Can you help me with this question?
What kind of discontinuity i have at the point $x=0$, if the function defined as bellow:
$f(x)=\left\{\begin{matrix} \frac{1}{x} &x<0 \\ x^{2}& x\geq 0 \end{matrix}\right.$
I thought that the function has a discontinuity of the second kind at the point $x=0$, because at least one of the one-sided limits is infinite:
$\lim_{x \to 0^{-} }\frac{1}{x}=- \infty $
Why is it a wrong answer?
Thanks!