) - - -

2 3

(E) -4

'47. A curve is given parametrically by the equations x = t, y = 1 - cos t. The area bounded by the curve and the x-axis on the interval 0 t 21T is equal to(A) 2(1T + 1) (B) 1T (C) 41T (D) 1T + 1 (E) 2-rr

dy 1TIf x = a cot 8 and y = a sin2 8, then -, when 8 = -,is equal to

dx 4

(A)1

2

1(B) -I (C) 2 (J[)J)

2

1(E)

4

'49. Which of the following improper integrals diverges?

(A) Jo e -x'dx (.B) _exdx (C) Jo L'd

'so. f 4

y( J o ('

dx00

duequals

(E)

2 16 - u2

(A) _:i:_12

'5ll. Jim isx-+0+ X

1T(B) -

6

1T(

C)-4

1T(ID) -

3

21T(E) -

3

(A) -oo(B) 0 (C) 1 (D) oo (E) nonexistent

I

·•52. If we substitute x = tan 0, which of the following is equivalent to V 1 + x2 dx?

J

(A) L sec 0 d8 (B)

sec3

0 d0 (C)

J sec 8 d0

I J' TI/4

0

(D) J -rr/4 tan I

sec3 e d0 (E)

0

sec3 0 de

0 0


2

f

0I234

y= f (x)

-2-I-1

y= h(x)


•·53,. cot x

hm · -.x-)O+ ln X(A) -co (B) -1 (C) 0 (D) 1 (E) co

3x + 2'54. When rewritten as partial fractions, includes which of the following?

x - x - 121 .

I.x + 3

(A) none

n. _1_x - 4

(B) I only

2llt --

x - 4

(C) II only

(D) III only CE) I and III11 - cos x

'55. Using two terms of an appropriate Maclaurin series, estimate0 x dx.

1 23 1 25(A) 96 (B) 96 (C) 4 (D) 96

(E) undefined; the integral is improper

'56. The slope of the spiral r = e at e = 41T

is

(A) - Yi (113) -1 (C) 1 (D)

4 + 1T--4 - 1T

(E) undefined

Part B. Directions: Some of these questions require the use of a graphing calculator.

57. The graph of function h is shown here. Which of these state ments is (are) true?

I. The first derivative is never negative.II. The second derivative is constant.

III. The first and second derivatives equal 0 at the same point.

h(x)

(A) I only (B) III only (C) I and II(D) I and III (E) all three

58. Graphs of functions f (x), g(x), and h(x) are shown below. Consider the following statements:

I. g(x) = f' (x)II. f (x) = g '(x)

III. h (x) = g"(x)Which of these statements is (are) true?(A) I only (B) II only (C) II and III only (D) all three(E) none of these

y y

y = g(x)

-->--+-+--->--++-->- X-2 -I -I 2 3

=



59. If y =

J

, 1 d 2

-J3+21 dt, then -{=3 3 + 2t dx

(A) l , (B)3

,(3+ 2x)' (3 + 2x)'

(JD) (3 + 2x) (E) o3

60. If r,f ( x ) dx = 6, then f 4 f (x +1)

dx =

(C) J3+2x2

(A) -6 (B) -5 (C) 5 (D) 6 (E) 7

61. At what point in the interval [1, 1.5] is the rate of change of /(x) = sin x equal to its average rate of change on the interval?(A) 0.995 (1:1) 1.058 (C) 1.239 (JD) 1.253 (E) 1.399

62. Supposej' (x) = x2 (x - 1). Thenf"(x) = x (3x - 2). Over which interval(s) is the graph of / both increasing and concave up?

2 2I. x < 0

(A) I only(E) IV only

H. O < x < - IU. - < x < l

3 3(1:1) II only (C) II and IV

IV. x > l

(JD) I and IV

63. Which of the following statements is true about the graph of j (x) in Question 62?(A) The graph has no relative extrema.(B) The graph has one relative extremum and one inflection point.(C) The graph has two relative extrema and one inflection point.(D) The graph has two relative extrema and two inflection points.(E) None of the preceding statements is true.

