Continuity has no breaks no jumps no holes, you can draw it without lifting your pencil , it is predictable and when the limit and value are the same it is continuous.

discontinuity is broken down into two families- removable and non removable they are broken down into two because one has limits and the other doesn't . a discontinuity has limits. the non removable discontinuities re jump infinite and oscillating

A limit is an intended value it exists when it is a continuous function or if it is a hole a limit does not exist when there is a vertical asymptote because it has unbounded behavior or when it is oscillating and when it jumps because it is different from left to right. the difference of a limit and a value is that a limit is an intended height and a value is the actual height

We evaluate limits numerically by using a table, graphically we just go from left to right going toward the same point, algebraically nu using substitution which is plunging in the limit and if we get 0/0 we use different algebraic methods that can work