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f(x)={(b sin^(-1)((x+c)/2),-1/2ltxlt0),(...

`f(x)={(b sin^(-1)((x+c)/2),-1/2ltxlt0),(1/2, x=0),((e^(ax//2)-1)/x,0ltxlt1/2):}` If f(x) is differentiable at x=0 and `|c|lt1/2`, then find the values of a and prove that `64b^(2)-(4-c^(2))`

A

`16b^(2)=4-c^(2)`

B

`16b^(2)=1-4c^(2)`

C

`64b^(2)=4-c^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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