Question

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

Answer 1

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

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

= $\frac{a}{b}\underset{x\to 0}{\text{lim}}\frac{\text{sin ax}}{\text{ax}}=\frac{a}{b}\times 1=\frac{a}{b}$.