无穷大的和与差等价代换定理及应用  

Equivalent substitution theorem of sum and difference of infinity and its application

作　　者：田学刚 王少英 TIAN Xuegang;WANG Shaoying(School of Science,Binzhou University,Binzhou 256603,China)

机构地区：[1]滨州学院理学院,山东滨州256603

出　　处：《高师理科学刊》2022年第11期26-30,36,共6页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(61703050)——网络化随机系统的事件触发滤波与故障检测;滨州学院重点教改项目(BYJYZD201808)——新工科下基于应用型人才培养的高等数学模块化分层教学研究与实践;滨州学院教改项目(BYJYYB201733)——基于专业服务的应用型本科院校高等数学课程改革研究与实践。

摘　　要：研究自变量趋于有限值情形下无穷大的和与差等价代换问题.利用泰勒公式刻画出任意2个无穷大的和与差,当2个无穷大等价时,给出它们差的等价代换定理;当2个无穷大负等价时,给出它们和的等价代换定理.结合具体实例探讨等价代换定理在解决含无穷大和差的复杂未定式极限中的应用.The equivalent substitution of the sum and difference of infinity was studied when the independent variable tends to finite value.The sum and difference of any two infinities are firstly characterized by Taylor formula,and then the equivalent substitution theorem of their difference is given when two infinities are equivalent,and meanwhile the equivalent substitution theorem of their sum is provided when two infinities are negatively equivalent.Finally,some specific examples are given to show the application of equivalent substitution theorem in the calculation of complex indefinite form limit with infinite sum and difference.

关 键 词：无穷大 等价 泰勒公式 

分 类 号：O172[理学—数学]