Discontinuities

Definition

A continuous function is one you can write without taking the hand off the paper.

Alternate Definition

For the function to be discontinuous at a point, 2 conditions: $li{m}_{x\to a}f(x)\ne f(a)$ OR ${\lim }_{x\to a}f(x)DNE$ OR $L=\pm \infty ORf(x)=\pm \infty$

Types

• Jump Discontinuities
• Essential Discontinuity
• Removable Discontinuity