1. What is Continuity? What is Discontinuity?
Continuity is the state of being continuous. Graphically, it occurs when the graph is go on forever to infinity. These graphs include strait lines and parabolas. Discontinuity is the state when there is an end or limit. This separates to removable discontinuity , and non-removable discontinuity. Removable discontinuity includes point discontinuity, where there is a hole on the graph. Non-removable discontinuity includes jump discontinuity, oscillating behavior, and infinite discontinuity.
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 a function. It exist as long is the same height is reached between both sides of the graph, the left side and the right side. If the same height is not reached by both the left direction and the right direction of the function, then the limit does not exist. The main difference between a value and a limit is that a value is the actual height of a function, while the limit is the intended height. For example, in a jump discontinuity function, the limit does not exist, but there is a value because there is a point on the graph that does exist.
3. How do we evaluate limits numerically, graphically, and algebraically?
Numerically: We can evaluate a limit numerically using a table. we plot the values of the numbers for the limits, as x approaches a number.
Graphically: We can simply plug in any function on the calculator ans LOOK where the limit exist or not, looking for and discontinuities.
http://www.calculus-help.com/tutorials
http://www.sagemath.org/calctut/onesided.html
http://www.cliffsnotes.com/math/calculus/calculus/limits/evaluating-limits
http://www.showme.com/search/?q=1.3%20evaluating%20limits%20analytically