64. The nth derivative of In (x + 1) at x = 2 equals

(- l)n-1 (-1)" - nl (- l)n- l (n - 1)!(A) 3" (B) 3n+l (C) 3n

(-1r' - n!

(.I}) 3n+l .

(-1)"+1(E) 3n+ l

65. If f (x ) is continuous at the point where x = a, which of the following statements may be false?(A) lim f (x) exists. (B) lim / (x) = f ( a). (C) f' (a) exists.

x-7 a x a

(D) / (a) is defined. (E) limf\x) = limf( x).x---ta- x---ta"-

'

sm


66. Suppose f3 3 + k

f (x + k) dx = 4, where k is a constant. Then fk f (x) dx equals0

(A) 3 (B) 4 - k (C) 4 (D) 4 + k (JE) none of these

67. The volume, in cubic feet, of an "inner tube" with inner diameter 4 ft and outer diameter 8 ft is(A) 41T2 (B) 121T2 (C) 81T2 (D) 241T2 (E) 6TI2

68. If f (u) = tan- 1 u2 and g(u) = e", then the derivative of j(g (u)) is2ue" 2ue"' 2e" 2e2

"

(A) 1 + u4 (B) 1 + u4 (C) 1 + 4e2u (D) 1 + e4u2e2u

(E) --;==

\11 - e4"

6'91. If . dy

(xy) = y, then -equalsdx

(A) sec (xy) (B) y cos (xy) - 1(C) 1 - y cos (xy )

x cos (xy)(D) y cos (xy)

1 - x cos (xy)

(E) cos (xy)

70. Let x > 0. Suppose

:I:_f (x) = g (x) and :I:_ g (x) =f (Vx );dx dx

d 2

then dx2 j(x2) =

(A) f (x4) (B) f

(x2)

(E) 2g(x2) + 4x2f (x)

(C) 2xg(x2)

1(D) -f (x)

2x

71. The region bounded by y = e',y = 1, and x = 2 is rotated about the x-axis. The volume of the solid generated is given by the integral

,,

(B) 21T J, (2 - In y )( y - I

) dy

2

(C) 1TJ, (e2- l ) dx

(D) 21Tf0

,,y (2 - In y ) dy

0

+ --2

y = 4

\(x,4)

>----- ,, (x,y)


72. Suppose the functionf is continuous on 1 x 2, thatf'(x) exists on 1 < x < 2, thatf (l) = 3, and thatf (2) = 0. Which of the following statements is not necessarily true?(A) The Mean-Value Theorem applies to f on 1 x 2.

2

(B) J, f (x) dx exists.

(<C) There exists a number c in the closed interval [l, 2) such thatf'(c) = 3.(]!)) If k is any number between 0 and 3, there is a number c between 1 and 2

such thatf (c) = k.(lE) If c is any number such that l < c < 2, then lim f (x) exists.

x-t c

y

73. The region S in the figure is bounded by y = sec x, the y-axis, and y = 4. What is the volume of the solid formed when S is rotated about the y-axis?(A) 0.791 (B) 2.279 (C) 5.692 (D) 11.385 (E) 17.217

74. If 40 g of a radioactive substance decomposes to 20 g in 2 yr, then, to the nearest gram, the amount left after 3 yr is(A) 10 (JB) 12 (<C) 14 (D) 16 (E) 17

75.2

An object in motion along a line has acceleration a (t) = -rrt and is at rest1 + I

when t = I . Its average velocity from t = 0 to t = 2 is(A) 0.362 (B) 0.274 (<C) 3.504 (]!)) 7.008 (E) 8.497

76. Find the area bounded by y = tan x and x + y = 2, and above the x-axis on the interval [O, 2).(A) 0.919 (B) 0.923 (C) 1.013 (D) 1.077 (E) 1.494

77. An ellipse has major axis 20 and minor axis 10. Rounded off to the nearest integer, the maximum area of an inscribed rectangle is(A) 50 (B) 79 (C) 80 (D) 82 (E) 100

