Ans: (C)
Hint : \(\operatorname{lt}_{x \rightarrow 0} \frac{x \sin x-3(1-\cos x)}{3 x^{k}}=\frac{1}{3} \operatorname{lt}_{x \rightarrow 0}\left(\frac{\sin x / 2}{x / 2}\right) \operatorname{lit}_{x \rightarrow 0}\left(\frac{2 x \cos x / 2-6 \sin x / 2}{2 x^{k-1}}\right)\) \(\mathrm{k}-1=1 \Rightarrow \mathrm{k}=2\)