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MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

MCQs in Differential Calculus (Limits and Derivatives) Part 2

This is the Multiple Choice Questions Part 2 of the Series in Differential Calculus (Limits and Derivatives) topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

  • MCQ in Derivatives | MCQ in Derivatives of Algebraic functions | MCQ in Derivatives of Exponential functions | MCQ in Derivatives of Logarithmic functions | MCQ in Derivatives of Trigonometric functions | MCQ in Derivatives of Inverse Trigonometric functions | MCQ in Derivatives of Hyperbolic functions

Continue Practice Exam Test Questions Part 2 of the Series

MCQ in Differential Calculus (Limits and Derivatives) Part 1 | Math Board Exam

Choose the letter of the best answer in each questions.

51. Evaluate
MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. 0

B. 1

C. 2

D. 3

View Answer:

Answer: Option B

Solution:

52. Simplify the expression:
MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. 1

B. 8

C. 0

D. 16

View Answer:

Answer: Option B

Solution:

53. Evaluate the following limit:

MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. 2/5

B. infinity

C. 0

D. 5/2

View Answer:

Answer: Option A

Solution:

54. Evaluate the limit ( x – 4 ) / (x2 – x – 12) as x approaches 4.

A. 0

B. undefined

C. 1/7

D. infinity

View Answer:

Answer: Option C

Solution:

55. Evaluate the limit (1n x ) / x as x approaches positive infinity.

A. 1

B. 0

C. e

D. infinity

View Answer:

Answer: Option B

Solution:

56. Evaluate the following limit:
MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. 1

B. Indefinite

C. 0

D. 2

View Answer:

Answer: Option A

Solution:

57. Evaluate:
MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. 0

B. ½

C. 2

D. -1/2

View Answer:

Answer: Option B

Solution:

58. Evaluate the following:

MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

A. Infinity

B. eπ

C. 0

D. e2/π

View Answer:

Answer: Option D

Solution:

59. Find dy/dx if y = 52x – 1

A. 52x – 1 ln 5

B. 52x – 1 ln 25

C. 52x – 1 ln 10

D. 52x – 1 ln 2

View Answer:

Answer: Option B

Solution:

60. Find dy/dx if y = e√x

A. e√x  / 2√x

B. e√x / √x

C. ex  / √x

D. e√x – 2√x

View Answer:

Answer: Option A

Solution:

61. Find dy/dx if y = x2 + 3x + 1 and x = t2 + 2.

A. 4t3 + 14t2

B. t3 + 4t

C. 4t3 + 14t

D. 4t3 + t

View Answer:

Answer: Option C

Solution:

62. Evaluate the first derivative of the implicit function: 4x2 + 2xy + y2 = 0

A. (4x + y) / (x + y)

B. –[(4x + y) / (x + y)]

C. (4x – y) / (x + y)

D. –[(4x + y) / (x –y)]

View Answer:

Answer: Option B

Solution:

63. Find the derivative of (x + 5) / (x2 – 1) with respect to x.

A. DF(x) = (-x2 – 10x – 1) / (x2 – 1)2

B. DF(x) = (x2 + 10x – 1) / (x2 – 1)2

C. DF(x) = (x2 –10x – 1) / (x2 – 1)2

D. DF(x) = (-x2 –10x + 1) / (x2 – 1)2

View Answer:

Answer: Option A

Solution:

64. If a simple constant, what is the derivative of y = xa?

A. a xa – 1

B. (a – 1)x

C. xa – 1

D. ax

View Answer:

Answer: Option A

Solution:

65. Find the derivative of the function 2x2 + 8x + 9 with respect to x.

A. Df(x) = 4x – 8

B. Df(x) = 2x + 9

C. Df(x) = 2x + 8

D. Df(x) = 4x + 8

View Answer:

Answer: Option D

Solution:

66. What is the first derivative dy/dx of the expression (xy)x = e?

A. – y(1 + ln xy) / x

B. 0

C. – y(1 – ln xy) / x2

D. y/x

View Answer:

