相加或相减的无穷小量进行等价替换的充分条件  

Sufficient Conditions for Equivalent Substitution of Sums or Subtractions of Infinitesimal Variables

作　　者：吴昌健 WU Chang-jian(Department of Basic Courses,Zhujiang College of South China Agricultural University,Guangzhou 510900,China)

机构地区：[1]华南农业大学珠江学院基础部

出　　处：《工业技术创新》2019年第3期91-94,共4页Industrial Technology Innovation

基　　金：广东省特色创新类项目(2016GXJK222);广东省特色创新类项目(2017GXJK240);2017年广东省本科高校教学质量与教学改革工程项目(340)

摘　　要：等价无穷小量替换求极限是算法处理中的关键。以往研究只给出了对所求极限式中相乘或相除的无穷小量因式进行等价替换的充分条件,而忽视了极限式中存在相加或相减的无穷小量因式的情形。对此进行深入研究,表明:1)若两个无穷小量商的极限存在且不为-1或者为无穷大,则两者相加或相减时可以进行等价替换;2)若两个无穷小量保持同号,则两者相加或相减时可以进行等价替换;3)若存在子列使得两个无穷小量之和或之差为零,则两者相加或相减时不一定可以进行等价替换。Finding the limit by the equivalent infinitesimal variable substitution is the key to the algorithm processing.Previous studies only gave sufficient conditions for the equivalent substitution of multiplications or divisions of infinitesimal variables in the limit formulas,but neglected the cases of sums or subtractions of infinitesimal variables in the limit formulas.A thorough study is carried out,showing that:1)If the limits of two infinitesimal variables exist and are neither-1,or they are both infinities,equivalent substitution can be carried out when they are added or subtracted;2)If the two infinitesimal variables remain the same sign,equivalent substitution can be carried out when they are added or subtracted;3)If there are subsequences that make the sum or subtraction of two infinitesimal variables be zero,they do not necessarily allow for equivalent substitution when they are added or subtracted.

关 键 词：等价无穷小量 等价替换 极限 充分条件 

分 类 号：O22[理学—运筹学与控制论]