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

This is the Multiple Choice Questions Part 1 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

#### Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

Problem 1: CE Board November 1997

Evaluate the Limit:

A. 1/5

B. 2/5

C. 3/5

D. 4/5

Solution: Review Solution for Number 1

Problem 2: ECE Board April 1998

Evaluate the Limit:

A. undefined

B. 0

C. Infinity

D. 1/7

Solution: Review Solution for Number 2

Problem 3: ME Board April 1998

Evaluate the Limit:

A. 0

B. 1

C. 8

D. 16

Solution: Review Solution for Number 3

Problem 4: ECE Board April 1993

Evaluate the Limit:

A. 0

B. 2

C. 4

D. 6

Solution: Review Solution for Number 4

Problem 5: EE Board April 1995

Evaluate the Limit:

A. 0

B. 1/2

C. 2

D. -1/2

Solution: Review Solution for Number 5

Problem 6: ME Board October 1997

Compute the following limit:

A. 1

B. 0

C. 2

D. Infinite

Solution: Review Solution for Number 6

Problem 7: EE Board October 1994

Evaluate the Limit:

A. Undefined

B. 3/5

C. Infinity

D. Zero

Solution: Review Solution for Number 7

Problem 8: ECE Board November 1991

Evaluate the Limit:

A. 24

B. 26

C. 28

D. 30

Solution: Review Solution for Number 8

Problem 9: ECE Board November 1994

Evaluate the Limit:

A. e2ฯ

B. e2/ฯ

C. 0

D. ฮฑ

Solution: Review Solution for Number 9

Problem 10: EE Board October 1997

Differentiate y = ex cos x2

A. โex sin x2

B. ex (cos x2 โ 2x sin x2)

C. ex cos x2 โ 2x sin x2

D. -2xex sin x

Solution: Review Solution for Number 10

Problem 11: EE Board October 1997

Differentiate y = sec (x2 + 2)

A. 2x cos (x2 + 2)

B. โcos (x2 + 2) cot (x2 + 2)

C. 2x sec (x2 + 2) tan (x2 + 2)

D. cos (x2 +2)

Solution: Review Solution for Number 11

Problem 12: CE Board October 1994

What is the derivative with respect to x of (x + 1)3 โ x3?

A. 3x + 6

B. 3x โ 3

C. 6x โ 3

D. 6x + 3

Solution: Review Solution for Number 12

Problem 13: EE Board October 1997

Differentiate y = log10 (x2 + 1)2

A. 4x (x2 + 1)

B. (4x log10 e) / (x2 + 1)

C. log e(x) (x2 + 1)

D. 2x (x2 + 1)

Solution: Review Solution for Number 13

Problem 14: EE Board October 1997

Differentiate (x2 + 2)1/2

A. ((x2 + 2)1/2) / 2

B. x / (x2 + 2)1/2

C. (2x) / (x2 + 2)1/2

D. (x2 + 2)3/2

Solution: Review Solution for Number 14

Problem 15: EE Board October 1997

If y = (t2 + 2)2 and t = x1/2, determine dy/dx

A. 3/2

B. (2x2 + 2x) / 3

C. 2(x + 2)

D. x5/2 + x1/2

Solution: Review Solution for Number 15

Problem 16: ME Board April 1997

What is the first derivative of the expression (xy)x = e?

A. 0

B. x/y

C. โy [(1 + ln xy) / x)]

D. โy [(1 โ ln xy) / x2)]

Solution: Review Solution for Number 16

Problem 17: ME Board April 1998

Find the derivative with respect to x function โ(2 โ 3x2)

A. (-2x2) / โ(2 โ 3x2)

B. (-3x) / โ(2 โ 3x2)

C. (-3x2) / โ(2 โ 3x2)

D. (3x) / โ(2 โ 3x2)

Solution: Review Solution for Number 17

Problem 18: EE Board April 1995

Find yโ if y = arc sin cos x

A. -1

B. -2

C. 1

D. 2

Solution: Review Solution for Number 18

Problem 19: CE Board May 1997

Find the derivative of arc cos 4x.

A. -4 / (1 โ 16x2)0.5

B. 4 / (1 โ 16x2)0.5

C. -4 / (1 โ 4x2)0.5

D. 4 / (1 โ 4x2)0.5

Solution: Review Solution for Number 19

Problem 20: CE Board November 1996

Find the derivative of (x + 1)3 / x

A. ((x + 1)2 / x) โ ((x + 1)3 / x)

B. (4(x + 1)2 / x) โ (2(x + 1)3 / x)

C. (2(x + 1)3 / x) โ ((x + 1)3 / x3)

D. (3(x + 1)2 / x) โ ((x + 1)3 / x2)

Solution: Review Solution for Number 20

Problem 21: ECE Board November 1991

Differentiate the equation y = x2 / (x + 1)

