## 6.3. Discontinuous Functions

### Definition 6.3.3: Classification of Discontinuities

Suppose

*f*is a function with domain*and***D***c*is a point of discontinuity of**D***f*.- if
*f(x)*exists, then*c*is called**removable discontinuity**. - if
*f(x)*does not exist, but both*f(x)*and*f(x)*exit, then*f*is called a**discontinuity of the first kind**, or**jump**discontinuity - if either
*f(x)*or*f(x)*does not exist, then*c*is called a**discontinuity of the second kind**, or essential discontinuity.