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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 Binomial approximation ： ウィキペディア英語版 Binomial approximation The binomial approximation is useful for approximately calculating powers of sums of a small number and 1. It states that if $x$ is a real number close to 0 and $\backslash alpha$ is a real number, then : $(1\; +\; x)^\backslash alpha\; \backslash approx\; 1\; +\; \backslash alpha\; x.$ This approximation can be obtained by using the binomial theorem and ignoring the terms beyond the first two. By Bernoulli's inequality, the left-hand side of this relation is greater than or equal to the right-hand side whenever $x>-1$ and $\backslash alpha\; \backslash geq\; 1$. == Derivation using linear approximation== The function :$f(x)\; =\; (1\; +\; x)^$ is a smooth function for ''x'' near 0. Thus, standard linear approximation tools from calculus apply: one has :$f\text{'}(x)\; =\; \backslash alpha\; (1\; +\; x)^$ and so :$f\text{'}(0)\; =\; \backslash alpha.$ Thus :$f(x)\; \backslash approx\; f(0)\; +\; f\text{'}(0)(x\; -\; 0)\; =\; 1\; +\; \backslash alpha\; x.$ 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「Binomial approximation」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.