Let $$R \rightarrow R$$ be a differentiable function such that $$f(0) = 0, f\left(\frac{\pi}{2}\right) = 3$$ and $$f'(0) = 1$$. If $$ g(x) = \int_{x}^{\frac{\pi}{2}}\left[f'(t) \cosec t - \cos t \cosec t f(t)\right] dt$$ for $$x \in \left(0, \frac{\pi}{2}\right]$$, then $$\lim_{x \rightarrow 0}g(x) =$$