Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 18

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IMPORTANT

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$\lim_{x \to \infty} (\sin \sqrt{x + 1} - \sin \sqrt{x})$ is equal to

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Important Questions on Limits

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 19

\lim_{x \to 0} (\frac{\log_{e} \cos x}{x^{2}})

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 20

\lim_{x \to 0} (\frac{10^{x} - 2^{x} - 5^{x} + 1}{x \tan x})

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 21

\lim_{x \to \infty} {(\frac{2 x^{2} + 3}{2 x^{2} + 5})}^{8 x^{2} + 3}

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 22

If

\lim_{x \to \infty} {(1 + \frac{a}{x} + \frac{b}{x^{2}})}^{2 x} = e^{2},

then the values of

a

and

b

are

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 23

\lim_{x \to 0} {(\frac{3}{1 + \sqrt{4 + x}})}^{cosec x}

has the value equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 24

The value of

\lim_{x \to 0} {(\cos a x)}^{{cosec}^{2} b x}

is

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 25

Let

r = \lim_{x \to 0} {(\frac{\sin x}{x})}^{\frac{1}{x}}

and

m = \lim_{x \to 0} {(\frac{\sin x}{x})}^{\frac{1}{x^{2}}}

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-1>Q 26

\lim_{x \to 0} (\frac{\sqrt[3]{1 + 3 x} - 1 - x}{{(1 + x)}^{101} - 1 - 101 x})

has the value equal to-