EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2018>Q 3

HARD

Assam CEE

IMPORTANT

Earn 100

If $f$ is a continuous function on the real line, and $x^{2} + (f (x) - 2) x - \sqrt{3} f (x) + 2 \sqrt{3} - 3 = 0$ . Then the value of $f (\sqrt{3})$

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Important Questions on Limits

HARD

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2018>Q 4

Let for all

x > 0, f (x) = \lim_{n \to \infty} n (x^{1 / n} - 1),

then

HARD

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2017>Q 5

Value of

\lim_{y \to \infty} (\sqrt{y + \sqrt{y + \sqrt{y}}} - \sqrt{y})

is:

EASY

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2016>Q 6

If

\lim_{x \to 0} \frac{x^{a} \sin^{b} x}{\sin x^{c}}, a, b, c, \in R ~ \{0\}

exists and has non-zero value, then

EASY

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2016>Q 7

If the function

f (x)

satisfies

\lim_{x \to 2} \frac{f (x) - 1}{x^{2} - 4} = e

then

\lim_{x \to 2} f (x)

is equal to

MEDIUM

Assam CEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Limits>Assam CEE 2016>Q 8

l_{n}

and

k_{n}

are positive integers and

l_{n} + \sqrt{3} k_{n} = {(3 + \sqrt{3})}^{n}

, then

\lim_{n \to \infty} \tan^{- 1} (\frac{l_{n}}{k_{n}})

is