Question

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

Answer 1

As $\underset{\theta \to 0}{lim}\frac{\sin \theta }{\theta }=1$

$\Rightarrow \underset{\theta \to 0}{lim}\sin \theta =\underset{\theta \to 0}{lim}$

$\Rightarrow \underset{x\to 0}{lim}\frac{\sin ax}{\sin bx}=\underset{x\to 0}{lim}\frac{ax}{bx}=\frac{a}{b}$.