This set of Engineering Mathematics MCQs focuses on “Indeterminate Forms – 3”.

1. What are Intermediate Forms ?

a) Forms(f(x)/g(x)) whose limits x tends to ‘a’ can give rational number directly

b) Forms(f(x)/g(x)) whose limits x tends to ‘a’ can give finite number directly

c) Forms(f(x)/g(x)) whose limits x tends to ‘a’ can not be infinite output or cannot be solved directly

d) Forms(f(x)/g(x)) whose limits x tends to ‘a’ can gives finite output

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Explanation:

=

^{0}⁄

_{0}=

^{0}⁄

_{∞}=

^{∞}⁄

_{0}=

^{∞}⁄

_{∞}are all intermediate forms.

Special Rules are made to solve these forms. They cannot be solved directly.

2. L’Hospital Rule states that

a) If is an ideterminate form than = if has a finite value

b) always equals to

c) if an indeterminate form than cannot be solved

d) if an indeterminate form than it is equals to zero.

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Explanation: According to L’Hospital Rule, if img src=”https://www.sanfoundry.com/wp-content/uploads/2017/07/engineering-mathematics-questions-answers-indeterminate-forms-3-q1.png” /> is indeterminate and has a finite value then = . It is helpful in solving limits of indeterminate forms.

3. If f(x) = x^{2} – 3x + 2 and g(x) = x^{3} – x^{2} + x – 1 than find value of

a) 0.5

b) 1

c) -.5

d) -1

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4. If f(x) = Tan(x)-1 and g(x) = Sin(x) – Cos(x) than find value of lim_{x → π⁄4} ^{f(x)}⁄_{g(x)}

a) -√2

b) √(-2)

c) √2

d) √3

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5. If f(x) = Tan(x) and g(x) = e^{x} – 1 than find value of lim_{x → 0} ^{f(x)}⁄_{g(x)}

a) 1

b) 0

c) -1

d) 2

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6. Find the value of

a) e-1

b) e

c) e + 1

d) 1

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7. If f(x) = x^{3} + 3x^{2} + Sin(x) and g(x) = e^{x} – 1 than find value of

a) e^{6e}

b) e^{(e/6)}

c) e^{6}

d) e^{(6/e)}

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8. If f(x) = Sin(x) and g(x) = x than find value of lim_{x → 0} ^{f(x)}⁄_{g(x)}

a) -1

b) 0

c) 1

d) 2

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Explanation: lim

_{x → 0}

^{f(x)}⁄

_{g(x)}= lim

_{x → 0}

^{sin(x)}⁄

_{x}=

^{0}⁄

_{0}(Indeterminate forms)

By L’Hospital rule

lim

_{x → 0}

^{cos(x)}⁄

_{1}= 1.

9. If f(x) = sin(x)cos(x) and g(x) = x^{2} than find value of lim_{x → 0} ^{f(x)}⁄_{g(x)}

a) 2

b) 0

c) -1

d) Cannot be found

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10. If f(x) = e^{x} + xcos(x) and g(x) = Sin(x) than find value of lim_{x → 0} ^{f(x)}⁄_{g(x)}

a) 2

b) 1

c) 3

d) 4

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11. Find the value of is, where {x} is the fractional part of x.

a) ^{2}⁄_{e}

b) ^{1}⁄_{e}

c) 0

d) –^{1}⁄_{e}

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

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