Question

The value of $\underset{x\to 0}{\lim }\frac{x^3\cot x}{1-\cos x}$ is

• A. 1
• B. -2
• C. 2
• D. 0

Answer 1

Answer: (C)

$\underset{x\to 0}{\lim }\frac{x^3\cot x}{1-\cos x}$
$=\underset{x\to 0}{\lim }\left(\frac{x^3\cot x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x}\right)$
$=\underset{x\to 0}{\lim }{\left(\frac{x}{\sin x}\right)}^3\times \underset{x\to 0}{\lim }\cos x\times \underset{x\to 0}{\lim }(1+\cos x)=2$