JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim \limits_{{x \rightarrow \infty}} \frac{\int\limits_{0}^x \tan ^{-1} t \, d t}{\sqrt{x^2+1}}

is equal to:

View answer and explanation

Correct option: A

\frac{\pi}{2}

Option A (

\frac{\pi}{2}

) is correct because after applying L'Hôpital's rule, the limit simplifies to

\frac{\pi}{2}

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\lim \limits_{{x \rightarrow 0}}\left(\frac{1}{x^2}-\operatorname{cosec}^2 x\right)

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\lim \limits_{{x \rightarrow \infty}} x\left(e^{1 / x}-1\right)

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