Unit U Big Questions

1. What is continuity? What is discontinuity?
Continuity is the unbroken and consistent existence of something over a period of time. This means that something continues forever. An example of this would be a linear function.  Discontinuity is a point at which a graph or a function is discontinuous. This means that something happens in the graph that causes it to become discontinuous, or broken. An example of a discontinuity is a point discontinuity which is a hole, jump discontinuity which is when the left and right side are different, unbounded behavior which is an asymptote, or oscillating behavior which is when the graph is wiggly.

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. A limit exists when you reach the same height from both the left and right side of the graph. Both the left and the right side must be the same in order for the limit to exist. A limit does not exist when there are discontinuities in the graph such as asymptotes and jump discontinuities. The limit still exists when there is a point discontinuity (hole) because even though there is a hole at that point, the graph still reached its limit or its intended height. The difference between a limit and a value is that a limit is the intended height of a function and the value is the actual height of a function.

3.How do we evaluate limits numerically, graphically, and algebraically?
We evaluate limits numerically by using a table. When we do this, we list the values from the left and the values from the right and we determine the limit based on the number that the values from the left and the right approach. We evaluate limits graphically by using a graphing calculator or by looking at a picture of the graph. When we use our graphing calculator, we simply need to graph the function and trace to an x-value to see what the limit is. When we are given a picture of the graph, we can just look at the x-values and see what the limit is. Lastly, we can evaluate limits algebraically by using the direct substitution method. The direct substitution method is when you take the number the limit is approaching and plug it in anytime you see "x'.

Works Cited:
http://mathworld.wolfram.com/Discontinuity.html