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Given that for each a in(0,1) underset...

Given that for each `a in(0,1)`
`underset(hto0^(+))limint_(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).
The value of `g((1)/(2))` is

A

`pi`

B

`2pi`

C

`(pi)/(2)`

D

`(pi)/(4)`

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