If f(x) = \ cases ( 2x)/(cx) + x 4( x + a ^ 2 - a) & ; x ≠ 0, (a...

$∵ f$\left(x\right)$is continuous at$x = 0$<br />$∴ \lim_{x \to 0}f\left(x\right) = f\left(0\right)$<br />$\lim_{x \to 0}\dfrac{\sin 2x}{cx} + \dfrac{x}{4\left(\sqrt{x + {a}^{2}} - a\right)}\left(\dfrac{\sqrt{x + {a}^{2}} + a}{\sqrt{x + {a}^{2}} + a}\right) = b$<br />$\lim_{x \to 0}\dfrac{2}{c} + \dfrac{x\left(\sqrt{x + {a}^{2}} + a\right)}{4\left(\left(x + {a}^{2}\right) - {a}^{2}\right)} = b ⇒ \dfrac{2}{c} + 0 = b ( asa < 0 )$<br />$⇒ bc = 2