探求和差运算中无穷小的等价代换方法  

Exploring the method of equivalent substitution for infinite small in calculation of sum and difference

作　　者：李胜正[1] 王茂强 房毅宪[1] 

机构地区：[1]山东轻工业学院数理学院,山东济南250353 [2]山东省烟台市二中,山东烟台264000

出　　处：《山东轻工业学院学报（自然科学版）》2008年第2期71-72,102,共3页Journal of Shandong Polytechnic University

摘　　要：等价无穷小代换求极限的一般原则是无穷小因子进行等价代换,对于和差运算中的无穷小一般不能直接代换。本文讨论了在一定条件下,和差运算中的无穷小可直接进行等价代换,否则和差运算中的无穷小可按泰勒公式适当提高等价无穷小的阶数进行代换,从而使某些极限运算大大简化。The common principle of finding limit with equivalent infinite small substitution is equivalent substitution with infinite small factors, infinite small can＇t commonly be substituted in sum/difference operation. In this paper, in a certain condition, infinite small can directly be substituted in sum/difference operation , otherwise infinite small in sum/difference operation can be substituted by increasing orders of equivalent infinite small according to Taylor formula. Consequently, certain limit operations are greatly predigested.

关 键 词：和差运算 等价无穷小 等价无穷小代换 泰勒公式 

分 类 号：O171[理学—数学]