Question

Evaluate : ${lim}_{x\to \frac{3\pi }{4}}\frac{2+\tan x}{5+4\tan x}$

Answer 1

${lim}_{x\to \frac{3\pi }{4}}\frac{2+\tan x}{5+4\tan x}$

$=\frac{2+\tan \frac{3\pi }{4}}{5+4\tan \frac{3\pi }{4}}$

$=\frac{2+\tan (\pi -\frac{\pi }{4})}{5+4\tan (\pi -\frac{\pi }{4})}$

$=\frac{2-\tan \frac{\pi }{4}}{5-4\tan \frac{\pi }{4}}$

$=\frac{2-1}{5-4}=\frac{1}{1}=1$