EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th January 2019 Shift 1>Q 37

MEDIUM

JEE Main

IMPORTANT

Earn 100

The value of $\underset{y \to 0}{l i m} \frac{\sqrt{1 + \sqrt{1 + y^{4}}} - \sqrt{2}}{y^{4}}$

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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 - 9th January 2019 Shift 2>Q 38

For each

x \in R

, let

[x]

be the greatest integer less than or equal to

x

. Then

\underset{x \to 0^{-}}{l i m} \frac{x ([x] + |x|) \sin [x]}{|x|}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2019 Shift 1>Q 39

\underset{x \to 0}{l i m} \frac{{s i n}^{2} x}{\sqrt{2} - \sqrt{1 + c o s x}}

equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2019 Shift 2>Q 40

Let

f : R \to R

be a differentiable function satisfying

f^{^{'}} (3) + f^{^{'}} (2) = 0 .

Then

\underset{x \to 0}{l i m} {(\frac{1 + f (3 + x) - f (3)}{1 + f (2 - x) - f (2)})}^{\frac{1}{x}}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2019 Shift 1>Q 41

If

\underset{x \to 1}{l i m} \frac{x^{4} - 1}{x - 1} = \underset{x \to k}{l i m} \frac{x^{3} - k^{3}}{x^{2} - k^{2}}

, then

k

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2019 Shift 2>Q 42

If

\lim_{x \to 1} \frac{x^{2} - a x + b}{x - 1} = 5,

then

a + b

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th January 2019 Shift 1>Q 43

For each

t \in R,

let

[t]

be the greatest integer less than or equal to

t

. Then,

\underset{x \to 1^{+}}{l i m} \frac{(1 - |x| + s i n |1 - x|) s i n ([1 - x] \frac{π}{2})}{|1 - x| [1 - x]}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 12th April 2019 Shift 2>Q 44

\underset{x \to 0}{l i m} \frac{x + 2 s i n x}{\sqrt{x^{2} + 2 s i n x + 1} - \sqrt{{s i n}^{2} x - x + 1}}

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 12th January 2019 Shift 1>Q 45

\underset{x \to \frac{π}{4}}{l i m} \frac{c o t^{3} x - t a n x}{c o s (x + \frac{π}{4})}

is