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$Let f (x) = \{\begin{array}{cl} \frac{{(e^{x} - 1)}^{2 n}}{\sin^{n} (\frac{x}{a}) {(\log (1 + (\frac{x}{a})))}^{n}} & for x \neq 0 \\ 16^{n} & for x = 0 \end{array}$ and f is a continuous at $x = 0$ then the value of a is

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Correct option is D

Ltx=0 fx=Ltx=0 ex−1x2nxansinnxa×xanlog1+xan.a2n=a2n=f0∴a2n=16n⇒a=4

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Let f(x)=ex−12nsinn⁡xalog⁡1+xan for x≠016n for x=0and f is a continuous at x=0 then the value of a is

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$Let f (x) = \{\begin{array}{cl} \frac{{(e^{x} - 1)}^{2 n}}{\sin^{n} (\frac{x}{a}) {(\log (1 + (\frac{x}{a})))}^{n}} & for x \neq 0 \\ 16^{n} & for x = 0 \end{array}$ and f is a continuous at $x = 0$ then the value of a is