Question

f there is a small circle point (open) on a graph in limits.... does that mean it does not exists or its dicontinued(ty)

Answer 1

It really depends on the function. Generally you will find that most of the open circles are a 'removable discontinuity', which means that after you perform some limit laws, the limit itself does exist there, however the graph of the derivative at that point would not exist and would equal zero.