Let \( f : R \to R \) be a differentiable function such that \( f\!\left(\frac{\pi}{4}\right) = \sqrt{2} , \ f\!\left(\frac{\pi}{2}\right) = 0 \) and \( f'\!\left(\frac{\pi}{2}\right) = 1 \) and let
\( g(x) = \int_{x}^{\pi/4} \left( f'(t)\sec t + \tan t \sec t \ f(t) \right) dt \) for \( x \in \left[ \frac{\pi}{4}, \frac{\pi}{2} \right) \). Then \( \displaystyle \lim_{x \to \left(\frac{\pi}{2}\right)^{-}} g(x) \) is equal to