Answer: Option A

Solution:

67. find the derivative of (x + 1)3 / x

MCQ in Differential Calculus (Limits and Derivatives) Part 2 | Math Board Exam

View Answer:

Answer: Option B

Solution:

68. Given the equation: y = (e ln x)2, find y’.

A. ln x

B. 2 (ln x) / x

C. 2x

D. 2 e ln x

View Answer:

Answer: Option C

Solution:

69. Find the derivatives with respect to x of the function √(2 – 3x2)

A. -2x2 / √(2 – 3x2)

B. -3x / √(2 – 3x2)

C. -2x2 / √(2 + 3x2)

D. -3x / √(2 + 3x2)

View Answer:

Answer: Option B

Solution:

70. Differentiate ax2 + b to the ½ power.

A. -2ax

B. 2ax

C. 2ax + b

D. ax + 2b

View Answer:

Answer: Option B

Solution:

71. Find dy/dx if y = ln √x

A. √x / ln x

B. x / ln x

C. 1 / 2x

D. 2 / x

View Answer:

Answer: Option C

Solution:

72. Evaluate the differential of tan Ѳ.

A. ln sec Ѳ dѲ

B. ln cos Ѳ dѲ

C. sec Ѳ tan Ѳ dѲ

D. sec2 Ѳ dѲ

View Answer:

Answer: Option D

Solution:

73. If y = cos x, what is dy/dx?

A. sec x

B. –sec x

C. sin x

D. –sin x

View Answer:

Answer: Option D

Solution:

74. Find dy/dx: y = sin (ln x2).

A. 2 cos (ln x2)

B. 2 cos (ln x2) / x

C. 2x cos (ln x2)

D. 2 cos (ln x2) / x2

View Answer:

Answer: Option B

Solution:

75. The derivative of ln (cos x) is:

A. sec x

B. –sec x

C. –tan x

D. tan x

View Answer:

Answer: Option C

Solution:

76. Find the derivative of arc cos 4x with respect to x.

A. -4 / [1 – (4x)^2]^2

B. -4 / [1 – (4x)]^0.5

C. 4 / [1 – (4x)^2]^0.5

D. -4 / [(4x)^2 – 1]^0.5

View Answer:

Answer: Option B

Solution:

77. What is the first derivative of y = arc sin 3x.

A. –[3 / (1 + 9x2)]

B. 3 / (1 + 9x2)

C. –[3 / √(1 – 9x2)]

D. 3 / √(1 – 9x2)

View Answer:

Answer: Option D

Solution:

78. If y = x (ln x), find d2y / dx2.

A. 1 / x2

B. -1 / x

C. 1 / x

D. -1 / x2

View Answer:

Answer: Option C

Solution:

79. Find the second derivative of y = x – 2 at x = 2.

A. 96

B. 0.375

C. -0.25

D. -0.875

View Answer:

Answer: Option B

Solution:

80. Given the function f(x) = x3 – 5x + 2, find the value of the first derivative at x = 2, f’ (2).

A. 7

B. 3x2 – 5

C. 2

D. 8

View Answer:

Answer: Option A

Solution:

81. Given the function f(x) = x to the 3rd power – 6x + 2, find the value of the first derivative at x = 2, f’(2)

A. 6

B. 3x2 – 5

C. 7

D. 8

View Answer:

Answer: Option A

Solution:

82. Find the partial derivatives with respect to x of the function: xy2 – 5y + 6.

A. y2 – 5

B. xy – 5y

C. y2

D. 2xy

View Answer:

Answer: Option C

Solution:

83. Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are equal.

