This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Indeterminate Forms – 2”.

1. Find

a) ∞

b) 0

c) 2

d) -∞

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Explanation: First evaluate

This is true for the above problem

Thus, we can deduce the limit as

= 1

Hence, 2 is the right answer.

2. Find

a) ^{3}⁄_{2}

b) 0

c) ^{4}⁄_{3}

d) –^{4}⁄_{3}

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3. Find relation between a and b such that the following limit is got after a single application of L hospitals Rule

a) ^{b}⁄_{a} = 2

b) ^{a}⁄_{b} = 2

c) a = b

d) a = -b

View Answer

Explanation: Given differentiation is applied once we get

ae

^{0}+ be

^{0}= 0 = a + b (numerator → zero)

be

^{0}+ ae

^{0}= 0 = a + b (denominator → zero)

Thus the relation between (a, b) and is

a + b = 0

OR

a = -b.

4. Find

a) -76

b) -6

c) -7

d) 0

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5. Find how many rounds of differentiation are required to have finite limit for given that a ≠ b ≠ c

a) 3

b) 0

c) 2

d) 4

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Explanation: Applying L hospitals rule

Assume now that

a + b + 2c = 0 and a + 2b – 3c = 0

We must have

a = c = b but given a ≠ c ≠ b

Thus, our assumption is false and a finite limit exists after first round of differentiation.

Hence, 2 is the right answer.

6. Find

a) 4!

b) 5!

c) 0

d) ∞

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7. Find

a) 0

b) 2

c) ∞

d) 1

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8. Find

a) ^{1}⁄_{cosh(1012345)}

b) 90987

c) 1012345

d) ∞

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9. Let f o ^{n} (f(x)) denote the composition of f(x) with itself n number of times then the value of lt_{n → ∞ } f o ^{n} (sin(x)) =

a) -1

b) 2

c) ∞

d) 0

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Explanation: Drawing the graph of y = x and y = sin(x) we can write the limit value as 0.

10. Find

a) ∞

b) -1

c) 0

d) 2^{2}

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11. Find

a) -33

b) ^{1}⁄_{2}

c) 0

d) ^{31}⁄_{32}

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12. Find

a) √π

b) ∞

c) √^{π}⁄_{2}

d) 0

View Answer

13. Find

a) e

b) e – 1

c) 0

d) ∞

View Answer

**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__.