Question

Evaluate ${lim}_{x\to 0}\frac{x^2-\tan 2x}{\tan x}$

Answer 1

${lim}_{x\to 0}(\frac{x^2-tan2x}{tanx})$

$={lim}_{x\to 0}(\frac{x^2}{tanx}-\frac{tan2x}{tanx})$

$={lim}_{x\to 0}\left(\frac{x^2}{tanx}\right)-{lim}_{x\to 0}\left(\frac{tan2x}{tanx}\right)$

$=0-2=-2$ (Answer)