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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Approximate limit ： ウィキペディア英語版 Approximate limit In mathematics, the approximate limit is a generalization of the ordinary limit for real-valued functions of several real variables. A function ''f'' on $\backslash mathbb^k$ has an approximate limit ''y'' at a point ''x'' if there exists a set ''F'' that has density 1 at the point such that if ''x''''n'' is a sequence in ''F'' that converges towards ''x'' then ''f''(''x''''n'') converges towards ''y''. ==Properties== The approximate limit of a function, if it exists, is unique. If ''f'' has an ordinary limit at ''x'' then it also has an approximate limit with the same value. We denote the approximate limit of ''f'' at ''x''0 by $\backslash lim\_\; \backslash operatorname\; \backslash \; f(x).$ Many of the properties of the ordinary limit are also true for the approximate limit. In particular, if ''a'' is a scalar and ''f'' and ''g'' are functions, the following equations are true if values on the right-hand side are well-defined (that is the approximate limits exist and in the last equation the approximate limit of ''g'' is non-zero.) :$\backslash begin$ \lim_ \operatorname \ a\cdot f(x) & =a \cdot \lim_ \operatorname \ f(x) \\ \lim_ \operatorname \ (f(x)+g(x)) & = \lim_ \operatorname \ f(x) + \lim_ \operatorname \ g(x) \\ \lim_ \operatorname \ (f(x)-g(x)) & = \lim_ \operatorname \ f(x)-\lim_ \operatorname \ g(x) \\ \lim_ \operatorname \ (f(x)\cdot g(x)) & = \lim_ \operatorname \ f(x) \cdot \lim_ \ g(x) \\ \lim_ \operatorname \ (f(x)/g(x)) & = \lim_ \operatorname \ f(x) / \lim_ \operatorname \ g(x) \end 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Approximate limit」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.