Let $f(x)=\left\{\begin{matrix}\frac{x}{2x^2+|x|},&x≠0\\1,&x=0\end{matrix}\right\}$, then f(x) is

discontinuous at x = 0

$f(0+0)=\underset{h→0}{\lim}f(h)=\underset{h→0}{\lim}\frac{h}{2h^2+h}=\underset{h→0}{\lim}\frac{1}{2h+h}=1$

and $f(0+0)=\underset{h→0}{\lim}f(-h)=\underset{h→0}{\lim}\frac{-h}{2h^2+|-h|}=\underset{h→0}{\lim}\frac{-h}{2h^2+h}=\underset{h→0}{\lim}\frac{-1}{2h+h}=-1$

as f(0 + 0) ≠ f(0 − 0), thus f(x) is discontinuous at x = 0.