78. The average value of y = x In x on the interval 1 x e is(A) 0.772 (B) 1.221 (C) 1.359 (D) 1.790 (E) 2.097

)

T

=


79. Let f (x) = f (1 - 2 cos3 t) dt for 0 x 2'IT . On which interval is f increasing?

(A) 0 < x < 'IT (B) 0.654 < x < 5.629 (C) 0.654 < x < 21T(D) 1T < x < 2'1T (E) none of these

80. The table shows the speed of an object (in ft/sec) during a 3-sec period. Estimate itsacceleration (in ft/sec2 at t = 1.5 sec.

time, sec 0 1 2 3

speed, ft/sec 30 22 12 0

(A) -17 (B) -13 (C) -10 (D) -5 (E) 17

SL A maple-syrup storage tank 16 ft high hangs on a wall. The back is in the shape of the parabola y = x2 and all cross sections parallel to the floor are squares. If syrup ispouring in at the rate of 12 ft3/lir, how fast (in ft/hr) is the syrup level rising when it is 9 ft deep?

16'

9'

l2 1 4

(A) - (B) - (C) - (D) 36 (E) 162 27 3 3

82. In a protected area (no predators, no hunters) the deer population increases at a ratedP

of - k(l 000 - P), where P( t) represents the population of deer at t yr. If 300dt .

deer were originally placed in the area, and a census showed the population had grown to 500 in 5 yr, how many deer will there be after 10 yr?(A) 608 (B) 643 (C) 700 (D) 833 (E) 892

J

I

----->-


§3. Shown is the graph of f (x) = - 4

-.

x2 + 1

Let H( x ) = J>( t) dt. The local linearization of H at x = 1 is H( x) equals

(A) 2x (B) -2x - 4 (C) 2x + 'Tl' - 2 (D) -2x + 'Tl' + 2(E) 2x + In 16 + 2

84. A smokestack I 00 ft tall is used to treat industrial emissions. The diameters, mea sured at 25-f t intervals, are shown in the table. Using the midpoint rule, estimate the

volume of the smokestack to the nearest I 00 ft3.

ht dia

100'

75'

5'

7'

50' 9'

25' 15'

O' 17'

(A) 8100 (B) 9500 (C) 9800 (D) 12,500 (E) 39,300

8

I I

2V2

-

-

(5,4)4

2f' (7,2)

x

2 4 6 8

-2(2,-2)


For questions 85-89 the table shows the values of differentiable functions f and g.

x f !' g g'

I 21-2

_c3 5

2 3 I 0 4

3 4 2 2 3

4 6 4 3I-2

· f (x) ,85. If P(x) = g (x)' then P (3) =

(A) -2 (B) - 9 (C)I

2(]))

2

3(E) 2

86. If H( x) =f (g (x)), then H '( 3) =(A) I (B) 2 (C) 3 (D) 6 (E) 9

87. If M( x) =f (x) ·g (x), then M' ( 3) =(A) 2 (B) 6 (C) 8 (D) 14 (E) 16

88. If K(x) = g- 1(x), then K '(3) =

(A) - 2 (B) - 3 (C)3

(])) I

2(E) 2

89. If R(x) = VJW, then R '(3) =I I I

(A) - (B) -4

(C) -2

(D) Yl (E) 2

90. Water is poured into a spherical tank at a constant rate. If W( t) is the rate of increase of the depth of the water, then W is(A) constant (B) linear and increasing (C) linear and decreasing(D) concave up (E) concave down

91. The graph of f ' is shown below. lf f (7) = 3 thenf (l) =

f'

(A) -10 (B) -4 (C)-3 (I>) 10 (E) 16

20

)

4

(2,1)

2

6 8


92. At an outdoor concert, the crowd stands in front of the stage filling a semicircular disk of radius 100 yd. The approximate density of the crowd x yd from the stage is given by

D(x) = Yx2 x + 1

people per square yard. About how many people are at the concert?

