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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 Increment theorem ： ウィキペディア英語版 Increment theorem In non-standard analysis, a field of mathematics, the increment theorem states the following: Suppose a function ''y'' = ''f''(''x'') is differentiable at ''x'' and that Δ''x'' is infinitesimal. Then :$\backslash Delta\; y\; =\; f\text{'}(x)\backslash ,\backslash Delta\; x\; +\; \backslash varepsilon\backslash ,\; \backslash Delta\; x\backslash ,$ for some infinitesimal ε, where : $\backslash Delta\; y=f(x+\backslash Delta\; x)-f(x).\backslash ,$ If $\backslash scriptstyle\backslash Delta\; x\backslash not=0$ then we may write : $\backslash frac\; =\; f\text{'}(x)+\backslash varepsilon,$ which implies that $\backslash scriptstyle\backslash frac\backslash approx\; f\text{'}(x)$, or in other words that $\backslash scriptstyle\; \backslash frac$ is infinitely close to $\backslash scriptstyle\; f\text{'}(x)\backslash ,$, or $\backslash scriptstyle\; f\text{'}(x)\backslash ,$ is the standard part of $\backslash scriptstyle\; \backslash frac$. == See also == *Non-standard calculus *''Elementary Calculus: An Infinitesimal Approach'' *Abraham Robinson 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「Increment theorem」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.