Karl Jones at 16:52, 6 September 2016

2016-09-06T16:52:42Z

Karl Jones: Created page with "In mathematics, the '''limit of a function''' is a fundamental concept in calculus and mathematical analysis concerning the behavior of that Function (mathematic..."

2016-09-06T16:51:45Z

Created page with "In mathematics, the '''limit of a function''' is a fundamental concept in calculus and mathematical analysis concerning the behavior of that Function (mathematic..."

New page

In [[mathematics]], the '''limit of a function''' is a fundamental concept in [[calculus]] and [[mathematical analysis]] concerning the behavior of that [[Function (mathematics)|function]] near a particular [[Dependent and independent variables|input]].

== Description ==

Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f(x) to every input x. We say the function has a limit L at an input p: this means f(x) gets closer and closer to L as x moves closer and closer to p.

More specifically, when f is applied to any input sufficiently close to p, the output value is forced arbitrarily close to L.

On the other hand, if some inputs very close to p are taken to outputs that stay a fixed distance apart, we say the limit does not exist.

The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the limit: roughly, a function is continuous if all of its limits agree with the values of the function. It also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.

== See also ==

* [[Big O notation]]
* [[Dependent and independent variables]]
* [[Function (mathematics)]]
* [[l'Hôpital's rule]]
* [[Limit of a sequence]]
* [[List of limits]]
* [[Limit superior and limit inferior]]
* [[Net (topology)]]
* [[Non-standard calculus]]
* [[One-sided limit]]
* [[Squeeze theorem]]
* [[Special trig limits]]

== External links ==

* [https://en.wikipedia.org/wiki/Limit_of_a_function Limit of a function] @ Wikipedia

[[Category:Mathematics]]]

@@ Line 9: / Line 9: @@
 On the other hand, if some inputs very close to p are taken to outputs that stay a fixed distance apart, we say the limit does not exist.
-The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the limit: roughly, a function is continuous if all of its limits agree with the values of the function. It also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.
+The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the limit: roughly, a function is continuous if all of its limits agree with the values of the function.
 == See also ==

Limit of a function - Revision history

Karl Jones at 16:52, 6 September 2016

Karl Jones: Created page with "In mathematics, the '''limit of a function''' is a fundamental concept in calculus and mathematical analysis concerning the behavior of that Function (mathematic..."