Question

Evaluate the following limits: ${lim}_{x\to 0}x\text{cosec}x$

Answer 1

We have,

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

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

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

We know that

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

Therefore,

$=\frac{1}{1}$

$=1$

Hence, this is the answer.