[理學]不等式證明的若干方法(已修改)
2025-09-02 15:17 本頁面
【正文】 河南師范大學本科畢業(yè)論文重慶師范大學本科畢業(yè)論文 學號：20080511757用高等數學知識求函數極限的探究學院名稱： 數學學院 專業(yè)名稱： 數學與應用數學 年級班別： 2008級4班 姓 名： 朱興杭 指導教師： 張守貴 2012年03月2用高等數學知識求函數極限的探究摘 要在整個高等數學的學習中，我們所學習的許多知識都可以用于求函數的極限，諸如利用初等函數的連續(xù)性、利用等價無窮小代換求極限、利用夾逼準則求極限、以及利用洛必達法則求函數極限等等。同時，極限的思想方法也貫穿于整個高等數學中，一些基本概念如微分、積分的定義都與極限有密不可分的聯(lián)系。在本文中，我主要總結了一些常用的利用高等數學知識求函數極限的方法，并用具體實例加以說明。關鍵詞 函數極限；連續(xù)性；洛必達法則；泰勒公式 A Lot of Methods about Inequality ProofAbstractIn elementary mathematics and higher mathematics, inequalities are very important elements. Inequality is an important ponent in the inequality proof. In this paper, I summarized some mathematical inequality proof methods. Inequality in elementary mathematical proof monly use in parative law, for mercial, analysis, synthesis, mathematical induction, the reduce tion to absurdity, discriminant, function, Geometry, and so on. Inequality in higher mathematics proof often use the intermediate value theorem, Taylor formula, the Lagranga function and some famous inequality, such as : mean inequality, Kensen inequality, Johnson in equality, Helder inequality, and so on. Inequality proof methods get more efficient and help us further explore and study the inequality proof. Through the study of these proof methods, we can solve some practical problems, develop logical reasoning ability and demonstrated the ability to abstract thinking and grow hard thinking and good at thinking of the good study habit.Key words inequality。 parative law。 mathematical induction。 function 目 錄摘要……………………………………………………………………………………………ⅠAbstract………………………………………………………………………………………Ⅱ前言……………………………………………………………………………………………11 常用方法……………………………………………………………………………………11．1比較法（作差法）………………………………………………………………………1 1．2作商法 ………………………………………………………………………………1 1．3分析法（逆推法）………………………………………………………………………1 1．4綜合法…………………………………………………………………………………2 1．5反證法…………………………………………………………………………………2 1．6迭合法…………………………………………………………………………………2 1．7放縮法…………………………………………………………………………………3 1．8數學歸納法……………………………………………………………………………3 1．9換元法…………………………………………………………………………………3 1．10三角代換法…………………………………………………………………………4 1．11判別式法……………………………………………………………………………41．12標準化法……………………………………………………………………………41．13等式法………………………………………………………………………………5 1．14分解法………………………………………………………………………………6 1．15構造法………………
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