JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{\int_2^{\sec ^2 x} f(t) d t}{x^2-\frac{\pi^2}{16}}

is equal to

View answer and explanation

Correct option: A

\frac{8}{\pi} f(2)

Option A (

\frac{8}{\pi} f(2)

) is correct because applying L'Hopital's rule to the limit results in the expression

\frac{8f(2)}{\pi}

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

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