不等式證明方法的綜合討論

不等式證明方法的綜合討論

不等式證明方法的綜合討論

摘  要

不等式的證明方法靈活多樣，技巧性和綜合性較強(qiáng)，每種方法具有1定的使用性，并有1定的規(guī)律可循．本文綜述了證明不等式的若干方法．通過對例題的分析，回顧了幾種常用的不等式證明的初等方法．但是用初等方法證明往往會造成復(fù)雜的運(yùn)算過程，本文接著充分利用微積分的知識探究不等式的證明方法，并指出微分學(xué)和積分學(xué)在不等式的證明的具體應(yīng)用，那就是在構(gòu)造函數(shù)的背景下運(yùn)用函數(shù)的單調(diào)性、微積分中值定理、函數(shù)的極值和最值、定積分，那么就可以10分有效地解決不等式中的證明問題，從而歸納出幾種方便而又簡捷的方法，這樣對我們解題將會起到很大的作用．

關(guān)鍵詞：　不等式；　證明；　微積分；　綜合討論．

Inequality Proof comprehensive discussion
 

ABSTRACT

Inequality proven flexibility、diversity、Skills and more 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 several common inequality prove elementary method．However，To prove Inequality with 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，integral， 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．

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