If $\lim _\limits {x \rightarrow 0} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^2}=0$, where $n$ is $a$ non-zero real number, then $a$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim \limits_{{x \rightarrow 0}} \frac{\{(a-n) n x-\tan x\} \sin n x}{x^2}=0

, where

n

a

non-zero real number, then

a

is equal to

View answer and explanation

Correct option: D

n+\frac{1}{n}

Option D (

n+\frac{1}{n}

) is correct because by applying L'Hopital's rule or simplifying the limit expression, we find that a must equal

n+\frac{1}{n}

for the limit to be 0.

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