EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 25 June 2022 Shift 1>Q 61

HARD

JEE Main

IMPORTANT

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Let $f (x)$ be a polynomial function such that $f (x) + f^{'} (x) + f^{''} (x) = x^{5} + 64$ . Then, the value of $\lim_{x \to 1} \frac{f (x)}{x - 1}$ is equal to

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Important Questions on Limits

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 25 June 2022 Shift 2>Q 62

\lim_{x \to \frac{π}{2}} (\tan^{2} x ({(2 \sin^{2} x + 3 \sin x + 4)}^{\frac{1}{2}} - {(\sin^{2} x + 6 \sin x + 2)}^{\frac{1}{2}}))

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 26 June 2022 Shift 1>Q 63

\lim_{x \to \frac{1}{\sqrt{2}}} \frac{\sin (\cos^{- 1} x) - x}{1 - \tan (\cos^{- 1} x)}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 26 June 2022 Shift 2>Q 64

\lim_{x \to 0} \frac{\cos (\sin x) - \cos x}{x^{4}}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 27 June 2022 Shift 1>Q 65

Let

a

be an integer such that

\lim_{x \to 7} \frac{18 - [1 - x]}{[x - 3 a]}

exists, where

[t]

is greatest integer

\leq t

. Then

a

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 27 June 2022 Shift 2>Q 66

Let

[t]

denote the greatest integer

\leq t

and

\{t\}

denote the fractional part of

t

. Then integral value of

α

for which the left hand limit of the function

f (x) = [1 + x] + \frac{α^{2 [x] + \{x\}} + [x] - 1}{2 [x] + \{x\}}

at

x = 0

is equal to

α - \frac{4}{3}

is _____

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 28 June 2022 Shift 2>Q 67

If

\lim_{x \to 1} (\frac{\sin (3 x^{2} - 4 x + 1) - x^{2} + 1}{2 x^{3} - 7 x^{2} + a x + b}) = - 2

, then the value of

(a - b)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 29 June 2022 Shift 2>Q 68

The value of

\lim_{x \to 1} \frac{(x^{2} - 1) \sin^{2} (π x)}{x^{4} - 2 x^{3} + 2 x - 1}

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 25 July 2022 Shift 1>Q 69

If

\lim_{n \to \infty} (\sqrt{n^{2} - n - 1} + n α + β) = 0

then

8 (α + β)

is equal to