Question

${lim}_{x\to 0}\frac{sin5x}{tan3x}$

Answer 1

${lim}_{x\to 0}\frac{sin5x}{tan3x}$

$=\frac{{lim}_{x\to 0}sin5x}{li{m}_{3x\to 0}tan3x}$

$=\frac{{lim}_{5x\to 0}\frac{sin5x}{5x}\times 5}{{lim}_{3x\to 0}\frac{tan3x}{3x}\times 3}$

$[\because Ifx\to 0then3x\to 0,5x\to 0]$

$=\frac{5}{3}\times 1[\because {lim}_{5x\to 0}\frac{sinx}{x}=also{lim}_{5x\to 0}\frac{tanx}{x}=1]$

$=\frac{5}{3}$