A) 1
B) 0
C) \[\frac{n}{m}\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin {{x}^{n}}}{{{(\sin x)}^{m}}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{\sin {{x}^{n}}}{{{x}^{n}}} \right)\left( \frac{{{x}^{n}}}{{{x}^{m}}} \right){{\left( \frac{x}{\sin x} \right)}^{m}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,{{x}^{n-m}}=0\] \[(\because m<n)\]
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