与--不是等价无穷小量) =lim 例5.求极限im a+b+c +b2+ a+6+c-3 解:lin lim 1 rIna-1terInb lim/1, a+hnb+xInc 3 =lim 1+xIn( abc)3rIn(abd =enac=(abc) 上述例题告诉我们,在计算极限时,正确运用等价无穷小量作替换,使计算 大大的简便。 Discussion on some concepts of infinitesimal quantity Department of Financial Mathematics and Control Science, School of Mathematical Science, Fudan University Zhu huimin Abstract: The article is aimed at clarifying some vague concepts of infinitesimal quantity and common errors by means of related theoretical analysis and its extension, which is helpful for students to study the solution of limit by replacement of equivalent infinitesimal quantity Key words: infinitesimal quantity, equivalent infinitesimal quantity, oppositely equivalent infinitesimal quantity, limit 参考文献 [1]陈纪修等.数学分析.高等教育出版社2004 [2]华东师范大学数学系.数学分析.北京高等教育出版社1986 3]同济大学数学教研室.高等数学.北京高等教育出版社1989 [4]龚冬保.数学考研教程.西安交通大学出版社20052 3 2 3 2 1 1 1 1 1 1 1 lim x x x x                        （ 2 3 1 x  与 2 3 1 x  不是等价无穷小量） 2 2 2 1 3 1 3 1 lim x x x x           3 2  例 5．求极限 x x x x x a b c 1 0 3 lim            解： x x x x x a b c 1 0 3 lim            x x x x x a b c 1 0 3 3 lim 1               x x a x b x c x e e e 1 l n l n l n 0 3 1 1 1 lim 1                 x x x a x b x c 1 0 3 ln ln ln lim 1            3 1 3 1 ln( ) ln( ) 1 3 1 0 lim 1 ln( ) abc x abc x x abc                    3 1 ln(abc)  e 3 1  (abc) 上述例题告诉我们，在计算极限时，正确运用等价无穷小量作替换，使计算 大大的简便。 Discussion on some concepts of infinitesimal quantity Department of Financial Mathematics and Control Science, School of Mathematical Science, Fudan University Zhu Huimin Abstract: The article is aimed at clarifying some vague concepts of infinitesimal quantity and common errors by means of related theoretical analysis and its extension, which is helpful for students to study the solution of limit by replacement of equivalent infinitesimal quantity. Key words: infinitesimal quantity, equivalent infinitesimal quantity, oppositely equivalent infinitesimal quantity, limit 参考文献 [1].陈纪修等. 数学分析. 高等教育出版社.2004. [2].华东师范大学数学系. 数学分析. 北京高等教育出版社.1986. [3].同济大学数学教研室. 高等数学. 北京高等教育出版社.1989. [4].龚冬保. 数学考研教程. 西安交通大学出版社.2005