Limit of a sequence
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ). If such a limit exists, the sequence is called convergent.
In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their
In mathematics, a subsequential limit of a sequence is the limit of some subsequence. Every subsequential limit is a cluster point, but not conversely. In first-countable spaces, the two concepts coin
In calculus, a one-sided limit refers to either one of the two limits of a function of a real variable as approaches a specified point either from the left or from the right. The limit as decreases in
Limit inferior and limit superior
In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion fo
In mathematics, the approximate limit is a generalization of the ordinary limit for real-valued functions of several real variables. A function f on has an approximate limit y at a point x if there ex
In calculus, the squeeze theorem (also known as the sandwich theorem, among other names) is a theorem regarding the limit of a function that is trapped between two other functions. The squeeze theorem
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
In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. It consists of a sequence of "staircase" polygonal cha
In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form ,, or other similar forms. An iterated limit is only defined for an expression whose value de
Interchange of limiting operations
In mathematics, the study of interchange of limiting operations is one of the major concerns of mathematical analysis, in that two given limiting operations, say L and M, cannot be assumed to give the
In calculus, L'Hôpital's rule or L'Hospital's rule (French: [lopital], English: /ˌloʊpiːˈtɑːl/, loh-pee-TAHL), also known as Bernoulli's rule, is a theorem which provides a technique to evaluate limit
In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point. As is
In mathematical analysis, Tannery's theorem gives sufficient conditions for the interchanging of the limit and infinite summation operations. It is named after Jules Tannery.
List of limits
This is a list of limits for common functions such as elementary functions. In this article, the terms a, b and c are constants with respect to SM
In linear algebra, a convergent matrix is a matrix that converges to the zero matrix under matrix exponentiation.
Limit of a function
In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Formal definitions, first devised in the ear