Question

Evaluate: $\underset{x\to 0}{lim}\frac{\sin 5x}{\sin 3x}$

Answer 1

$\underset{x\to 0}{lim}\frac{\sin 5x}{\sin 3x}=\underset{x\to 0}{lim}\frac{\frac{\sin 5x}{5x}\times 5x}{\frac{\sin 3x}{3x}\times 3x}$

$=\frac{1\times 5}{1\times 3}=\frac{5}{3}$.