Let f: R → R be a differentiable function such that f((π)/4)=√ 2, f((π)/2)=0 and f^′((π)/2)=1 and let g(x)=∫_x^π / 4(f^′( t ). sect.+ tant sect f( t…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a differentiable function such that $\displaystyle f\left(\frac{\pi}{4}\right)=\sqrt{2}, f\left(\frac{\pi}{2}\right)=0$ and $\displaystyle f^{\prime}\left(\frac{\pi}{2}\right)=1$ and let $\displaystyle g(x)=\int_x^{\pi / 4}\left(f^{\prime}(\mathrm{t})\right.$ sect $\displaystyle \left.+\operatorname{tant} \operatorname{sect} f(\mathrm{t})\right) \mathrm{dt}$ for $\displaystyle x \in\left[\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then $\displaystyle \lim _{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} g(x)$ is equal to :