Section: STEM · MathematicsDifficulty: Medium
Limits
USUK
The value a function or sequence approaches as the input approaches a given value.
Definition
A limit describes the value that a function or sequence approaches as the input (or index) approaches some value, even if the function is undefined at that exact point. Limits are the rigorous foundation of calculus, used to define continuity, derivatives, and integrals. They are expressed using the epsilon-delta formal definition or more intuitively as the behavior of a function near a point.
Example
“The instantaneous speed of a car at a given moment is found using a limit: as the time interval shrinks toward zero, the average speed over that interval approaches the instantaneous speed, which is the derivative of position.”
Synonyms
- limiting value
- mathematical limit
- asymptotic value
Antonyms / Opposites
- divergence
- unbounded
Images
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Related Terms
- Differentiation
- Integration
- Continuity
- Calculus