Given that for each a∈(0,1), limh→0+1−h∫ht−a(1� – InterviewSolution

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1.	Given that for each a∈(0,1), limh→0+1−h∫ht−a(1−t)a−1 dtexists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0,1).The value of g′(12) is
Answer» Given that for each $a \in (0, 1),$ $lim h \to 0^{+} 1 - h \int h t^{- a} (1 - t)^{a - 1} d t$ exists. Let this limit be $g (a)$ . In addition, it is given that the function $g (a)$ is differentiable on $(0, 1)$ . The value of $g^{'} (\frac{1}{2})$ is

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