数学分析中的不等式证明问题

Inequality Proof Problems in Mathematical Analysis

不等式形式是高等数学和数学分析中的常见数学形式,它反映了变量之间的一种关系。本文总结了数学分析中有关不等式证明的三种重要方法:拉格朗日中值定理法,柯西中值定理法,定积分理论法。对每种方法都是以先概括要点,再选取典型而又有不同难度的例题,逐层剖析,归类讲解。通过以上方法的应用使我们对不等式证明的相关知识有更加深刻系统的理解,从而为数学中许多其他内容的学习提供了一个重要工具。

Inequality is common mathematical form in higher mathematics and mathematical analysis, it reflects a relationship between variables. In this paper we gave three important methods in mathematical analysis to proof inequalities. There are Lagrange mean - value theorem, Cauchy mean - value theorem and method of integral theo- ry. For each of methods we summarize the main points firstly, and then select examples of different difficulty and typical, layer - by - layer analysis, classified explanation.