極限求值的若干方法


摘要
極限的概念是高等數(shù)學(xué)中最重要、最基本的概念之一，并且在高等數(shù)學(xué)當(dāng)中占有十分重要的位置。許多重要的數(shù)學(xué)概念如連續(xù)、導(dǎo)數(shù)、定積分、無窮級數(shù)的和及廣義積分等都是用極限來定義的，所以極限運(yùn)算時高等數(shù)學(xué)的基本運(yùn)算。并且極限概念又高度抽象，又由于極限運(yùn)算分布于整個高等數(shù)學(xué)的始終，因此掌握好極限的計算方法與技巧是學(xué)習(xí)高等數(shù)學(xué)相當(dāng)關(guān)鍵的一個環(huán)節(jié)。雖然極限的計算方法比較多，但都不是萬能的。因此對于某個具體的極限的計算問題，我們應(yīng)該要去追求最簡便、快捷的計算方法。本文介紹了極限計算的一些方法與技巧并通過實例加以說明了。有關(guān)的命題和結(jié)論在文中也均有說明。

【關(guān)鍵詞】：高等數(shù)學(xué)，極限，極限求值的方法 ，技巧。


Abstract
Limit is higher mathematics concepts most important, the most basic concepts and occupies a very important position among the higher mathematics. Many important mathematical concepts such as continuous, derivatives, definite integrals, infinite series and generalized integral and so are defined by the limit, so the ultimate computing basic operations of higher mathematics. And the limit and highly abstract concepts, and because the limit is always distributed computing throughout mathematics, so mastering the limit calculation methods and techniques to learn mathematics is quite critical link. Although the calculation of the limit more, but not a panacea. So for a specific limit calculation, we should go to the pursuit of the most convenient and efficient method of calculation. This article describes some of the methods and techniques to calculate limits and by example to illustrate it. Relevant propositions and conclusions are also described in the text.
Key words: methods of higher mathematics, ultimate, ultimate eva luation of skills.


目錄
第一章 引言 1
第二章：極限的基本概念 2
2.1極限的基本概念 2
2.2利用極限定義求解的方法 3
第三章：極限的幾個重要性質(zhì) 4
3.1函數(shù)極限的相關(guān)性質(zhì) 4
3.2收斂數(shù)列相關(guān)性質(zhì) 5
3.3極限的幾個重要性質(zhì)的求解方法 5
第四章：幾種初等的方法求極限 7
4.1幾種初等的方法求極限 7
第五章：極限的相關(guān)定理 9
5.1極限的定理 9
5.2極限計算的方法與技巧 13
5.2.1單調(diào)有界定理 13
5.2.2利用兩個重要極限求極限 14
5.2.3利用等價無窮下求極限 15
5.2.4利用洛必達(dá)法則求極限 16
5.2.5 泰勒展開式求極限 20
5.2.6利用中值定理求極限 22
5.2.7利用定積分求極限. 23
總結(jié) 25
致謝 26
參考文獻(xiàn) 27