摘要：極限一直是數(shù)學(xué)分析中的一個(gè)重點(diǎn)內(nèi)容，而對(duì)數(shù)列極限的求法可謂是多種多樣，通過歸納和總結(jié)，我們羅列出一些常用的求法。本文主要?dú)w納了數(shù)學(xué)分析中求極限的十四種方法, 1：利用兩個(gè)準(zhǔn)則求極限, 2:利用極限的四則運(yùn)算性質(zhì)求極限, 3:利用兩個(gè)重要極限公式求極限, 4：利用單側(cè)極限求極限，5：利用函數(shù)的連續(xù)性求極限, 6：利用無窮小量的性質(zhì)求極限, 7：利用等價(jià)無窮小量代換求極限, 8：利用導(dǎo)數(shù)的定義求極限, 9：利用中值定理求極限, 10：利用洛必達(dá)法則求極限, 11：利用定積分求和式的極限,12：利用級(jí)數(shù)收斂的必要條件求極限, 13：利用泰勒展開式求極限, 14：利用換元法求極限。

關(guān)鍵詞：夾逼準(zhǔn)則, 單調(diào)有界準(zhǔn)則, 函數(shù)的連續(xù)性，無窮小量的性質(zhì), 洛必達(dá)法則, 微分中值定理, 定積分, 泰勒展開式.

Abstract：Mathematical analysis of the limit has been a focus of the content, while the series to Limit can be described as diverse, and concluded by induction, we set out the requirements of some commonly used method. This paper summarizes the mathematical analysis of fourteen methods of limit, 1: Limit of using two criteria, 2: the use of arithmetic nature of the limits of the Limit, 3: Limit use of two important limit of the Formula 4: Using a single side of the limit of limit, 5: Using the continuity of functions of limit, 6: the nature of the use of limit infinitesimals, 7: Substitution of equivalent limit Infinitesimal, 8: Using the definition of derivative of the Limit, 9: Using the value theorem of limit, 10: Using the Limit Hospital's Rule 11: the use of the definite integral summation type limit, 12: Convergence of the necessary conditions using the Limit, 13: Limit of using the Taylor expansion, 14: the use of Method substitution limit.

Keywords：Squeeze guidelines, criteria for bounded monotone function continuity, the nature of infinitesimals, Hospital's Rule, Mean Value Theorem, definite integral, the Taylor expansion.

目錄

一、引言 ……………………………………………………………………

二、極限的求法 ………………………………………………………………

2.1：利用兩個(gè)準(zhǔn)則求極限………………………………………………

2.2：利用極限的四則運(yùn)算性質(zhì)求極限……………………………………

2.3：利用導(dǎo)數(shù)的定義求極限………………………………………………

2.4：利用兩個(gè)重要極限公式求極限………………………………………

2.5：利用級(jí)數(shù)收斂的必要條件求極限…………………………………

2.6：利用單側(cè)極限求極限………………………………………………

2.7：利用函數(shù)的連續(xù)性求極限…………………………………………

2.8：利用無窮小量的性質(zhì)求極限………………………………………

2.9：利用等價(jià)無窮小量代換求極限………………………………………

2.10：利用中值定理求極限…………………………………………………

2.11：洛必達(dá)法則求極限……………………………………………………

2.12：利用定積分求和式的極限……………………………………………

2.13：利用泰勒展開式求極限………………………………………………

2.14：換元法求極限………………………………………………………

結(jié)論………………………………………………………………………………

參考文獻(xiàn)……………………………………………………………………………

致謝…………………………………………………………………………………