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

EASY

JEE Main

IMPORTANT

Earn 100

For each $t \in R,$ let $[t]$ be the greatest integer less than or equal to $t$ . Then $\lim_{x \to 0^{+}} x ([\frac{1}{x}] + [\frac{2}{x}] + \dots + [\frac{15}{x}])$

50% studentsanswered this correctly

Important Questions on Limits

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 9th April 2016>Q 52

If

\lim_{x \to \infty} {(1 + \frac{a}{x} - \frac{4}{x^{2}})}^{2 x} = e^{3}

, then

a

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 3rd April 2016>Q 53

Let

P = \lim_{x \to 0^{+}} {(1 + \tan^{2} \sqrt{x})}^{\frac{1}{2 x}}

, then

\log P

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2016>Q 54

\lim_{x \to 0} \frac{{(1 - \cos 2 x)}^{2}}{2 x \tan x - x \tan 2 x}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 24 - Limits>JEE Main - 10th April 2015>Q 55

\lim_{x \to 0} \frac{e^{x^{2}} - \cos x}{\sin^{2} x}

is equal to