$\lim _\limits{x \rightarrow 0}(\cos x)^{\cot ^2 x}$ is

JEE MATHEMATICS MCQ: LIMITS

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Application +4 | -1

\lim \limits_{{x \rightarrow 0}}(\cos x)^{\cot ^2 x}

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Correct option: D

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

Option D (

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

) is correct because by applying L'Hôpital's rule to the logarithmic form of the limit, we find the limit to be

e^{-\frac{{1}}{{2}}} = \frac{{1}}{{\sqrt{{e}}}}

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