infinite discontinuity as limit approaches x and f(x) is defined

Question

If $\lim\limits_{x \to c^-} f(x) = -\infty$, and if $\lim\limits_{x \to c^+} f(x) = \infty$, and f(c) = d, is there both a removable and infinite discontinuity or just a removable discontinuity? Thanks!

Answer 1

There cannot be a removable discontinuity, as $\lim_{x\to c} f(x)$ doesn't exist (the lateral limits don't have the same value). So the discontinuity is not removable. It is infinite.