The value of $\underset{x→\frac{π}{4}}{\lim}\frac{\int\limits_{2}^{\sec^2x}f(t)dt}{x^2-\frac{π^2}{16}}$ is equal to
Answer & explanation
Correct answer: option 1
$\underset{x→\frac{π}{4}}{\lim}\frac{\int\limits_{2}^{\sec^2x}f(t)dt}{x^2-\frac{π^2}{16}}=\underset{x→\frac{π}{4}}{\lim}\frac{f(\sec^2x)×2\sec^2x\tan x}{2x}=\frac{8}{π}f(2)$