关于极限的几种求解方法_精品.docVIP

论文题目来源： 国家自然科学基金项目 编号： 四川省自然科学研究项目 编号： 校级自然科学研究项目 编号： 关于极限的几种求解方法 学生：唐莉 指导教师：唐玲 摘 要：极限分为函数极限和数列极限．其中数列可以看作是定义在正整数集上的函数=f（n）（n=1,2,…）．各种极限的基本含义是自变量的变化趋势引起的因变量的变化趋势．在高等数学中，极限理论是微分学的基础，是数学分析的灵魂，研究函数的性质实际上就是研究各种类型的极限.本文通过对极限的有关概念、定理和公式的介绍，对高等数学课程中所学的求极限的基本方法进行了比较系统的总结.论文采用由易至难、层层递进前后共归纳了12种求数列极限的方法，用典型例题阐述了每种方法的思路、内容及解题技巧，其中涉及到单调原理、微分中值定理、泰勒展开式、归结原则、两边夹定理等知识点，运用了极限定义法，定积分法、初等变形法、变量替换法、利用函数连续性等方法，体现了对极限的掌握应从近似认识精确，从有限认识无限，从量变认识质变的特点. 关键词：函数 数列 极限 Several methods of solving about limit Undergraduate: Supervisor: TangLing Abstract: the limit is divided into several columns limit. One series can be seen as defined in the function on the set of positive integers = f (n) (n = 1,2, ...). The basic meaning of a variety of extreme trends in the independent variable caused the trend of the dependent variable. In mathematics, the limit theory is the basis of differential calculus, is the soul of mathematical analysis to study the nature of the function is actually the limit of all types. Based on the limits of the relevant concepts, theorems and formulas of the introduction of higher mathematics Course Limit of learned the basic methods are compared systematically summarized. thesis, from easy to difficult, progressive layers before and after induction of the 12 series limit demand method, a typical example describes the idea of ??each method , Content and problem-solving skills, involving monotone theory, differential mean value theorem, Taylor expansion, attributed the principle of knowledge points on both sides of the folder theorem, using the limit definition of law, will be integral, elementary deformation, variable substitution, Method using the function continuity, reflects the understanding of the limits of precision grasp should be similar, from the limited understanding of infinity, from the quantitative understanding of qualitative features. Key words: function rule-governed series of numbers limit 目　　录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc292444131 1绪论 PA