不等式证明方法的综合讨论

不等式证明方法的综合讨论

摘 要

不等式的证明方法灵活多样，技巧性和综合性较强，每种方法具有1定的使用性，并有1定的规律可循．本文综述了证明不等式的若干方法．通过对例题的分析，回顾了几种常用的不等式证明的初等方法．但是用初等方法证明往往会造成复杂的运算过程，本文接着充分利用微积分的知识探究不等式的证明方法，并指出微分学和积分学在不等式的证明的具体应用，那就是在构造函数的背景下运用函数的单调性、微积分中值定理、函数的极值和最值、定积分，那么就可以10分有效地解决不等式中的证明问题，从而归纳出几种方便而又简捷的方法，这样对我们解题将会起到很大的作用．

关键词： 不等式； 证明； 微积分； 综合讨论．

Inequality Proof comprehensive discussion

ABSTRACT

Inequality proven flexibility、diversity、Skills and m£ore integrated,each method is the use of Usability，it also has to follow the law．This paper reviews the☮ evidence of inequality in a number of ways.Examples of the analysis， we will recall severaลl common inequality prove elementary method．However，To prove Inequality wi✔th elementary method，we often create complex computational process． The second ，we will take full advantage of the knowledge of calculus Inquiry Testimony of inequality，and concluded the higher mathematics to prove Inequality several main method and its application conditions．Constructors in the context of the use of the monotone function，Calculus value theorem，function and the most extreme value，i ☻ntegral， it can be a very effective solution to the inequality problem proof． At last，we summed up several convenient and simple way to prove Inequality．It will be play a great role in our problem Solving．

Keywords： Inequality；Prove；Calculus；Comprehensive discussion．