Limits

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Limits

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In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.[1] Limits are essential to calculus and mathematical analysis, and are used to define continuityderivatives, and integrals.

The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.

In formulas, a limit of a function is usually written as

{\displaystyle \lim _{x\to c}f(x)=L,}

(although a few authors may use "Lt" instead of "lim"[2]) and is read as "the limit of f of x as x approaches c equals L". The fact that a function f approaches the limit L as x approaches c is sometimes denoted by a right arrow (→ or {\displaystyle \rightarrow }), as in

{\displaystyle f(x)\to L{\text{ as }}x\to c,}

which reads "{\displaystyle f} of {\displaystyle x} tends to {\displaystyle L} as {\displaystyle x} tends to {\displaystyle c}".

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