Calculus review 2

The second is sequence limit

This series of articles refer to 《 Zhang Yu high number 18 speak 》, In order to summarize the knowledge of calculus in higher mathematics , This series of articles is divided into 18 A section , See the table of contents in this section below ：

• Introduction
• Definition and application of sequence limit
• Existence and calculation of sequence limit

The following will be explained according to the above contents

refer:

1. 《 Zhang Yu high number 18 speak 》

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1 Introduction

2 Definition and application of sequence limit

2.1 Definition

The definition of sequence limit is equivalent to the definition when the function tends to infinity .

2.2 Use （ The existence of limit ）

The properties of sequence limit and function limit , Article 5 different , All child columns converge to A.

3 Existence and calculation of sequence limit

3.1 Calculation

3.1.1 Resolution principle

That is, when the limit of the sequence xn In existence , take xn As an independent variable f（xn） in , If f(x) At a specific point x0 The limits of exist , You can use the resolution principle Transform sequence limit into function limit calculation .

3.1.2 Direct calculation

First, we use the monotone bounded criterion to prove ,n Tends to infinity ,xn The limit of the sequence exists . Then order xn+1=xn=a, Into the a Solution a. be a That is, the limit of the sequence .

3.1.3 Definition

Post tectonic scaling .

3.2 prove

3.2.1 Monotone bounded criteria

3.2.2 Pinch rule

3.3 Comprehensive questions