Question

Does a limit exist if the left hand side and the right hand side limit are not the same? Especially when there is only a line to the right side of the limit, but not a line to the left side.

Answer 1

I agree with the answer below. The right side limit exists in this case, however, the left side limit doesn't exist, because there is not a line (think of it as a route) for the point to travel from left side of the limit to the point, so left side is basically DNE.

Answer 2

No, the limit does not exist if the left-sided limit does not equal to the right-sided limit. Furthermore, if the limit lets say is x --> 2, and there is a line from the 2+ direction but not a line from 2- direction, then the left-sided limit doesn't even exist.