Work out one sided limit instantly with clear inputs, formula shown and shareable results.
One-sided limits approach a point from below or above. The ordinary two-sided limit exists only when both agree, which is why a removable discontinuity still has a limit but a jump does not.
Two-sided limit
lim exists ⇔ left limit = right limit
The factor (x − 3) cancels leaving x + 2, so both one-sided limits are 5 and the limit exists.
At a jump, as with |x|/x at zero, which approaches −1 from the left and +1 from the right.