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limit

/lim"it/, n.
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. Math.
a. 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.
b. 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.
c. 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.
v.t.
7. to restrict by or as if by establishing limits (usually fol. 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.
[1325-75; ME lymyt < L limit- (s. of limes) boundary, path between fields]
Syn. 2. confine, frontier, border. 8. restrain, bound.

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I
Mathematical concept based on the idea of closeness, used mainly in studying the behaviour of functions close to values at which they are undefined.

For example, the function 1/x is not defined at x = 0. For positive values of x, as x is chosen closer and closer to 0, the value of 1/x begins to grow rapidly, approaching infinity as a limit. This interplay of action and reaction as the independent variable moves closer to a given value is the essence of the idea of a limit. Limits provide the means of defining the derivative and integral of a function.
II
(as used in expressions)
limited obligation bond

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mathematical concept based on the idea of closeness, used primarily to assign values to certain functions (function) at points where no values are defined, in such a way as to be consistent with nearby values. For example, the function (x2 −  1)/(x −  1) is not defined when x is 1, because division by zero is not a valid mathematical operation. For any other value of x, the numerator can be factored and divided by the (x −  1), giving x + 1. Thus, this quotient is equal to 2 for all values of x except 1, which has no value. However, 2 can be assigned to the function (x2 −  1)/(x −  1) not as its value when x equals 1 but as its limit when x approaches 1. See analysis: Continuity of functions (analysis).

One way of defining the limit of a function f(x) at a point x0, written as

is by the following: if there is a continuous (continuity) (unbroken) function g(x) such that g(x) = f(x) in some interval around x0, except possibly at x0 itself, then

The following more-basic definition of limit, independent of the concept of continuity, can also be given:

if, for any desired degree of closeness ε, one can find an interval around x0 so that all values of f(x) calculated here differ from L by an amount less than ε (i.e., if |x −  x0| < δ, then |f (x) −  L| < ε). This last definition can be used to determine whether or not a given number is in fact a limit. The calculation of limits, especially of quotients, usually involves manipulations of the function so that it can be written in a form in which the limit is more obvious, as in the above example of (x2 −  1)/(x −  1).

Limits are the method by which the derivative, or rate of change, of a function is calculated, and they are used throughout analysis as a way of making approximations into exact quantities, as when the area inside a curved region is defined to be the limit of approximations by rectangles.

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Universalium. 2010.

Synonyms:

Look at other dictionaries:

• Limit — Limit …   Deutsch Wörterbuch

• limit# — limit n Limit, bound, confine, end, term are comparable when they mean an actual or imaginary line beyond which a thing does not or cannot extend. Limit is the most inclusive of these terms because it carries no necessary implication of number,… …   New Dictionary of Synonyms

• limit*/*/*/ — [ˈlɪmɪt] noun [C] I 1) the greatest amount or level of something that is possible or allowed The speed limit here is forty miles an hour.[/ex] There is a limit to what we can do in two weeks.[/ex] 2) the outer edge of an area No bombs landed… …   Dictionary for writing and speaking English

• Limit — Lim it (l[i^]m [i^]t), v. t. [imp. & p. p. {Limited}; p. pr. & vb. n. {Limiting}.] [F. limiter, L. limitare, fr. limes, limitis, limit; prob. akin to limen threshold, E. eliminate; cf. L. limus sidelong.] To apply a limit to, or set a limit for;… …   The Collaborative International Dictionary of English

• Limit — Lim it (l[i^]m [i^]t), n. [From L. limes, limitis: cf. F. limite; or from E. limit, v. See {Limit}, v. t.] 1. That which terminates, circumscribes, restrains, or confines; the bound, border, or edge; the utmost extent; as, the limit of a walk, of …   The Collaborative International Dictionary of English

• Limit — steht für eine Mengengrenze oder Betragsgrenze, siehe Grenzwert einen Begriff aus dem Pokerspiel, siehe Liste von Pokerbegriffen einen Orderzusatz einer Wertpapierorder in Form einer Kursober oder untergrenze, siehe Limitorder Limit… …   Deutsch Wikipedia

• limit — [lim′it] n. [OFr limite < L limes (gen. limitis), border, frontier] 1. the point, line, or edge where something ends or must end; boundary or border beyond which something ceases to be or to be possible 2. [pl.] bounds; boundary lines 3. the… …   English World dictionary

• limit — I noun ambit, border, bound, boundary, boundary line, circumscriptio, circumscription, extreme boundary final point, finis, fringe, frontier, furthest point, line of demarcation, outer edge, outer line, outer point, perimeter, rim, terminus,… …   Law dictionary

• Limit — Sn Grenze, Preisrahmen erw. fach. (20. Jh.) Entlehnung. Entlehnt aus ne. limit, dieses aus frz. limite f., aus l. līmes (limitis) m. Grenzlinie, Querweg, Rain . Schon früher aus dem Französischen entlehnt ist die verbale Ableitung limitieren.… …   Etymologisches Wörterbuch der deutschen sprache

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• limit — {{/stl 13}}{{stl 8}}rz. mnż I, D. u, Mc. limiticie {{/stl 8}}{{stl 7}} nieprzekraczalna granica określająca ilość czegoś, np. kosztów, czasu, etatów, studentów : {{/stl 7}}{{stl 10}}Limit czasu. Przekroczyć limit pieniężny. Limit przyjęć na… …   Langenscheidt Polski wyjaśnień