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Limits

A way to talk about what a function approaches as inputs get close to a point.

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Field

Mathematics

Topic

Calculus

Estimated Time

22 min

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Definition

The limit of a function near a point is the value the function gets closer and closer to as the input moves toward that point. The function does not need to equal that value at the point itself for the limit to exist.

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What you should take away

Explain a limit as an approaching behavior rather than a final jump.
Connect limits to continuity and derivatives.
Use a graph and a real-world analogy to explain the same idea.

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Sources & evidence

These selected references support the explanation. They are not a live literature search or an exhaustive review.

Reference checked · 2026-10-06 · Educational sample

Educational sample: references and basic claims checked against the linked sources. This is not a claim of human expert editorial approval.

Textbook
Calculus Volume 1 · 2.2 The Limit of a Function
Gilbert Strang, Edwin Herman · OpenStax
Supports: Limits describe nearby function behavior independently of the value at the point.
Checked 2026-10-06

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