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

HARD

JEE Main

IMPORTANT

Earn 100

For each $t \in R,$ let $[t]$ be the greatest integer less than or equal to $t$ . Then, $\underset{x \to 1^{+}}{l i m} \frac{(1 - |x| + s i n |1 - x|) s i n ([1 - x] \frac{π}{2})}{|1 - x| [1 - x]}$

50% studentsanswered this correctly

Important Questions on Limits

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 12th January 2019 Shift 2>Q 46

\lim_{x \to 1^{-}} \frac{\sqrt{π} - \sqrt{2 \sin^{- 1} x}}{\sqrt{1 - x}}

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2018>Q 47

For each

t \in R,

let

[t]

be the greatest integer less than or equal to

t

. Then

\lim_{x \to 0^{+}} x ([\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{15}{x}])

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 16th April 2018>Q 48

\lim_{x \to 0} \frac{{(27 + x)}^{\frac{1}{3}} - 3}{9 - {(27 + x)}^{\frac{2}{3}}}

equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 2nd April 2017>Q 49

\lim_{x \to \frac{π}{2}} \frac{\cot x - \cos x}{{(π - 2 x)}^{3}}

equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 8th April 2017>Q 50

\lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th April 2016>Q 51

If

f (x)

is a differentiable function in the interval

(0, \infty)

such that

f (1) = 1

and

\lim_{t \to x} \frac{t^{2} f (x) - x^{2} f (t)}{t - x} = 1,

for each

x > 0,

then

f (\frac{3}{2})

is equal to