A. (1, 2)

B. (2, 1)

C. (4, 4)

D. (-1, 4)

View Answer:

Answer: Option A

Solution:

84. Find the slope of the line tangent to the curve y = x3 – 2x + 1 at x = 1.

A. 1

B. ½

C. 1/3

D. ¼

View Answer:

Answer: Option A

Solution:

85. Determine the slope of the curve x2 + y2 – 6x – 4y – 21 = 0 at (0, 7).

A. 3/5

B. -2/5

C. -3/5

D. 2/5

View Answer:

Answer: Option A

Solution:

86. Find the slope of the tangent to a parabola y = x2 at a point on the curve where x = ½.

A. 0

B. 1

C. ¼

D. -1/2

View Answer:

Answer: Option B

Solution:

87. Find the slope of the ellipse x2 + 4y2 – 10x + 16y + 5 = 0 at the point where y = -2 + 80.5 and x = 7.

A. -0.1654

B. -0.1538

C. -0.1768

D. -0.1463

View Answer:

Answer: Option C

Solution:

88. Find the slope of the tangent to the curve y = x4 – 2x2 + 8 through point (2, 16).

A. 20

B. 1/24

C. 24

D. 1/20

View Answer:

Answer: Option C

Solution:

89. Find the slope of the tangent to the curve y2 = 3x2 + 4 through point (-2, 4)

A. -3/2

B. 3/2

C. 2/3

D. -2/3

View Answer:

Answer: Option A

Solution:

90. Find the slope of the line whose parametric equations are x = 4t + 6 and y = t – 1.

A. -4

B. ¼

C. 4

D. -1/4

View Answer:

Answer: Option B

Solution:

91. What is the slope of the curve x2 + y2 – 6x + 10y + 5 = 0 at (1, 0).

A. 2/5

B. 5/2

C. -2/5

D. -5/2

View Answer:

Answer: Option A

Solution:

92. Find the slope of the curve y = 6(4 + x)½ at (0, 12).

A. 0.67

B. 1.5

C. 1.33

D. 0.75

View Answer:

Answer: Option B

Solution:

93. Find the acute angle that the curve y = 1 – 3x2 cut the x-axis.

A. 77°

B. 75°

C. 79°

D. 120°

View Answer:

Answer: Option A

Solution:

94. Find the angle that the line 2y – 9x – 18 = 0 makes with the x-axis.

A. 74.77°

B. 4.5°

C. 47.77°

D. 77.47°

View Answer:

Answer: Option D

Solution:

95. Find the equation of the tangent to the curve y = x + 2x1/3 through point (8, 12)

A. 7x – 6y + 14 = 0

B. 8x + 5y + 21 = 0

C. 5x – 6y – 15 = 0

D. 3x – 2y – 1 = 0

View Answer:

Answer: Option A

Solution:

96. What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0?

A. 6.21

B. 5.21

C. 5.66

D. 6.66

View Answer:

Answer: Option C

Solution:

97. Find the radius of curvature at any point of the curve y + ln (cos x) = 0.

A. cos x

B. 1.5707

C. sec x

D. 1

View Answer:

Answer: Option C

Solution:

98. Determine the radius of curvature at (4, 4) of the curve y2 – 4x = 0.

A. 24.4

B. 25.4

C. 23.4

D. 22.4

View Answer:

Answer: Option D

Solution:

99. Find the radius of curvature of the curve x = y3 at (1, 1)

A. 4.72

B. 3.28

C. 4.67

D. 5.27

View Answer:

Answer: Option D

Solution:

100. The chords of the ellipse 64x2 + 25y2 = 1600 having equal slopes of 1/5 are bisected by its diameter. Determine the equation of the diameter of the ellipse.

A. 5x – 64y = 0

B. 64x – 5y = 0

C. 5x + 64y = 0

D. 64x + 5y = 0

View Answer:

Answer: Option D

Solution:

Online Question and Answer in Differential Calculus (Limits and Derivatives) Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Differential Calculus (Limits and Derivatives)
PART 1: MCQ from Number 1 – 50                                Answer key: PART 1
PART 2: MCQ from Number 51 – 100                           Answer key: PART 2

Online Question and Answer in Differential Calculus (Maxima/Minima and Time Rates) Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Differential Calculus (Maxima/Minima and Time Rates)
PART 1: MCQ from Number 1 – 50                             Answer key: PART 1
PART 1: MCQ from Number 2 – 100                           Answer key: PART 2
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