Question

Evaluate : ${lt}_{x\to 0}xcosecx$

Answer 1

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

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

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

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

$=\frac{1}{1}=1$