文档介绍：毕业设计(论文)
课题名称极限求解的若干方法
学生姓名
学号
系、年级专业理学系08信息与计算科学
指导教师
职称讲师
2012年 5 月 25 日
摘要
极限理论是一种近代发展起来的重要数学思想,也是数学分析的基础和首要的教学内容。极限理论所研究的是变量在其变化过程中的趋势问题,在数学分析课程教学中所讨论的极限问题大体上分为两类:一类是数列的极限,它是微积分的基础,贯穿于微积分学的始终,是微积分学的重要研究方法。数列极限是极限理论的重要组成部分,而数列极限的求法可以通过定义法,两边夹法,单调有界法,施笃兹公式法等方法进行求解。另一类是函数的极限,它也是微积分学中的一个关键问题,是学习的主要内容之一,对函数极限概念的理解及对函数极限求法的掌握至关重要。。求极限是数学分析中困难问题之一,中心问题有两个:一、证明极限的存在性,二、求解极限值。这两者有密切关系,两者是辩证统一的。用极限解决问题的方式通常是先考察未知量并设法将其与变量相关联,并确认以无限的过程来得到未知结果。
本文主要探讨、总结求极限的一般方法并补充利用级数收敛及利用积分等求极限的特殊方法,而且把每一种方法的特点及注意事项作了详细重点说明,并以实例加以例解,弥补了一般教材的不足。
关键词:函数极限,数列极限,中值定理,洛必达法则,泰勒展开式,换元法
Abstract
Limit theory is a modern development important mathematics thought, mathematics is of basic and important content of teaching. Limit theory is variable in its changes during the course of the trend, in the teaching of mathematical analysis are discussed in the ultimate problem is roughly divided into two categories: one is the limit of number sequence, which is the basis of calculus, throughout the calculus calculus from beginning to end, is an important research method. The limit of the sequence is the main constituent of the limit theory, and the limit of a sequence of law can be defined by law, both sides grip, monotone bounded method, applying Duzi formula method for solving. Another kind is the limit of a function, it is also the calculus is one of the key problems in the study, is one of the main contents of the understanding of the concept of limit of function, and the function method of solving limit can be critical.. Solution of limit in mathematical analysis is one of the difficult problems, center problem has two: one, to prove the existence of the limit, two, solving the limit value. There is a close relationship between the two, both it is adj and unified. Using the ultimate way to solve the problem is usually visit the unknown quantity and to bring its associated with variables, and confirm to the infinite process to get the unknown result.
This paper mainly discusses the li