Limit



noun
1.
the final, utmost, or furthest boundary or point as to extent, amount, continuance, procedure, etc.:
the limit of his experience; the limit of vision.
2.
a boundary or bound, as of a country, area, or district.
3.
Mathematics.

a number such that the value of a given function remains arbitrarily close to this number when the independent variable is sufficiently close to a specified point or is sufficiently large. The limit of 1/ x is zero as x approaches infinity; the limit of (x − 1) 2 is zero as x approaches 1.
a number such that the absolute value of the difference between terms of a given sequence and the number approaches zero as the index of the terms increases to infinity.
one of two numbers affixed to the integration symbol for a definite integral, indicating the interval or region over which the integration is taking place and substituted in a primitive, if one exists, to evaluate the integral.

4.
limits, the premises or region enclosed within boundaries:
We found them on school limits after hours.
5.
Games. the maximum sum by which a bet may be raised at any one time.
6.
the limit, Informal. something or someone that exasperates, delights, etc., to an extreme degree:
You have made errors before, but this is the limit.
verb (used with object)
7.
to restrict by or as if by establishing limits (usually followed by to):
Please limit answers to 25 words.
8.
to confine or keep within limits:
to limit expenditures.
9.
Law. to fix or assign definitely or specifically.
noun
1.
(sometimes pl) the ultimate extent, degree, or amount of something: the limit of endurance
2.
(often pl) the boundary or edge of a specific area: the city limits
3.
(often pl) the area of premises within specific boundaries
4.
the largest quantity or amount allowed
5.
(maths)

a value to which a function f(x) approaches as closely as desired as the independent variable approaches a specified value (x = a) or approaches infinity
a value to which a sequence an approaches arbitrarily close as n approaches infinity
the limit of a sequence of partial sums of a convergent infinite series: the limit of 1 + ½ + ¼ + ⅛ + … is 2

6.
(maths) one of the two specified values between which a definite integral is evaluated
7.
(informal) the limit, a person or thing that is intolerably exasperating
8.
off limits

out of bounds
forbidden to do or use: smoking was off limits everywhere

9.
within limits, to a certain or limited extent: I approve of it within limits
verb (transitive) -its, -iting, -ited
10.
to restrict or confine, as to area, extent, time, etc
11.
(law) to agree, fix, or assign specifically

limit lim·it (lĭm’ĭt)
n.

The point, edge, or line beyond which something cannot or may not proceed.

A confining or restricting object, agent, or influence.

The greatest or least amount, number, or extent allowed or possible.

v. lim·it·ed, lim·it·ing, lim·its

To confine or restrict within a boundary or bounds.

To fix definitely; to specify.

lim’it·a·ble adj.
limit
(lĭm’ĭt)
A number or point for which, from a given set of numbers or points, one can choose an arbitrarily close number or point. For example, for the set of all real numbers greater than zero and less than one, the numbers one and zero are limit points, since one can pick a number from the set arbitrarily close to one or zero (even though one and zero are not themselves in the set). Limits form the basis for calculus, where a number L is defined to be the limit approached by a function f(x) as x approaches a if, for every positive number ε, there exists a number δ such that |f(x)-L| < ε if 0 < |x-a| < δ. see:go whole hog (the limit) sky's the limit the limit

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