Mathematics - Limits Question with Solution | TestHub

${\lim }_{x\to \frac{x}{4}}\frac{{\int }_2^{{\sec }^{2}x}f(t)dt}{x^2-\frac{{\pi }^2}{16}}$ $[\therefore \frac{0}{0}$ form $]$ Let $$\begin{array}{ll}\text{ Let }& L={\lim }_{x\to \frac{x}{4}}\frac{f\left({\sec }^{2}x\right)2\sec x\sec x\tan x}{2x}\\ \therefore & L=\frac{2f(2)}{\pi /4}=\frac{8f(2)}{\pi }\end{array}$$