Given that for each $$a \in (0, 1)$$ $$\lim_{h \rightarrow 0^+} \int_{h}^{1 - h}t^{-a}(1 - t)^{a - 1}dt $$ exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).
Question 54
The value of $$g^{'} \left(\frac{1}{2}\right)$$ is