This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Limits and Derivatives of Several Variables – 1”.

1. Find

a) ∞

b) 0

c) Does Not Exist

d) 121

View Answer

Explanation: Put x = t : y = a.t

^{3⁄2}we have

By varying a we get different limits along different

paths

Hence, Does Not Exist is the right answer.

2. Find

a) 0

b)

c) Does Not exist

d) ∞

View Answer

Explanation: Put Put x = t : y = a.t

^{5⁄2}we have

By varying a we get different limits along different

paths

Hence, Does Not exist is the right answer.

3. Find

a) ∞

b) ^{1}⁄_{2}

c)

d) ^{1}⁄_{3}

View Answer

Explanation: Treating limits separately we have

lt_{(x, y)→(0, 0)} ^{sin(x)}⁄_{x} * lt_{(x, y)→(0, 0)} sec(y)

= 1 * 1

= 1.

4. Find

a) 1

b) 0

c) ∞

d) -90

View Answer

5. Find

a) 9

b) 0

c) 6

d) 2

View Answer

6. Find

a) 0

b) ∞

c)

d) -1

View Answer

7. Find

a)

b) 0

c) ∞

d) Does Not Exist

View Answer

Explanation: Put x = t : y = at

By varying a we get different limits

Hence, Does Not Exist is the right answer.

8. Find

a)

b) -1

c) ∞

d) Does not Exist

View Answer

Explanation: Multiplying and dividing by we have

.

9. Find

a) Does Not Exist

b) 0

c)

d) ∞

View Answer

Explanation: Put x =r.cos(ϴ) : y = r.sin(ϴ)

10. Find

a) 0

b) ∞

c)

d) Does Not Exist

View Answer

Explanation: Put x = at : y = t

By varying n we get different limits

Hence, Does Not Exist is the right answer.

11. Find

a) Does not Exist

b) 0

c) ∞

d)

View Answer

Explanation: Put x = at : y = t

By varying n we get different values of limits.

12. Find

a) ∞

b)

c) ^{1}⁄_{2}

d) Does Not Exist

View Answer

Explanation: Put x = t :y = at

By varying the value of a we get different limits.

13. Find

a)

b) ∞

c) 0

d) 990

View Answer

Explanation:

= 1 * 1 * 1

= 1.

14. Find

a)

b) ∞

c) 0

d) 990

View Answer

Explanation: lt

_{(x, y)→(0, 0)}

^{sinh(x)}⁄

_{x}* lt

_{(x, y)→(0, 0)}

^{sinh(y)}⁄

_{y}

= 1 * 1

= 1.

**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

To practice all areas of Engineering Mathematics, __here is complete set of 1000+ Multiple Choice Questions and Answers__.