Unit U Big Question

1. What is continuity? What is discontinuity? 
Continuity: predictable; it has no breaks, no holes, and no jumps. It can be drawn with a single, unbroken pencil stroke and makes a good bridge (can't fall off/fall through). Discontinuity is the exact opposite (breaks, holes, jumps)..

2. What is a limit? When does a limit exist? When does a limit not exist? What is the difference between a limit and a value? 
A limit is the intended height of the function. Limits exist at removal discontinuities: point discontinuity (hole). It exists here because it is the intended height of a function. Limits do not exist at the three non-removable discontinuities: l/r behavior (jump behavior), unbounded behavior (vertical asymptotes/approaches different values from the left and the right), and oscillating behavior (wiggly/does not approach any single value). A value is the actual height of a function.

3. How do we evaluate limits numerically, graphically, and algebraically?
Numerically - We evaluate limits numerically by using a table. The table will contain the x and y values and helps us find the lim f(x) by using our graph to trace.
Graphically - Go to the 'y=' screen, plug in your f(x), press GRAPH, hit TRACE, and trace to the value you are looking for.
Algebraically - you can use the method of substitution (taking the number the limit is approaching and plugging it in anywhere you see "x"), the factoring/dividing out method when substitution gives us 0/0 and when the numerator/denominator is factorable, or rationalizing by multiplying by the conjugate.

Citations!:
Removable/nonremovable discontinuities image: www.kirchmathanalysis.blogspot.com