函数极限的若干求法.doc

函数极限的若干求法

目录

引言................................................................................................................................3
摘要................................................................................................................................3
关键词............................................................................................................................3
第一章：有关函数极限的概念..............................................................................4
1.1数列极限的定义..............................................................................................4
1.2函数极限的定义..............................................................................................4
1.3函数极限的性质..............................................................................................4
第二章：求解函数极限的方法............................................................................5
2.1.定义法..............................................................................................................5
2.2利用极限四则运算法则..................................................................................6
2.3.利用两个重要极限求极限..............................................................................7
2.4.利用迫敛性来求极限......................................................................................8
2.5.利用洛必达法则求极限..................................................................................8
2.6.利用定积分求极限........................................................................................12
2.7.利用无穷小量的性质和无穷小量和无穷大量之间的关系求极限............13
2.8.利用变量替换求极限....................................................................................13
2.9.利用递推公式计算或证明序列求极限........................................................14
2.10.利用等价无穷小量代换来求极限 .............................................................15
2.11.利用函数的连续性求极限..........................................................................16
2.12.利用泰勒公式求极限..................................................................................16
2.13.利用导数的定义求极限..............................................................................18
2.14.利用级数收敛的必要条件求极限 .............................................................18
2.15.利用单侧极限求极限..................................................................................19
2.16.利用中值定理求极限..................................................................................20
结论..............................................................................................................................23
致谢...............................................................................................................................................24
参考文献......................................................................................................................25


摘要： 高等数学是许多课程的基础，而在高数中极限的概念又是一个比较基础的概念，因此本文主要讨论函数极限的若干求解方法，希望对读者有所帮助。本文归纳总结了一般情况下我们常用的几种方法，也包括几种比较特殊的求解方法，包括利用泰勒公式来求解函数极限等。在每一种方法后面都附有例题说明，尽可能的详细解释用法。
关键词： 函数极限 洛必达法则 变量替换 迫敛性 等价无穷小量

Several methods for the limit

Abstract: Advanced mathematics is the base of many courses, and the concept of limit in Advanced mathematics is also a basic concept, this paper mainly discusses some methods to solve the limit of function, we hope to help readers realizing the concept of limit. This paper summarizes the general situation we used frequently, several special methods also included, including the use of the Taylor formula to solve the function limit.Behind each method with examples to explain, explain in detail the usage as possible.

Keywords: The limit of function L'Hospital Rule Variable substitution Forced convergence property The equivalent infinitesimal