This set of Engineering Mathematics Multiple Choice Questions & Answers focuses on “Indeterminate Forms – 4”.

1. is

a) 0

b) 1

c) 2

d) 3

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2. Value of lim_{x → 0}(1+Sin(x))^{Cosec(x)}

a) e

b) 0

c) 1

d) ∞

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Explanation: lim

_{x → 0}(1+Sin(x))

^{Cosec(x)}

Put sin(x) = t we get

lim_{t → 0}(1+t)^{(1⁄t)} = e.

3. Value of lim_{x → 0}(1 + cot(x))^{sin(x)}

a) e

b) e^{2}

c) ^{1}⁄_{e}

d) Can not be solved

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4.

a) True

b) False

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Explanation: It is a property of limits.

5.

a) True

b) False

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6. Evaluate lim_{x → 1}[(x^{x} – 1) / (xlog(x))]
a) e^{e}

b) e

c) 1

d) e^{2}

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Explanation: lim

_{x → 1}[(x

^{x}– 1) / (xlog(x))] = (

^{0}⁄

_{0})

By L hospital rule,

lim_{x → 1} [x^{x} (1+xlog(x))/ (1+xlog(x))] = lim_{x → 1} [x^{x}] = 1.

7. Find n for which , has non zero value.

a) >=1

b) >=2

c) <=2

d) ~2

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Explanation:

Hence, limit have non zero limit, if n ≠ 0 and (n-1) ≠ 0 and (n-2) >= 0 means n >= 2.

8. Find the value of lim_{x → 0}(Sin(2x))^{Tan2 (2x)} ?

a) e^{0.5}

b) e^{-0.5}

c) e^{-1}

d) e

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9. Evaluate

a) ^{1}⁄_{4}

b) ^{1}⁄_{3}

c) ^{1}⁄_{2}

d)1

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**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__.