L stage

(A) 200 (B) 19,500 (C) 21,000 ([)J) 165,000 (JS) 591,000

93. The Centers for Disease Control announced that, although more AIDS cases were reported this year, the rate of increase is slowing down. If we graph the number of AIDS cases as a function of time, the curve is currently(A) increasing and linear (B) increasing and concave down(C) increasing and concave up CD) decreasing and concave down(E) decreasing and concave up

The graph below is for Questions 94-96. It shows the velocity, in feet per second, for 0 < t < 8, of an object moving along a straight line.

v(fUsec)

(3,2)

2

-I(6,-1) (8,-1)

-2

94. The object's average speed (in ft/sec) for this 8-sec interval was

w o 00 3 8

1 00 8

95. When did the object return to the position it occupied at t = 2?

(A) t = 4 (B) t = 5 (C) t = 6 (D) t = 8 (E) never

96. The object's average acceleration (in ft/sec2for this 8-sec interval was

(A) -2 (B)1 1

(C) 0 (D) (E) 14

2 (2)" L

394\ Chapter 11: Miscellaneous Multiple-Choice Practice Questions

7297. If a block of ice melts at the rate of--cm3/min, how much ice melts during the

2t + 3first 3 min?

(A) 8 cm3 (B) 16 ci:n3 (C) 21 cm3 (D) 40 cm3 (E) 79 cm3

'98. A particle moves counterclockwise on the circle x2 + y2 = 25 with a constant speed of 2 ft/sec. Its velocity vector, v, when the particle is at (3, 4), equals

(A) _.!. (si -6j) (B) .!.(si -6j) (C) -2,l3i + 2j5 5

(D) 2i -2,'3j (JE) -2,/2(i -j)

'99. Let R = a cos kti + a sin ktj be the (position) vector xi + yj from the origin to a moving point P(x, y ) at time t, where a and k are positive constants. The acceleration vector, a, equals(A) ·-k2R (B) a2 k2 R (C) -aR (J)) -ak2 (cos ti + sin tj )(E) -R

'100. The length of the curve y = 2x between (0, 1) and (2, 4) is(A) 3.141 (B) 3.664 (C) 4.823 . (D) 5.000 (lE) 7.199

'101. The position of a moving object is given by P(t) = (31, e' ). Its acceleration is(A) undefined (B) constant in both magnitude and direction(C) constant in magnitude only (J)) constant in direction only(E) constant in neither magnitude nor direction

'102. Suppose we plot a particular solution of = 4y from initial point (0, 1) using

Euler's method. After one step of size l:u = 0.1, how big is the error?(A) 0.09 (B) 1.09 (C) 1.49 (D) 1.90 (E) 2.65

'103. We use the first three terms to estimate i (;l)" . Which of the followingnO n + 1

statements is (are) true?

I. The estimate is 0.7.U. The estimate is too low.

UI. The estimate is off by less than 0. l .(A) Ionly (B) llonly (C) Iand II (D) I and III (E) all three

'104. Which of these diverges?00 00

(A) 3" (B) 300 2

(C) °2: 311=1 n

00 2(D) 3

n = l n(E) i :

n::= l


L

e

Answers to Miscellaneous Multiple-Choice Practice Questions 395

oo I

'1105. Find the radius of convergence of n x'' .n l n

W O )! I e OO oo

2

']Jl6. When we use e'= I + x + :_ to estimate Ye, the Lagrange remainder is no2

greater than(A) 0.021 (J.l) 0.034 (C) 0.042 (ID) 0.067 (E) 0 742

'Hl . An object in motion along a curve has position P(t) = (tan t, cos 2t) for 0 t ,,; I . How far does it travel?(A) 0.96 (J.l) 1.73 (C) 210 (D) 2.14 (E) 3.98

Date post:	16-Jan-2016
Category:	Documents
Upload:	pyoon399
View:	45 times
Download:	0 times

BarronsCalculus-Set12 MCQ

Documents