If limx→0 xn−sin⁡xnx−sinn⁡x is nonzero and finite,then n in equal to

$lim_{x \to 0} \frac{x^{n} - \sin x^{n}}{x - \sin^{n} x} (\frac{0}{0})$

$= lim_{x \to 0} \frac{n x^{n - 1} (1 - \cos x^{n})}{1 - n \sin^{n - 1} x \cos x}$ (L Hopital Rule)

$= \frac{0}{1} = 0, if n > 1$

For $n = 0, lim_{x \to 0} \frac{x^{n} - \sin x^{n}}{x - \sin^{n} x} = lim_{x \to 0} \frac{1 - \sin 1}{x - 1} = \sin 1 - 1$

For $n = 1, lim_{x \to 0} \frac{x^{n} - \sin x^{n}}{x - \sin^{n} x} = lim_{x \to 0} \frac{x - \sin x}{x - \sin x} = 1$

If $lim_{x \to 0} \frac{x^{n} - \sin x^{n}}{x - \sin^{n} x}$ is nonzero and finite,
then $n$ in equal to