翻訳と辞書 Words near each other ・ Iter.Viator ・ ITERA ・ Itera ・ Itera ASA ・ Itera-Katusha ・ Iterable cardinal ・ Iteradensovirus ・ Iteraplan ・ Iterated binary operation ・ Iterated conditional modes ・ Iterated filtering ・ Iterated forcing ・ Iterated function ・ Iterated function system ・ Iterated integral ・ Iterated limit ・ Iterated local search ・ Iterated logarithm ・ Iterated monodromy group ・ Iteratee ・ ITerating ・ Iteration ・ Iteration (disambiguation) ・ Iteration mark ・ Iterations of I ・ Iterative and incremental development ・ Iterative aspect ・ Iterative closest point ・ Iterative compression ・ Iterative deepening A* Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Iterated limit ： ウィキペディア英語版 Iterated limit In multivariable calculus, an iterated limit is an expression of the form : $\backslash lim\_\; \backslash big(\; \backslash lim\_\; f(x,\; y)\; \backslash big).\; \backslash ,$ One has an expression whose value depends on at least two variables, one takes the limit as one of the two variables approaches some number, getting an expression whose value depends only on the other variable, and then one takes the limit as the other variable approaches some number. This is not defined in the same way as the limit : $\backslash lim\_\; f(x,\; y),\; \backslash ,$ which is not an iterated limit. To say that this latter limit of a function of more than one variable is equal to a particular number ''L'' means that ''ƒ''(''x'', ''y'') can be made as close to ''L'' as desired by making the point (''x'', ''y'') close enough to the point (''p'', ''q''). It does not involve first taking one limit and then another. It is not in all cases true that : $\backslash lim\_\; f(x,\; y)\; =\; \backslash lim\_\; \backslash lim\_\; f(x,\; y)\; =\; \backslash lim\_\; \backslash lim\_\; f(x,\; y).$ See interchange of limiting operations. Among the standard counterexamples are those in which : $$ f(x,y) = \frac and : $f(x,y)\; =\; \backslash frac,$ and (''p'', ''q'') = (0, 0). In the first example, the values of the two iterated limits differ from each other: : $$ \lim_ \left( \lim_ \frac \right) = \lim_ 0 = 0, and : $$ \lim_ \left( \lim_ \frac \right) = \lim_ 1 = 1. In the second example, the two iterated limits are equal to each other despite the fact that the limit as (''x'', ''y'') → (0, 0) does not exist: : $$ \lim_ \left( \lim_ \frac \right) = \lim_ 0 = 0 and : $$ \lim_ \left( \lim_ \frac \right) = \lim_ 0 = 0, but the limit as (''x'', ''y'') → (0, 0) along the line ''y'' = ''x'' is different: : $$ \lim_ \frac = \lim_ \frac = \frac12. It follows that : $\backslash lim\_\; \backslash frac$ does not exist. ==References== 〔 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「Iterated 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.