不等式证明的若干方法 毕业论文 (2).doc

不等式证明的若干方法 摘 要 无论在初等数学还是高等数学中,不等式都是十分重要的内容.而不等式的证明则是不等式知识的重要组成部分.在本文中，我总结了一些数学中证明不等式的方法.在初等数学不等式的证明中经常用到的有比较法、作商法、分析法、综合法、数学归纳法、反证法、放缩法、换元法、判别式法、函数法、几何法等等.在高等数学不等式的证明中经常利用中值定理、泰勒公式、拉格朗日函数、以及一些著名不等式，如：均值不等式、柯西不等式、詹森不等式、赫尔德不等式等等.从而使不等式的证明方法更加的完善，有利于我们进一步的探讨和研究不等式的证明. 通过方法解决一些实际问题，培养逻辑推理论证抽象思维的能力勤于思考、善于思考的良好学习习惯A Lot of Methods about Inequality Proof Abstract In elementary mathematics and higher mathematics, inequalities are very important elements. Inequality is an important component in the inequality proof. In this paper, I summarized some mathematical inequality proof methods. Inequality in elementary mathematical proof commonly use in comparative law, for commercial, 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; comparative law; mathematical induction; function 目 录 摘要…………………………………………………………………………………………… Abstract……………………………………………………………………………………… Ⅱ 前言…………………………………………………………………………………………… 1 …………………………………………………………………………………… 1 1．1比较法（作差法）……………………………………………………………………… 1 1．2作商法 ……………………………………………………………………………… 1 1．3分析法（逆推法）……………………………………………………………………… 1 1．4综合法………………………………………………………………………………… 2 1．5反证法………………………………………………………………………………… 2 1．6迭合法………………………………………………………………………………… 2 1．7放缩法………………………………………………………………………………… 3 1．8数学归纳法………………………………