Question

Evaluate the following limits :

$\underset{x\to 0}{lim}$ x cosec x

Answer 1

${lim}_{x\to 0}x\csc x$

$={lim}_{x\to 0}x\times \frac{1}{\sin x}$

$={lim}_{x\to 0}\frac{x}{\sin x}$

$=1$ since ${lim}_{x\to 0}\frac{\sin x}{x}=1$