1.) A continuity is a predictable line, that contains absolutely no jumps, breaks, or holes in it. The line can also has to be able to be drawn without lifting one's pen/pencil off of the paper. On the other hand a Discontinuity is that of a point, jump, infinite, or oscillating. At a point discontinuity there is a difference in the limit and value of the function. When there is a jump discontinuity there is literally a jump in the graph, the graph stops at one point and then starts anew at another point. Infinite discontinuity occurs when there are vertical asymptotes in the function, this leads to unbounded behavior. Oscillating discontinuity occurs plain and simply because it is oscillating.
2.) A limit is the intended height that a function is intending on reaching, where as a value is the actual height that the function reaches. The limit exists at a point discontinuity because the line can still meet at the given point even if there is nothing there. The limit does not exist at the following: jump, infinite and oscillating discontinuity.
3.) One evaluates limits numerically through the use of a table. Graphically, it is as simple as making sure the graph meets at a given point. As far as solving the limit algebraically there is a number of ways to solve which include: direct substitution, dividing out, and rationalizing.
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