Question

Evaluate the following limits :
$\underset{x\to 0}{lim}x\cos ecx$

Answer 1

${lim}_{x\to 0}xcosecx={lim}_{x\to 0}\frac{x}{sinx}$

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

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