What is a One-sided Limit?
Image from mathwarehouse.com
Sometimes f(x) approaches different values when x approaches x0 from different directions; this happens in the case of a jump discontinuity. [Steal the image we use for Jump Discontinuity, and re-use it here.] In this case, f(x) can't be said to have a unique limit at x0, but it may well have two one-sided limits: one as x approaches from the left, and one as x approaches from the right.