Question

Evaluate $\underset{x\to 0}{lim}\frac{sin5x}{tan3x}$

Answer 1

$\underset{x\to 0}{lim}\frac{sin5x}{tan3x}=\underset{x\to 0}{lim}\frac{5x.\left(\frac{sin5x}{5x}\right)}{3x.\left(\frac{tan3x}{3x}\right)}$

$=\frac{5}{3}\frac{\underset{5x\to 0}{lim}\left(\frac{sin5x}{5x}\right)}{\underset{3x\to 0}{lim}\left(\frac{tan3x}{3x}\right)}=(\frac{5}{3}\times \frac{1}{1})=\frac{5}{3}$