Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 10

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IMPORTANT

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If $\lim_{n \to \infty} \frac{1}{{(\frac{x^{2} + a}{x^{2} + 1})}^{n} + 1} = 1$ , for all $x \in R$ , then condition on $a$ is:

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Important Questions on Limits

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 11

The value of

\lim_{x \to 0} \frac{x \cos x - \log (1 + x)}{x^{2}},

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 12

What is

\lim_{x \to \infty} (\sqrt{a^{2} x^{2} + a x + 1} - \sqrt{a^{2} x^{2} + 1})

equal to?

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Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 13

What is the value of

\lim_{x \to \infty} {(\frac{x + 6}{x + 1})}^{x + 4}

?

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Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 14

\lim_{x \to 0} [\frac{\sin (x + a) + \sin (a - x) - 2 \sin a}{x \sin x}]

is equal to

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Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 15

If

f (9) = 9

and

f^{'} (9) = 4

, then what is

\lim_{x \to 9} \frac{\sqrt{f (x)} - 3}{\sqrt{x} - 3}

equal to?

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Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 16

What is

\lim_{x \to 0} \frac{{(1 + x)}^{n} - 1}{x}

equal to?

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Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 17

If

f (x) = \frac{\sin (e^{x - 2} - 1)}{\ln (x - 1)}

, then

\lim_{x \to 2} f (x)

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 16 - Limits>Level 1>Q 18

The value of

\lim_{x \to 0} \frac{x (e^{x} - 1)}{1 - \cos x}

is