Question

Evaluate:$\underset{x\to 0}{lim}\left(\frac{\sin ax}{\sin bx}\right)$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}$

$=\underset{x\to 0}{lim}\frac{\frac{\sin ax}{ax}\times ax}{\frac{\sin bx}{bx}\times bx}$

$\underset{x\to 0}{lim}\frac{1\times a}{1\times b}=\frac{a}{b}$