The value of \( f(0) \), so that the function \( f(x)=\frac{\sqrt{a...

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The value of \( f(0) \), so that the function \( f(x)=\frac{\sqrt{a^{2}-a x+x^{2}}-\sqrt{a^{2}+a x+x^{2}}}{\sqrt{a+x}-\sqrt{a-x}} \) becomes continuous for all \( x \), given by
(a) \( a^{3 / 2} \)
(b) \( a^{1 / 2} \)
(c) \( -a^{1 / 2} \)
(d) \( -a^{3 / 2} \)
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