等价无穷小代换在求解含和差运算因子的极限中的应用  

Application of Equivalent Substitution for Infinitesimal Quantity in Calculation of Additions and Subtractions

作　　者：赵玉杰[1] 李李[1] 

机构地区：[1]安庆师范学院物理与电气工程学院,安徽安庆246133

出　　处：《安庆师范学院学报（自然科学版）》2013年第4期104-106,共3页Journal of Anqing Teachers College(Natural Science Edition)

基　　金：安徽高校省级自然科学研究项目(KJ2012B086;KJ2010A227);中国博士后科学基金(2013M531530)资助

摘　　要：利用等价无穷小代换求极限可以简化计算过程,并能迅速得到正确结果。本文探讨了等价无穷小代换在求解极限式中含有和差运算式因子情况下的具体应用:在一定条件下,和差运算中的各部分无穷小可按泰勒公式展开,适当选取等价无穷小的阶数,则各部分无穷小也可直接分别等价代换。最后总结了和差运算中一些无穷小代换定理和推论,并加以证明和具体应用。求解过程和结果表明,这些定理和推论非常有效。Calculation of limit can be simplified by using the equivalent substitution for infinitesimal quantity .The applica-tions of those substitutions in the calculations of addition and subtractions are discussed in detail , which is seldom touched in some reference book.Some theorems of substitution for equivalent infinite small quantity in the sum and difference are generalized , which are also applied in some examples to calculate limits in this paper .Computed process and results indicate that these theo-rems are substantially efficient.

关 键 词：极限 和差运算 等价无穷小代换 TAYLOR公式 

分 类 号：O13[理学—数学]