Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 2

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If $f (x) = \frac{x + | x |}{x}$ , then the value of $\lim_{x \to 0} f (x)$ is

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Important Questions on Limits

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 3

Let

α

and

β

be the distinct roots of

a x^{2} + b x + c = 0

, then

\lim_{x \to a} \frac{1 - \cos (a x^{2} + b x + c)}{(x - α)^{2}}

is equal to

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 4

If

\lim_{x \to 0} \frac{((a - n) n x - \tan x) \sin n x}{x^{2}} = 0

, where

n

is non-zero real number, then

a

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 5

\lim_{x \to 2} [\frac{1}{x - 2} - \frac{2 (2 x - 3)}{x^{3} - 3 x^{2} + 2 x}]

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 6

If

\lim_{x \to 3} \frac{x^{n} - 3^{n}}{x - 3} = 108

, the positive integer

n

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 7

\lim_{x \to 0} \frac{\cos a x - \cos b x}{\cos c x - 1}

is equal to

\frac{m}{n}

, where

m

and

n

are respectively

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 8

\lim_{x \to 1} [x - 1]

, where

[\cdot]

is the greatest integer function, is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 9

\lim_{x \to 0} \frac{\tan x - \sin x}{\sin^{3} x}

is equal to

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 8 - Limits>Exercise 2>Q 10

\lim_{x \to 4} \frac{| x - 4 |}{x - 4}

is equal to