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复合函数极限的应用
引用本文:黄秋梅,范周田,张汉林.复合函数极限的应用[J].数学的实践与认识,2011,41(12).
作者姓名:黄秋梅  范周田  张汉林
作者单位:北京工业大学应用数理学院,北京,100124
基金项目:北京市自然科学基金,北京工业大学博士科研启动基金
摘    要:利用复合函数极限的运算法则给出收敛数列与其子列的关系、海涅定理以及数列重排的另一种证明,把三个重要的定理归结为复合函数极限的应用,将大学数学里三个重要但理解起来相对困难的定理纳入统一简单的框架.

关 键 词:复合函数的极限  收敛数列与其子列  海涅定理  数列的重排

The Applications of Limits for Compound Functions
HUANG Qiu-mei,FAN Zhou-tian,ZHANG Han-lin.The Applications of Limits for Compound Functions[J].Mathematics in Practice and Theory,2011,41(12).
Authors:HUANG Qiu-mei  FAN Zhou-tian  ZHANG Han-lin
Abstract:In this paper,we use the rule of the limits for compound functions to provide simple proofs for the relation between convergent number sequence and its subsequence, Heine's theorem,and the rearrangement of number sequence.These three difficult but important theorems therefore can be accepted by teachers and students easily.
Keywords:limits of compound functions  convergent number sequence and its subsequence  Heine's theorem  the rearrangement of number sequence
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