Science:Math Exam Resources/Courses/MATH100/December 2018/Question 02 (c)/Solution 1

We have

$\underset{x\to 0^{+}}{\lim }\frac{x}{|\tan x|}=\underset{x\to 0^{+}}{\lim }\frac{x}{\tan x}=1,$ but

$\underset{x\to 0^{-}}{\lim }\frac{x}{|\tan x|}=\underset{x\to 0^{-}}{\lim }\frac{x}{-\tan x}=-1,$ so $\text{the limit does not exist}$.