Hamilton A. answered • 02/03/16

Tutor

5.0
(38)
BA & MA in Math - 1000+ Hours Tutoring Calculus

A function f has a

**removable discontinuity**at x = x0 (a point in its domain, i.e. f(x0) exists) if two things are true:1. The limit as x -> x0 of f(x) = L exists and is finite

2. f(x0) isn't equal to L

A function f has an

**infinite discontinuity**at x = x0 (a point in its domain, i.e. f(x0) exists) if either (or both):1. The limit as x -> x0 from the left of f(x) doesn't exist

2. The limit as x -> x0 from the right of f(x) doesn't exist

Do you think it's possible for a function to exhibit both of these properties at the same point, or are they mutually exclusive?