函數(shù)極限的若干求法

目錄

引言................................................................................................................................3
摘要................................................................................................................................3
關(guān)鍵詞............................................................................................................................3
第一章：有關(guān)函數(shù)極限的概念..............................................................................4
1.1數(shù)列極限的定義..............................................................................................4
1.2函數(shù)極限的定義..............................................................................................4
1.3函數(shù)極限的性質(zhì)..............................................................................................4
第二章：求解函數(shù)極限的方法............................................................................5
2.1.定義法..............................................................................................................5
2.2利用極限四則運算法則..................................................................................6
2.3.利用兩個重要極限求極限..............................................................................7
2.4.利用迫斂性來求極限......................................................................................8
2.5.利用洛必達法則求極限..................................................................................8
2.6.利用定積分求極限........................................................................................12
2.7.利用無窮小量的性質(zhì)和無窮小量和無窮大量之間的關(guān)系求極限............13
2.8.利用變量替換求極限....................................................................................13
2.9.利用遞推公式計算或證明序列求極限........................................................14
2.10.利用等價無窮小量代換來求極限 .............................................................15
2.11.利用函數(shù)的連續(xù)性求極限..........................................................................16
2.12.利用泰勒公式求極限..................................................................................16
2.13.利用導(dǎo)數(shù)的定義求極限..............................................................................18
2.14.利用級數(shù)收斂的必要條件求極限 .............................................................18
2.15.利用單側(cè)極限求極限..................................................................................19
2.16.利用中值定理求極限..................................................................................20
結(jié)論..............................................................................................................................23
致謝...............................................................................................................................................24
參考文獻......................................................................................................................25


摘要： 高等數(shù)學(xué)是許多課程的基礎(chǔ)，而在高數(shù)中極限的概念又是一個比較基礎(chǔ)的概念，因此本文主要討論函數(shù)極限的若干求解方法，希望對讀者有所幫助。本文歸納總結(jié)了一般情況下我們常用的幾種方法，也包括幾種比較特殊的求解方法，包括利用泰勒公式來求解函數(shù)極限等。在每一種方法后面都附有例題說明，盡可能的詳細解釋用法。
關(guān)鍵詞： 函數(shù)極限 洛必達法則 變量替換 迫斂性 等價無窮小量

Several methods for the limit

Abstract: Advanced mathematics is the base of many courses, and the concept of limit in Advanced mathematics is also a basic concept, this paper mainly discusses some methods to solve the limit of function, we hope to help readers realizing the concept of limit. This paper summarizes the general situation we used frequently, several special methods also included, including the use of the Taylor formula to solve the function limit.Behind each method with examples to explain, explain in detail the usage as possible.

Keywords: The limit of function L'Hospital Rule Variable substitution Forced convergence property The equivalent infinitesimal