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Discussion Topics of Chapter 8

1. What is indeterminate form?

2. How to understand the key word “improper”?

3. How to understand the improper integrals about infinite limits of integrations?

4. How to understand the improper integrals about infinite integrands?

下一节:Homework for Chapter 8

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微积分1(Calculus I)课程列表:

Course Introduction

-Course Introduction

--Course Introduction

--Document

Chapter 1 Limits

-Introduction to Limits

--此章节内容为自学模块

-Rigorous Study of Limits

--Rigorous Study of Limits

--Document:Rigorous Study of Limits

--Document: 1.2 Supplement

-Limit Theorems

--Limit Theorems

--Document:Limit Theorems

--Document: 1.3 Supplement

-Limits Involving Trigonometric Functions

--Limits Involving Trigonometric Function

--Document:Limits Involving Trigonometric Function

--Document: 1.4 Supplement

-Limits at Infinity, Infinite Limits

--Limits at Infinity, Infinite Limits

--Document:Limits at Infinity; Infinite Limits

--Document: 1.5 Supplement

--Document: 1.5 supplement 2

-Continuity of Functions

-- Continuity of Functions

--Document:Continuity of Functions

--Document: 1.6 supplement

-Chapter Review

--Document: chapter 1 supplement

-Assignments for Chapter 1

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 1

--Discussion Topics of Chapter 1

-Homework and Answer of Chapter 1

--Homework for Chapter 1

--Answer for Chapter 1

Homework 1

-Homework 1

--Homework 1

Chapter 2 The Derivative

-Two Problems with One Theme

--此章节内容为自学模块

-The Derivative

--The Derivative

--Document: The Derivative

--Supplement:The Derivative

-Rules for Finding Derivatives

--Rules for Finding Derivatives

--Document: Rules for Finding Derivatives

--Supplement: Rulesfor Finding Derivatives

-Derivate of Trigonometric Functions

--此章节内容为自学模块

--Supplement: Derivatives of Trigonometric Functions

-The Chain Rule

--The Chain Rule

--Document: The Chain Rule

--Supplement: The Chain Rule

-Higher-Order Derivative

--Higher-Order Derivative

--Document: Higher-Order Derivatives

--Supplement: Higher-Order Derivatives

-Implicit Differentiation

--Implicit Differentiation

--Document: Implicit Differentiation

--Supplement: Implicit Differentiation

-Related Rates

--此章节内容为自学模块

-Differentials and Approximations

--此章节内容为自学模块

--Supplement: Differentials and Approximations

-Chapter Review

--此章节内容为自学模块

-Assignments for Chapter 2

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 2

--Discussion Topics of Chapter 2

-Homework and Answer of Chapter 2

--Homework for Chapter 2

--Answer for Chapter 2

Homework 2

-Homework 2

--Homework 2

Chapter 3 Applications of the Derivative

-Maxima and Minima

--Maxima and Minima

--Document: Maxima and Minima

--Supplement:Maxima and Minima

-Monotonicity and Concavity

--Monotonicity and Concavity

--Document: Monotonicity and Concavity

--Supplement: Monotonicity and Concavity

-Local Extrema and Extrema on Open Intervals

--Local Extrema and Extrema on Open Intervals

--Document: Local Extrema and Extrema on Open Intervals

--Supplement: Local Extrema and Extrema on Open Intervals

-Practical Problems

--Practical Problems

--Document: Practical Problems

--Supplement: Practical Problems

-Graphing Functions Using Calculus

--此章节内容为自学模块

-The Mean Value Theorem for Derivatives

--The Mean Value Theorem for Derivatives

--Document: The Mean Value Therorem for Derivatives

--Supplement:The Mean Value Therorem for Derivatives

-Solving Equations Numerically

--此章节内容为自学模块

--Supplement:Antiderivatives

-Anti-derivatives

--此章节内容为自学模块

-Introduction to Differential Equations

--此章节内容为自学模块

-Chapter Review

--此章节内容为自学模块

--Supplement: Supplement for Chapter 3

-Assignments for Chapter 3

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 3

--Discussion Topics of Chapter 3

-Homework and Answer of Chapter 3

--Homework for Chapter 3

--Answer for Chapter 3

Test 1

-Test 1

--Test 1

Chapter 4 The Definite Integral

-Introduction to Area

--此章节内容为自学模块

--Supplement: Introduction to Area

-The Definite Integral

--The Definite Integral

--Document: The Definite Integral

--Supplement: The Definite Integral

-The First Fundamental Theorem of Calculus

--The First Fundamental Theorem of Calculus

--Document: The First Fundamental Theorem of Calculus

--Supplement: The First Fundamental Theorem of Calculus

-The Second Fundamental Theorem of Calculus and the Method of Substitution

--The Second Fundamental Theorem of Calculus and the Method of Substitution

--Document: The Second Fundamental Theorem of Calculus and the Method of Substitution

