数学师范论文.doc

PAGE  积分型极限的解法探究 摘 要 积分型极限，即极限表达式中含有积分符号的极限，是极限运算问题中的一种特殊类型.本文主要探究含黎曼积分的积分型极限的解法.根据积分型极限中含积分的特点、性质，以及积分的运算法则，在极限一般解法的基础上，探究求解积分型极限的特殊解法和技巧处理，使得求解积分型极限问题变得简单化、系统化.本文得到的结论为解决更一般的与积分型极限相关问题提供了有益的思想和方法. 【关键词】积分型极限；解法；积分 Study on the solution of the integral type limit Abstract The integral type limit,the limit which the integral symbol is contained in, is a special type of the problem of limit calculation. The solution of the integral type limit with Riemann integral is mainly studied on in this paper. According to the integral characteristics, integral properties, and the integral algorithm included in the integral type limit, and on the basis of the limit of general solution, the special solutions to solve the integral type limit and skills to deal with are studied on in this paper. It is easier and more systematic to solve problems of the integral type limit. Associated with the conclusion in this paper, the useful of thought and method is provided about the more general problem of the integral type limit. [Key words] integral type limit, solution, integral 目 录  TOC \o 1-2 \h \z \u  HYPERLINK \l _Toc388611465 引 言  PAGEREF _Toc388611465 \h 1  HYPERLINK \l _Toc388611466 1 积分型极限的分类  PAGEREF _Toc388611466 \h 1  HYPERLINK \l _Toc388611467 2 积分型极限的一般解法  PAGEREF _Toc388611467 \h 2  HYPERLINK \l _Toc388611468 2.1 先求原函数再求极限  PAGEREF _Toc388611468 \h 2  HYPERLINK \l _Toc388611469 2.2 运用洛比达法则（L’Hospital’s Rule）  PAGEREF _Toc388611469 \h 2  HYPERLINK \l _Toc388611470 2.3 运用放缩法或夹逼准则  PAGEREF _Toc388611470 \h 4  HYPERLINK \l _Toc388611471 2.4 运用等价无穷小量  PAGEREF _Toc388611471 \h 5  HYPERLINK \l _Toc388611472 3 积分型极限的特殊解法  PAGEREF _Toc388611472 \h 8  HYPERLINK \l _Toc388611473 3.1 运用积分中值定理求解  PAGEREF _Toc388611473 \h 8  HYPERLINK \l _Toc388611474 3.2 拟合法、隔离法、分段法  PAGEREF _Toc388611474 \h 10  HYPERLINK \l _Toc388611475 3.3 概率方法  PAGEREF _Toc388611475 \h 12  HYPERLINK \l _Toc388611476 3.4 其他方法  PA