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The value of \mathrm{ \lim _{x \rightarrow \frac{\pi}{4}} \frac{\int_2^{\sec ^2 x} f(t) d t}{x^2-\frac{\pi^2}{16}} }is equal to
 

Option: 1

\mathrm{\frac{8}{\pi} f(2)}
 


Option: 2

\mathrm{\frac{2}{\pi} f(2)}
 


Option: 3

\mathrm{\frac{2}{\pi} f\left(\frac{1}{2}\right)}
 


Option: 4

\mathrm{4 f(2)}


Answers (1)

best_answer

\mathrm{\lim _{x \rightarrow \frac{\pi}{4}} \frac{\int_2^{\sec ^2 x} f(t) d t}{x^2-\frac{\pi^2}{16}}=\lim _{x \rightarrow \frac{\pi}{4}} \frac{f\left(\sec ^2 x\right) \times 2 \sec ^2 x \tan x}{2 x}=\frac{8}{\pi} f(2)}

Hence option 1 is correct.

Posted by

Anam Khan

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