A) 0
B) 1
C) 2
D) ?2
Correct Answer: C
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{x}^{3}}\cot x}{1-\cos x}=\underset{x\to 0}{\mathop{\lim }}\,\,\left( \frac{{{x}^{3}}\cot x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} \right)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,{{\left( \frac{x}{\sin x} \right)}^{3}}\times \underset{x\to 0}{\mathop{\lim }}\,\,\cos x\times \underset{x\to 0}{\mathop{\lim }}\,\,(1+\cos x)=2\]
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