Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 16

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Which of the following limits vanishes? where $[]$ denotes greatest integer function

50% studentsanswered this correctly

Important Questions on Limits

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 17

Consider the function

f (x) = {(\frac{a x + 1}{b x + 2})}^{x}

, where

a, b > 0

, then

\underset{x \to \infty}{Lim} f (x)

-

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 18

Which of the following limits is/are unity?

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 19

Let

f (x) = \frac{x \cdot 2^{x} - x}{1 - \cos x}

&

g (x) = 2^{x} \sin (\frac{ℓ n 2}{2^{x}})

then -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 20

If

\lim_{x \to 3} \frac{x^{3} + C x^{2} + 5 x + 12}{x^{2} - 7 x + 12} = ℓ

(finite real number) then -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 21

The graph of the function $y = f (x)$ is shown in the adjacent figure, then correct statement is -

Question Image

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 22

For

\underset{x \to 0}{Lim} \frac{\cot^{- 1} (\frac{1}{x})}{x}

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 23

If

ℓ = \lim_{x \to \infty} {(\frac{x + 1}{x - 1})}^{x}

, then

\{ℓ\}

and

[ℓ]

(where

\{.\}

&

[.]

denotes the fractional part function & greatest integer function respectively), is/are -

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 24

Which of the following limits is/are unity?