Question

The value of $\displaystyle \lim_{x\to0} \frac{x^{3} cot\,x}{1-cot\,x}$ is

• A. 1
• B. -2
• C. 2
• D. 0

Answer 1

Answer: (C)

$\displaystyle \lim_{x\to0} \frac{x^{3} cot\,x}{1-cot\,x}$
$= \displaystyle \lim_{x\to 0} \left(\frac{x^{3} cot\,x}{1-cot\,x}\times\frac{1+cot\,x}{1-cot\,x}\right)$
$= \displaystyle \lim_{x\to 0}\left(\frac{x}{sin\,x}\right)\times \displaystyle \lim_{x\to 0} cot\,x \times \displaystyle \lim_{x\to 0} \left(1+cot\,x\right) = 2$