Limit: Meaning, Notation, and Example
The value a function approaches as its input approaches a target.
Definition and meaning
A limit describes nearby behavior and may exist even when the function is undefined or has another value at the target.
The term limit names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.
Notation
Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.
Worked example
Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the limit statement permits.
Common confusion
Do not treat limit as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.