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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 L'Hôpital's rule ： ウィキペディア英語版 L'Hôpital's rule In mathematics, and more specifically in calculus, L'Hôpital's rule () uses derivatives to help evaluate limits involving indeterminate forms. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be evaluated by substitution, allowing easier evaluation of the limit. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. L'Hôpital's rule states that for functions and which are differentiable on an open interval except possibly at a point contained in , if :$\backslash lim\_f(x)=\backslash lim\_g(x)=0\; \backslash text\; \backslash pm\backslash infty$, :$g\text{'}(x)\backslash neq\; 0$ for all in with , and :$\backslash lim\_\backslash frac$ exists, then :$\backslash lim\_\backslash frac\; =\; \backslash lim\_\backslash frac$. The differentiation of the numerator and denominator often simplifies the quotient or converts it to a limit that can be evaluated directly. == History== Guillaume de l'Hôpital (also written l'Hospital〔In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. However, French spellings have been altered: the silent 's' has been removed and replaced with the circumflex over the preceding vowel. The former spelling is still used in English where there is no circumflex.〕) published this rule in his 1696 book ''Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes'' (literal translation: ''Analysis of the Infinitely Small for the Understanding of Curved Lines''), the first textbook on differential calculus.〔L’Hospital, ''Analyse des infiniment petits''... , (pages 145–146 ): "Proposition I. Problême. Soit une ligne courbe AMD (AP = x, PM = y, AB = a (Figure 130 ) ) telle que la valeur de l’appliquée y soit exprimée par une fraction, dont le numérateur & le dénominateur deviennent chacun zero lorsque x = a, c’est à dire lorsque le point P tombe sur le point donné B. On demande quelle doit être alors la valeur de l’appliquée BD. ()...si l’on prend la difference du numérateur, & qu’on la divise par la difference du denominateur, apres avoir fait x = a = Ab ou AB, l’on aura la valeur cherchée de l’appliquée bd ou BD." ''Translation'' : "Let there be a curve AMD (where AP = X, PM = y, AB = a) such that the value of the ordinate y is expressed by a fraction whose numerator and denominator each become zero when x = a; that is, when the point P falls on the given point B. One asks what shall then be the value of the ordinate BD. ()... if one takes the differential of the numerator and if one divides it by the differential of the denominator, after having set x = a = Ab or AB, one will have the value (was ) sought of the ordinate bd or BD."〕 However, it is believed that the rule was discovered by the Swiss mathematician Johann Bernoulli. 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「L'Hôpital's rule」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.