Discussion Forum



1)

The value of $\lim_{x \rightarrow 0}\frac{x^{3}\cot x}{1 - \cos x}$ is ;


A) 1

B) -2

C) 2

D) 0

Answer:

Option C

Explanation:

$\lim_{x \rightarrow 0}\frac{x^{3}\times\cot x}{1-\cos x}$

= $\lim_{x \rightarrow 0}\left(\frac{x^{3}\times\cot x}{1-\cos x}\times\frac{1+\cos x}{1+\cos x}\right)$

= $\lim_{x \rightarrow 0}\left(\frac{x}{\sin x}\right)^{3}\times\lim_{x \rightarrow 0}\cos x$

$\times\lim_{x \rightarrow 0}1+\cos x$ = 2