This function is not continuous at $x=0$. I know that function (in the example) is continuous if $$\lim\limits_{x\to0^-}f(x)=\lim\limits_{x\to0^+}f(x)=f(0)$$ and limits and $f(x_0)$ must be defined. I am getting that $$f(0)=\frac{0}{0}$$ which is not defined. What is the condition for $f(x)$ to be continuous at $x=0$? If the condition exists, how to find if $f(x)$ is differentiable at $x=0$?
Thanks for replies.