## Monday, May 12, 2014

### BQ#6 Unit U Concept 4:Continuous functions and types of discontinuities and limits numerically and graphically

1. A continuous function is predictable. It has no breaks, no holes, and no jumps. A continuous function can be drawn with a single, unbroken pencil stroke. Also, a continuous function is when the value is equal to the limit.
 http://www.intmath.com/differentiation/1-limits-and-differentiation.php
A discontinuous function is the opposite of a continuous function. It may contain breaks, holes, jumps. Also, the value does not equal the limit. There are two families of discontinuities: removable and non-removable discontinuities. In the removable family there is only point discontinuity. In removable discontinuities the limit DOES EXIST. In the other family, non-removable discontinuities the limit DOES NOT EXIST. The non-removable discontinuities family consists of jump discontinuity, oscillating behavior, and infinite discontinuity. In the jump discontinuities one hole has to be close and one open or both open or it will not be a function if both of the holes are closed. The reason the limit does not exist in jump discontinuities is because it approaches different values from the left and right. In oscillating behavior the graph is very wiggly and the limit does not exist because it doesn't approach any single value. Infinite discontinuities are caused by vertical asymptotes and the limit does not exist because of unbounded behavior (can't touch asymptotes) and because it approaches different values from the left and right.
 http://www.wyzant.com/resources/lessons/math/calculus/limits/continuity
 http://www.tutorvista.com/content/math/discontinuity/
 http://www.wyzant.com/resources/lessons/math/calculus/limits/continuity