limit

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





lim

x

c


f
(
x
)
=
L
,


{\displaystyle \lim _{x\to c}f(x)=L,}
(although a few authors may use "Lt" instead of "lim")
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




f
(
x
)

L

as

x

c
,


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



f


{\displaystyle f}
of



x


{\displaystyle x}
tends to



L


{\displaystyle L}
as



x


{\displaystyle x}
tends to



c


{\displaystyle c}
".

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