BQ #6 Unit U

1. What is a continuity?
A continuity is a graph that we can draw without lifting our pencil off the paper. It has  no holes jumps or breaks. The value and limit are the same.

Examples:

B) What is a discontinuity?
 There are two discontinuity families:removable and non removable discontinuities.A removable discontinuity is a point discontinuity which is known as a hole.Then we have a jump discontinuity in which the graph looks like it jumps lower i.n the coordinate plane. An oscillating graph looks wiggly because the graph is going up and down so many times we can see it. Finally we have an infinite graph that that results in unbounded behavior near a vertical asymptote.

Examples :

Jump discontinuity

                      Infinite discontinuity

Oscillating discontinuity

2) What is a limit?
A limit is the intended height of the graph. In other words its the height the graph wants to reach but doesn't actually reach it.

B) When does a limit exist?
A limit exists  when the function intends to reach its certain intended height. A limit usually exists with a point discontinuity.

C) When does a limit not exist?
There are 3 situations that a limit doesn't exist; jump,oscillating and infinite discontinuity.
A limit doesn't exist for a jump discontinuity because it "jumps" on the plane. The term its different from the left and right tells us it doesn't have a limit. Then an oscillating graph doesn't have a limit because it has oscillating behavior meaning we can see how many times the graph goes up and down. Finally, an infinite discontinuity doesn't have a limit because of unbounded behavior. The graph goes in opposite directions for infinity.Thos happens when we have a.vertical asymptote.