微積分在不等式中應用(已修改)
2025-07-02 06:27 本頁面
【正文】 Abstract摘要微積分是高等數學中研究函數的微分、積分以及有關概念和應用的數學分支。它是數學的一個基礎學科，內容主要包括：微分、積分及其應用。微積分是與應用聯(lián)系著發(fā)展起來的，微積分的發(fā)展極大的推動了數學的發(fā)展。不等式是數學學科中極為重要的內容，證明不等式的方法多種多樣，有些不等式用以前學習的方法來證明比較麻煩，其證明通常不太客易。本文回顧了幾種常用的證明不等式的初等方法，利用微分中值定理、函數的單調性、極值（最值）的判定法、函數凸凹性質、泰勒公式、定積分的性質等一些微積分知識探究了不等式的證明方法，本文探討了如何巧妙利用微積分中的知識和方法來解決一些不等式的問題。用微積分證明不等式成立, 基本思路是構造一個輔助函數,把不等式的證明轉化為利用微積分來研究函數的形態(tài)，然后利用微積分求出該函數的性質來證明不等式。希望通過本文的介紹能使人們意識到微積分與不等式的密切關系，讓大家能意識到理論與實際結合的重要性。關鍵詞： 微積分；不等式；證明；應用 AbstractThe calculus is study on the function of Higher Mathematics in the differential, integral and relevant concepts and applications of mathematics branch. It is a basic discipline of mathematics, mainly including: differential, integral and its application. Calculus develops with the application, the development of calculus greatly promoted the development of mathematics. Inequality is a very important content in mathematics, the various methods to prove inequality, some methods of inequality by the previous study to prove troublesome, it is usually not too easy.This paper reviews the elementary methods to prove inequality, the use of differential mean value theorem, the monotone of the function, extreme( maximum ) determination method, convexconcave function, the Taylor formula, the definite integral, some knowledge of calculus method to prove inequality, this paper discusses how to skillfully use the knowledge and method of the calculus to solve some of the problems of inequality. Using calculus to prove inequality, the basic idea is to construct an auxiliary function, the proof of inequality into to study function using calculus form, then use the calculus calculate the properties of the function to prove inequality. Hope that through this paper can make people aware of the close relationship between calculus and inequality, Let us be aware of the importance of integrating theory with practice.Keywords: calculus。 inequality。 prove。 application新!為您提供類似表述，查看示例用法： 分享到 翻譯結果重試抱歉，系統(tǒng)響應超時，請稍后再試 支持中英、中日在線互譯 支持網頁翻譯，在輸入框輸入網頁地址即可
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