Define jump discontinuity.
Understand the Problem
The question is asking for a definition of jump discontinuity, which refers to a specific type of discontinuity in a function where the left-hand limit and the right-hand limit at a certain point exist but are not equal.
Answer
A jump discontinuity occurs when the left-hand and right-hand limits of a function at a specific point are not equal.
A jump discontinuity occurs when the left-hand and right-hand limits of a function at a specific point are not equal.
Answer for screen readers
A jump discontinuity occurs when the left-hand and right-hand limits of a function at a specific point are not equal.
More Information
Jump discontinuities are often encountered in piecewise functions where the different pieces do not align smoothly.
Tips
Common mistakes include assuming the function values themselves have to be different (it's the limits that must differ), or neglecting to check both one-sided limits.
Sources
- Jump Discontinuity -- from Wolfram MathWorld - mathworld.wolfram.com
- Jump Discontinuity Definition - DeepAI - deepai.org
- Jump Discontinuity: Definition & Example - Vaia - vaia.com
