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`f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/x , o lt x lt 1/2` If `f(x)` is differentiable at `x=0 and |c|<1/2`, then find thevalue of a and prove that `64b^2=(4-c^2)`.

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