EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 3 September 2020 Shift 1>Q 27

HARD

JEE Main

IMPORTANT

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Let $[t]$ denote the greatest integer $\leq t$ . If $λ ε R - \{0, 1\}, \lim_{x \to 0} |\frac{1 - x + |x|}{λ - x + [x]}| = L$ , then $L$ is equal to

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Important Questions on Limits

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 3 September 2020 Shift 1>Q 28

If

\lim_{x \to 0} \{\frac{1}{x^{8}} (1 - \cos \frac{x^{2}}{2} - \cos \frac{x^{2}}{4} + \cos \frac{x^{2}}{2} \cos \frac{x^{2}}{4})\} = 2^{- k}

then the value of k is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 3 September 2020 Shift 2>Q 29

\lim_{x \to a} \frac{{(a + 2 x)}^{\frac{1}{3}} - {(3 x)}^{\frac{1}{3}}}{{(3 a + x)}^{\frac{1}{3}} - {(4 x)}^{\frac{1}{3}}} (a \neq 0)

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 5 September 2020 Shift 1>Q 30

If

α

is the positive root of the equation,

p (x) = x^{2} - x - 2 = 0

, then

\lim_{x \to α^{+}} \frac{\sqrt{1 - \cos p (x)}}{x + α - 4}

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 5 September 2020 Shift 2>Q 31

\lim_{x \to 0} \frac{x (e^{(\sqrt{1 + x^{2} + x^{4}} - 1) / x} - 1)}{\sqrt{1 + x^{2} + x^{4}} - 1}

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 6 September 2020 Shift 1>Q 32

\lim_{x \to 1} (\frac{\int_{0}^{(x - 1)^{2}} t \cos t^{2} d t}{(x - 1) \sin (x - 1)})

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 7th January 2020 Shift 1>Q 33

\underset{x \to 2}{l i m} \frac{3^{x} + 3^{3 - x} - 12}{3^{- \frac{x}{2}} - 3^{1 - x}}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 7th January 2020 Shift 2>Q 34

Let

f (x)

be a polynomial of degree

5

such that

x = \pm 1

are its critical points. If

\underset{x \to 0}{l i m} (2 + \frac{f (x)}{x^{3}}) = 4,

then which one of the following is not true?

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th January 2020 Shift 1>Q 35

\lim_{x \to 0} {(\frac{3 x^{2} + 2}{7 x^{2} + 2})}^{\frac{1}{x^{2}}}

is equal to