limxx0

Limxx0 is an informal, wiki-style notation used in some educational and collaborative resources to denote the limit of a function as its argument approaches zero. It is not part of standard mathematical notation, but serves as a compact shorthand in contexts where the limiting process is clear from the discussion. When limxx0 f(x) appears, it is generally interpreted as the ordinary limit lim_{x→0} f(x).

Because limxx0 is informal, its precise meaning should be stated in each context. In many tutorials, limxx0 is used to illustrate common limits without repeating the full lim notation, for example to show familiar results such as sin x / x approaching 1 or (1+x)^{1/x} approaching e as x→0. In such cases, the expression is understood to be evaluated by the standard limit process.

In multi-variable settings, limxx0 can be encountered to emphasize a limit as a single variable x tends to zero while other variables are fixed or follow a specified approach. However, this usage is ambiguous unless the limiting path or conditions are specified. Standard notation in those cases would be lim_{x→0} f(x, y) with y fixed, or lim_{(x,y)→(0,0)} f(x,y) if both variables approach zero.

Reception and use: limxx0 is primarily a pedagogical device in community-driven resources and informal notes. It can aid quick demonstrations, but readers should verify the exact definition presented in any given text to avoid misinterpretation. See also: Limit (mathematics); One-sided limit; Multi-variable limit.