1. Continuity is when a graph is predictable, has no breaks jumps or holes, can be drawn without lifting your pencil and has a value that is the same as the limit. Discontinuity is when a graph has any of these things or where the graph's value and limit aren't equal. There are different families of disc. they are removable and non-removable disc. In the removable family we have the point disc. which is similar to a hole, the limit still exists but the value does not unless these is another point on the same x value. In our next family non-removable we have jump which looks like what it sounds like a point jumping to a diff point and here the limit does not exist due to diff. left right. Also in this family we have oscillating which we tend to call wiggly because it is wiggly and the limit does not exist here because it is oscillating. The last type of disc in this family is infinite disc and the limit does not exist here because of unbounded behavior, in this kind of disc. we also have a vertical asymptote.
2. A limit is the intended height of a function, as so wonderfully explained above the only kind of disc in which a limit exists is at a point disc this is why the kinds of disc are divided into diff families. The limit is the intended height while the value is the actual height reached, this is why they can differ and exist while the other does not.
3. We evaluate limits numerically with a number table and place the limit in the center, from the left we subtract one tenth and keep getting it closer to the limit. And on the right we add one tenth and make it get closer to the limit. We evaluate a limit graphically by following the function from the left and the right and meet at the limit, if they don't meet then the limit does not exist. To solve a limit algebraically we use substitution where we plug it in and see what we get, if we get 0/0 then we move on to method two which is factoring where we try to factor something out and try to get things to cancel, and the last method is the rationalizing wherever the radical is and multiply by the conjugate.
