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.

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.

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.

I’d say letter a..

Ifound this on google “a skewed (non-symmetric) distribution is a distribution in which there is no such mirror-imaging. a "skewed right" distribution is one in which the tail is on the right side. a "skewed left" distribution is one in which the tail is on the left side. the above histogram is for a distribution that is skewed right.” i hope this you for what your looking for