极限求法综述.doc

摘要：极限一直是数学分析中的一个重点内容，而对数列极限的求法可谓是多种多样，通过归纳和总结，我们罗列出一些常用的求法。本文主要归纳了数学分析中求极限的十四种方法, 1：利用两个准则求极限, 2:利用极限的四则运算性质求极限, 3:利用两个重要极限公式求极限, 4：利用单侧极限求极限，5：利用函数的连续性求极限, 6：利用无穷小量的性质求极限, 7：利用等价无穷小量代换求极限, 8：利用导数的定义求极限, 9：利用中值定理求极限, 10：利用洛必达法则求极限, 11：利用定积分求和式的极限,12：利用级数收敛的必要条件求极限, 13：利用泰勒展开式求极限, 14：利用换元法求极限。

关键词：夹逼准则, 单调有界准则, 函数的连续性，无穷小量的性质, 洛必达法则, 微分中值定理, 定积分, 泰勒展开式.

Abstract：Mathematical analysis of the limit has been a focus of the content, while the series to Limit can be described as diverse, and concluded by induction, we set out the requirements of some commonly used method. This paper summarizes the mathematical analysis of fourteen methods of limit, 1: Limit of using two criteria, 2: the use of arithmetic nature of the limits of the Limit, 3: Limit use of two important limit of the Formula 4: Using a single side of the limit of limit, 5: Using the continuity of functions of limit, 6: the nature of the use of limit infinitesimals, 7: Substitution of equivalent limit Infinitesimal, 8: Using the definition of derivative of the Limit, 9: Using the value theorem of limit, 10: Using the Limit Hospital's Rule 11: the use of the definite integral summation type limit, 12: Convergence of the necessary conditions using the Limit, 13: Limit of using the Taylor expansion, 14: the use of Method substitution limit.

Keywords：Squeeze guidelines, criteria for bounded monotone function continuity, the nature of infinitesimals, Hospital's Rule, Mean Value Theorem, definite integral, the Taylor expansion.

目录

一、引言 ……………………………………………………………………

二、极限的求法 ………………………………………………………………

2.1：利用两个准则求极限………………………………………………

2.2：利用极限的四则运算性质求极限……………………………………

2.3：利用导数的定义求极限………………………………………………

2.4：利用两个重要极限公式求极限………………………………………

2.5：利用级数收敛的必要条件求极限…………………………………

2.6：利用单侧极限求极限………………………………………………

2.7：利用函数的连续性求极限…………………………………………

2.8：利用无穷小量的性质求极限………………………………………

2.9：利用等价无穷小量代换求极限………………………………………

2.10：利用中值定理求极限…………………………………………………

2.11：洛必达法则求极限……………………………………………………

2.12：利用定积分求和式的极限……………………………………………

2.13：利用泰勒展开式求极限………………………………………………

2.14：换元法求极限………………………………………………………

结论………………………………………………………………………………

参考文献……………………………………………………………………………

致谢…………………………………………………………………………………