Question

Evaluate the Given limit: $\underset{x\to 0}{lim}\frac{\sin ax}{bx}$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin ax}{bx}=\underset{x\to 0}{lim}\frac{\sin ax}{ax}\times \frac{ax}{bx}$
$=\underset{x\to 0}{lim}\left(\frac{\sin ax}{ax}\right)\times \left(\frac{a}{b}\right)$
$=\frac{a}{b}\underset{x\to 0}{lim}\left(\frac{\sin ax}{ax}\right)$ $=\frac{a}{b}\times 1=\frac{a}{b}$