求各位大虾翻译一下论文中文摘要!!!

来源:百度知道 编辑:UC知道 时间:2024/07/05 01:11:34
证明不等式是一种艺术,它具有自己独到丰富的技术手法。而微积分是研究函数性态的重要工具,利用微积分知识证明不等式,关键就在于抓住不等式的特点,充分运用函数的思想和数形结合的思想,巧妙的构造函数,将不等式问题转化为函数问题,然后运用我们已经掌握的微积分理论和方法,通过对函数性态的分析来证明不等式。本文对如何运用微积分知识证明不等式进行了深入的讨论,通过对十余种不同类型不等式的证明研究,用较多的例子分别研究了导数定义、单调性、极值与最大最小值、微分中值定理、函数凹凸性、积分、级数等知识在证明不等式中的运用,并对微积分不同知识点适用于哪些类型的不等式作了归纳总结。

That inequality is an art, it has its own unique wealth of technical practices. The calculus is to study the function of the state an important tool, used calculus knowledge that inequality, the key is to seize on the characteristics of inequality, and make full use of the function Shuxingjiehe of thinking and thinking, clever structural function, inequality problem will be transformed into Function of the problem, then we have already mastered the use of calculus theories and methods, through the function of the state to prove that the analysis of inequality. This article on how to apply calculus knowledge that inequality has conducted in-depth discussions by more than 10 different types of inequality that study, with more examples to study the definition of derivative, dull, extreme minimum and maximum, differential Value theorem, convex function, integration, series, and so that inequality of knowledge in the use and knowledge of different points of calculus applies to the types