A. (x2 + 2x) / (x + 1)2

B. x / (x + 1)

C. 2x

D. (2x2) / (x + 1)

Solution: Review Solution for Number 21

Problem 22: CE Board November 1995

The derivative with respect to x of 2cos2 (x2 + 2) is

A. 2sin (x2 + 2) cos (x2 + 2)

B. -2sin (x2 + 2) cos (x2 + 2)

C. 8x sin (x2 + 2) cos (x2 + 2)

D. -8x sin (x2 + 2) cos (x2 + 2)

Solution: Review Solution for Number 22

Problem 23: CE Board November 1993

Find the second derivative of y by implicit differentiation from the equation 4x2 + 8y2 = 36

A. 64x2

B. (โ 9/4) y3

C. 32xy

D. (- 16/9) y3

Solution: Review Solution for Number 23

Problem 24: ME Board April 1998

Find the partial derivative with respect to x of the function xy2 โ 5y + 6.

A. y2 โ 5

B. y2

C. xy โ 5y

D. 2xy

Solution: Review Solution for Number 24

Problem 25: ME Board October 1997

Find the second derivative of x3 โ 5x2 + x = 0

A. 10x โ 5

B. 6x โ 10

C. 3x + 10

D. 3x2 โ 5x

Solution: Review Solution for Number 25

Problem 26: ME Board April 1998

Given the function f(x) = x to the 3rd power โ 6x + 2. Find the first derivative at x = 2.

A. 6

B. 7

C. 3x2 โ 5

D. 8

Solution: Review Solution for Number 26

Problem 27: CE Board May 1996

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

A. -0.1463

B. -0.1538

C. -0.1654

D. -0.1768

Solution: Review Solution for Number 27

Problem 28: EE Board October 1997

If y = 4cos x + sin 2x, what is the slope of the curve when x = 2 radians?

A. -2.21

B. -4.94

C. -3.95

D. 2.21

Solution: Review Solution for Number 28

Problem 29: ECE Board November 1991

Find the slope of the line tangent to the curve y = x3 โ 2x + 1 at x = 1.

A. 1

B. 1/2

C. 1/3

D. 1/4

Solution: Review Solution for Number 29

Problem 30: ECE Board November 1991

Given the slope of the curve at the point (1, 1): y = (x3/4) โ 2x + 1

A. 1/4

B. -1/4

C. 1 1/4

D. -1 1/4

Solution: Review Solution for Number 30

Problem 31: ECE Board November 1998

Find the slope of x2y = 8 at the point (2, 2)

A. 2

B. -1

C. -1/2

D. -2

Solution: Review Solution for Number 31

Problem 32: CE Board May 1998

Find the slope of the curve x2 + y2 โ 6x + 10y + 5 + 0 at point (1, 0).

A. 1/5

B. 2/5

C. 1/4

D. 2

Solution: Review Solution for Number 32

Problem 33: CE Board May 1996

Find the slope of the tangent to the curve, y = 2x โ x2 + x3 at (0, 2).

A. 1

B. 2

C. 3

D. 4

Solution: Review Solution for Number 33

Problem 34: ECE Board April 1999

Find the coordinates of the vertex of the parabola y = x2 โ 4x + 1 by making use of the fact that at the vertex, the slope of the tangent is zero.

A. (2, -3)

B. (3, -2)

C. (-1, -3)

D. (-2, -3)

Solution: Review Solution for Number 34

Problem 35: ECE Board April 1999

Find the equation of the normal to x2 + y2 = 5 at the point (2, 1)

A. y = 2x

B. x = 2y

C. 2x + 3y = 3

D. x + y = 1

Solution: Review Solution for Number 35

Problem 36: CE Board May 1995

What is the equation of the normal to the curve x2 + y2 = 25 at (4, 3)?

A. 5x + 3y = 0

B. 3x โ 4y = 0

C. 3x + 4y = 0

D. 5x โ 3y = 0

Solution: Review Solution for Number 36

Problem 37: EE Board April 1997

Locate the points of inflection of the curve y = f(x) = x2 ex.

A. -2 ยฑ โ3

B. 2 ยฑ โ2

C. -2 ยฑ โ2

D. 2 ยฑ โ3

Solution: Review Solution for Number 37

Problem 38: ECE Board November 1991

In the curve 2 + 12x โ x3, find the critical points.

A. (2, 18) and (-2, -14)

B. (2, 18) and (2, -14)

C. (-2, 18) and (2, -14)

D. (-2, 18) and (-2, 14)

Solution: Review Solution for Number 38

Problem 39: CE Board November 1997

Find the radius of curvature of a parabola y2 โ 4x = 0 at point (4, 4).

A. 22.36 units

B. 25.78 units

C. 20.33 units

D. 15.42 units

Solution: Review Solution for Number 39

Problem 40: ECE Board November 1996

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

A. cos x

B. 1.5707

C. sec x

D. 1

Solution: Review Solution for Number 40

### 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 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 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 โ 50                             Answer key: PART 1
PART 1: MCQ from Number 2 โ 100                           Answer key: PART 2

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