等价无穷小的极限定理  

The limit theorem of equivalent infinitesimal

作　　者：姜根明[1] 魏孝章[2] 

机构地区：[1]长安大学基础部,陕西西安710054 [2]陕西教育学院数理系,陕西西安710061

出　　处：《西安文理学院学报（社会科学版）》2003年第4期59-61,共3页Journal of Xi’an University(Social Sciences Edition)

摘　　要：求极限时,正确使用等价无穷小代换,可以简化计算.在求两个无穷小之比的极限时,若分子及分母满足一定的条件,可将分子、分母用等价无穷小来代换.并进一步给出求极限时,若因式中某个因子是两个无穷小之和、差时,可用等价无穷小来代换的条件;给出了求幂指函数的极限时,其底和指数可分别用它相应的等价无穷小代换的条件及相关的一些结论.In the calculation of limits, suitable use of equivalent substitution can significantly simplify and shorten its manipulation. In the calculation of the limit of a ratio between two infinitesimals, if the numerator and denominator satisfy certain conditions, they can be substituted by their equivalent infinitesimals. The conditions are given for the case where some factor is the sum or difference of two infinitesimals. Furthermore, the conditions are given for the case where the limit of an exponential function is to be found, i.e., its base and exponent can be substituted by their equivalent infinitesimals. Some relevant conclusions about the equivalent substitution of infinitesimals are drawn.

关 键 词：极限 等价 无穷小 代换 

分 类 号：O122.5[理学—数学]