The function \(f(x)=\left\{\begin{matrix}\dfrac{|x|}{3x^2-5x},\ x\ne0 \\\ 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 0\end{matrix}\right.\)
is not continuous at x = 0, because
1
\(\displaystyle\lim_{x\rightarrow0}f(x)\ne{f(0)}\)
2
\(\displaystyle\lim_{x\rightarrow0^-}f(x)\) does not exist
3
\(\displaystyle\lim_{x\rightarrow0}f(x)\) does not exist
4
\(\displaystyle\lim_{x\rightarrow0^+}f(x)\) does not exist