Question

Evaluate: ${lim}_{x\to 0}\frac{\sin ax}{\sin bx}a,b\ne 0$

Answer 1

Now,

$\begin{array}{c}={lim}_{x\to 0}\frac{\sin ax}{\sin bx},ab\ne 0\\ ={lim}_{x\to 0}\frac{\left(\frac{\sin ax}{x}\right)}{\left(\frac{\sin bx}{x}\right)}=\frac{a}{b}\left({lim}_{x\to 0}\frac{\sin x}{x}=1\right)\end{array}$

Hence, this is the answer.