Eroxl's Notes
Discontinuity

A discontinuity is any location where a function is not continuous. There are 3 classifications of discontinuities.

Classifications

![[Removable Discontinuity]]

Jump Discontinuity

A jump discontinuity is any discontinuity where both the left sided limit and right sided limit are not infinity or equal but still exist at the discontinuity.

Example

Y axisX axis00-2-2-1-1112233-2-222Expression 1Expression 2Expression 3Expression 4Expression 5"x" Subscript, 1 , Baselinex1x1

In this example the function (graphed above in red) has a jump discontinuity at as both the left sided limit and the right sided limit are not infinity or equal.

Essential Discontinuity

An essential discontinuity is any discontinuity where either the left sided limit or right sided limit is infinity or does not exist at the discontinuity.

Example

Y axisX axis00-2-2-1-1112233551010Expression 1Expression 2Expression 3

In this example the function (graphed above in red) has a essential discontinuity at as the right sided limit goes to infinity.