毕业论文--求极限的几种方法及应用

2013届毕业设计（论文）分院计算机科学与技术学院专业信息与计算科学班级信计本0901学号09404038姓名王小宝指导教师王子龙（讲师）完成时间2013年5月求极限的几种方法及应用目录绪论.................................................................................................................................................11极限的概念..................................................................................................................................11.1极限的背景......................................................................................................................21.2极限的求解方法和在现实中的应用..............................................................................22极限的定义性质及作用函数极.................................................................................................22.1数列极限标准定义..........................................................................................................22.2函数极限具有的性质......................................................................................................33函数极限的计算及多种求法.....................................................................................................33.1定义法..............................................................................................................................33.2利用极限四则运算法则..................................................................................................43.3利用夹逼性定理求极限..................................................................................................43.4利用两个重要极限求极限..............................................................................................53.5利迫敛性来求极限..........................................................................................................53.6用洛必达法则求极限......................................................................................................53.7利用定积分求极限..........................................................................................................63.8利用无穷小量求极限......................................................................................................73.9利用变量替换求极限......................................................................................................73.10利用递推公式计算或证明序列求极限........................................................................83.11利用等价无穷小量代换来求极限................................................................................83.12利用函数的连续性求极限............................................................................................93.13利用泰勒公式求极限....................................................................................................93.14利用两个准则求极限..................................................................................................103.15利用级数收敛的必要条件求极限..............................................................................104极限思想在现实中的一些应用...............................................................................................114.1在物理中的应用............................................................................................................114.2在数学中的应用............................................................................................................11总结...............................................................................................................................................13参考文献.......................................................................................................................................14致谢...............................................................................................................................................15摘要在数学分析中，极限是一个蕴含深刻辩证法的数学概念，其中渗透着常数与变数，有限与无限，精确与近似等。研究函数的性质实质上是研究各种类型的极限，如连续，导数，定积分，级数等等。因此极限是数学分析中非常重要的一个概念。本文主要探讨了数学分析中极限求解的几种思路和技巧，结合具体的例子分析了一般极限的求解过程，给出了一般极限的方法和技巧，揭示了极限求解的解题思路。极限概念是微积分学中最重要，最基本的概念。掌握好利用定义证明函数极限是学好高等数学的基础，极限有数列极限，函数极限，多元函数极限等几类，本文直接或间接地用极限定义来证明一些我们经常见到高等数学问题.同时极限的思想方法是解决实际问题的一个重要方法，通过实例，给出用数学的极限思想去解决各个实际问题。关键词：函数，极限，方法，现实中的应用，实际问题AbstractLimitcontainsprofounddialecticalmathematicalconcepts,itcontainsconstantandvariable,limitedandvariable,limitedandinfinite,preciseandapproximate,inthemathematicalanalysis,ithasavarietyofformsoflimits.thispapermainlydiscussessomeideasandmethodsinsolvingthelimitsofmathematicalanalysis,analysisthesolvingprocessofagenerallimit,givesthegenealsolutionandskilloflimitandalsorevealsthethoughtsofgettingthelimit.Whichiscombinedwithconcreteexamples.Thedefinitionofthelimitisthemostimportantandbasicconceptintheinfinitesimalcalculus.Masteringthewaysofusingthedefinitiontoprobethelimitoffunctionlaysafoundationforstudyingthehighermathematicswell.Therearethelimitofseries,limitoffunctionandfunctionallimitofseveralvariablesandsoon.Inthispaper,thedefinitionofthelimitisuseddirectlyorindirectlytoprovesomecommonproblemsofhighermathematics.Limitthoughtisanimportantwaytosolvepracticalproblems.Thispapertriestoexplorebowtousemathematicallimitthoughttofindsolutionstoproblemsinpractice.Keywords:Function,Limit,Solution,Analysis,Problems商丘学院毕业设计（论文）1绪论在数学分析中，极限是一个蕴含深刻辩证法的数学概念，其中渗透着常数与变数，有限与无限，精确与近似等。研究函数的性质实质上是研究各种类型的极限，如连续，导数，定积分，级数等等。因