JEE MATHEMATICS MCQ: LIMITS

1 Easy

1 of 1

Analyzing +4 | -1

The value of

\lim \limits_{{x \rightarrow 0}}\left(\frac{2}{x^3}\left(\sin ^{-1} x-\tan ^{-1} x\right)\right)^{2 / x^2}

equals

View answer and explanation

Correct option: D

\frac{1}{\sqrt{e}}

The correct answer is D (

\frac{{1}}{{\sqrt{{e}}}}

) because by using Taylor series expansions for

\sin^{-1}x

and

\tan^{-1}x

, the limit can be evaluated to

e^{-1/2}

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