EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2018>Q 8

HARD

WBJEE

IMPORTANT

Earn 100

Let $f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7$ . Then, $\lim_{h \to 0} \frac{f (1 - h) - f (1)}{h^{3} + 3 h}$

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Important Questions on Limits

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2020>Q 1

Let

0 < α < β < 1

. Then,

\lim_{n \to \infty} \int_{1 / (k + β)}^{1 / (k + α)} \frac{d x}{1 + x}

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2020>Q 2

Let

f (x) = \frac{1}{3} x \sin x - (1 - \cos x)

. The smallest positive integer

k

such that

\lim_{x \to 0} \frac{f (x)}{x^{k}} \neq 0

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2019>Q 3

The limit of the interior angle of a regular polygon of

n

sides as

n \to \infty

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2020>Q 4

If

\lim_{x \to 0} {(\frac{1 + c x}{1 - c x})}^{1 / x} = 4,

then

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

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2020>Q 5

\lim_{x \to 1} (\frac{1}{\ln x} - \frac{1}{(x - 1)})

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2019>Q 6

\lim_{x \to 0^{+}} (x^{n} \ln x), n > 0

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2019>Q 7

\lim_{x \to 0^{+}} {(e^{x} + x)}^{1 / x}

HARD

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 21 - Limits>WBJEE 2018>Q 8

Let

f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7

. Then,

\lim_{h \to 0} \frac{f (1 - h) - f (1)}{h^{3} + 3 h}