--Supplement: The Second Fundamental Theorem of Calculus and the Method of Substitution

-The Mean Value Theorem for Integrals and the Use of Symmetry

--此章节内容为自学模块

--Supplement: The Mean Value Theorem for Integrals and the Use of Symmetry

-Numerical Integration

--此章节内容为自学模块

-Chapter Review

--此章节内容为自学模块

-Assignments for Chapter 4

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 4

--Discussion Topics of Chapter 4

-Homework and Answer of Chapter 4

--Homework for Chapter 4

--Answer for Chapter 4

Homework 4

-Homework 4

--Homework 4

Chapter 5 Applications of the Integral

-The Area of a plane region

--The Area of a plane region

--Document: The Area of a Plane Region

-Volumes of Solids: Slabs, Disks

--Volumes of Solids: Slabs, Disks

--Document: Volumes of Solids Disk Method

-Volumes of Solids of Revolution: Shells

--Volumes of Solids of Revolution: Shells

--Document: Volumes of Solids Shell Method

-Length of a plane curve

--Length of a plane curve

--Document: Length of a Plane Curve

-Work and Fluid Force

--此章节为自学模块

-Moments and Center of Mass

--此章节为自学模块

-Probability and Random Variables

--此章节为自学模块

-Chapter Review

--此章节为自学模块

-Assignments for Chapter 5

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 5

--Discussion Topics of Chapter 5

-Homework and Answer of Chapter 5

--Homework for Chapter 5

--Answer for Chapter 5

Homework 5

-Homework 5

--Homework 5

Chapter 6 Transcendental and Functions

-The Natural Logarithm Function

--此章节为自学模块

-Inverse Functions

--此章节为自学模块

-The Natural Exponential Function

--此章节为自学模块

-General Exponential and Logarithm Function

--此章节为自学模块

-Exponential Growth and Decay

--此章节为自学模块

-First-Order Linear Differential Equations

--此章节为自学模块

-Approximations for Differential Equations

--此章节为自学模块

-The Inverse Trigonometric Functions and Their Derivatives

--此章节为自学模块

-The Hyperbolic Functions and Their Derivatives

--此章节为自学模块

-Chapter Review

--此章节为自学模块

Chapter 7 Techniques of Integration

-Basic Integration Rules

--Basic Integration Rules

--Document: Basic Integration Rules

-Integration by parts

--Integration by parts

--Document: Integration by Parts

-Some Trigonometric Integrals

--Some Trigonometric Integrals

--Document: Some Trigonometric Integrals

-Rationalizing Substitutions

--Rationalizing Substitutions

--Document: Rationalizing Substitutions

-Integration of Rational Functions Using Partial Fraction

--Integration of Rational Functions Using Partial Fraction

--Document: Integration of Rational Functions Using Partial Fractions

-Strategies for Integration

--此章节为自学模块

-Chapter Review

--此章节为自学模块

-Assignments for Chapter 7

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 7

--Discussion Topics of Chapter 7

-Homework and Answer of Chapter 7

--Homework for Chapter 7

--Answer for Chapter 7

Homework 7

-Homework 7

--Homework 7

Chapter 8 Indeterminate Forms and Improper Integrals

-Indeterminate Forms of Type

--此章节为自学模块

-Other Indeterminate Forms

--此章节为自学模块

-Improper Integrals: Infinite Limits of Integration

--Improper Integrals: Infinite Limits of Integration

--"Improper Integrals Infinite Limits of Integration" Document

-Improper Integrals: Infinite Integrands

--Improper Integrals: Infinite Integrands

--"Improper Integrals Infinite Integrands" Document

-Chapter Review

--此章节为自学模块

-Assignments for Chapter 8

--Assignment 1

--Assignment 2

-Discussion Topics of Chapter 8

--Discussion Topics of Chapter 8

-Homework and Answer of Chapter 8

--Homework for Chapter 8

--Answer for Chapter 8

Test 2

-Test 2

--Test 2

Discussion Topics of Chapter 8笔记与讨论

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