If \( |\mathrm{c}| \leq \frac{1}{2} \) and \( f(x) \) is a differen...

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If \( |\mathrm{c}| \leq \frac{1}{2} \) and \( f(x) \) is a differentiable function at \( x=0 \) given by
\( \mathrm{P} \) \( f(x)=\left\{\begin{array}{lr}b \sin ^{-1}\left(\frac{c+x}{2}\right), & -\frac{1}{2}x0 \\ \frac{1}{2}, & x=0, \text { then } \\ \frac{e^{a x / 2}-1}{x}, & 0x\frac{1}{2}\end{array}\right. \)

W
Which of the following is true ?
(1) \( 16 b^{2}=4-c^{2} \)
(2) \( 16 b^{2}=1-4 c^{2} \)
(3) \( 64 b^{2}=4-c^{2} \)
(4) none of these
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