Discontinuity Definition
A function is discontinuous at a point x = a if the function is not continuous at a. The function “f” is said to be discontinuous at x = a in any of the following cases:
- f(a) is not defined
- limx⇢a+ f(x) and limx⇢a– f(x) exists, but are not equal.
- limx⇢a+ f(x) and limx⇢a– f(x) exists and are equal but not equal to f(a).
Continuity and Discontinuity in Calculus
Continuity and Discontinuity: Continuity and discontinuity are fundamental concepts in calculus and mathematical analysis, describing the behavior of functions. A function is continuous at a point if you can draw the graph of the function at that point without lifting your pen from the paper. Continuity implies that small changes in the input of the function result in small changes in the output, making the function predictable and smooth.
A function is discontinuous at a point x = c if it fails to be continuous at that point. In this article, we will discuss about the Continuity and Discontinuity of functions with their conditions and types.
Table of Content
- Continuity Definition
- Conditions for Continuity
- Discontinuity Definition
- Types of Discontinuity