Question

${lim}_{x\to 0}\frac{\sin mx}{\sin nx}\left[m/n\right]$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin mx}{\sin nx}$

$=\frac{\underset{x\to 0}{lim}\left(\frac{\sin mx}{mx}\right)\times mx}{\underset{x\to 0}{lim}\left(\frac{\sin nx}{nx}\right)\times nx}$

$=\underset{x\to 0}{lim}\frac{mx}{nx}$

$=\frac{m}{n}$