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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).
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