Calculus II（2023 ）

王姝娜

目录

  • 1 Basic Information
    • 1.1 Course Description
    • 1.2 Course Syllabus
    • 1.3 Schedule
    • 1.4 Grading
    • 1.5 Textbook and Website
  • 2 Chapter 6 Application of Definite Integral
    • 2.1 Volume Using Cross-section
      • 2.1.1 Quiz 6.1
      • 2.1.2 Supplement
    • 2.2 Volume Using Cylinder Shell
      • 2.2.1 Quiz 6.2
    • 2.3 Arc Length
      • 2.3.1 Quiz 6.3
    • 2.4 Area of Surfaces of Revolution
      • 2.4.1 Quiz 6.4
    • 2.5 Supplement:Moments and Center of Mass
    • 2.6 Test-Ch6 Application of Integral
    • 2.7 Light Your Way
  • 3 Chapter 7 Integrals and Transcendental Functions
    • 3.1 Definition of Log and Exp
      • 3.1.1 Quiz 7.1
    • 3.2 Separable Differential Equation
      • 3.2.1 Quiz 7.2
    • 3.3 Video:Hypobolic Function
      • 3.3.1 Quiz 7.3
    • 3.4 Relative Rates of Growth
      • 3.4.1 Quiz 7.4
    • 3.5 Test-Ch7 Integrals and Transcendental Functions
    • 3.6 Light your way
  • 4 Chapter 8 Techniques of Integration
    • 4.1 Integration Warm up
      • 4.1.1 Quiz 8.1
    • 4.2 Integration by Parts
      • 4.2.1 Quiz 8.2
    • 4.3 Trigonometric Integrals
      • 4.3.1 Quiz 8.3
    • 4.4 Trigonometric Substitution
      • 4.4.1 Quiz 8.4
    • 4.5 Integration of Rational Function by Partial Functions
      • 4.5.1 Quiz 8.5
    • 4.6 Numerical Integration
      • 4.6.1 Quiz 8.7
    • 4.7 Improper Integral
      • 4.7.1 Quiz 8.8
    • 4.8 Probability
    • 4.9 Test-Ch8 Techniques of Integration
    • 4.10 Light your way
  • 5 Chapter 9 First-Order Differential Equation
    • 5.1 Solution,Slope Field,and Euler’s Method
      • 5.1.1 Quiz 9.1
    • 5.2 First-Order Differential Equation
      • 5.2.1 Quiz 9.2
    • 5.3 Application
      • 5.3.1 Quiz 9.3
    • 5.4 Graphical Solutions of Autonomous Equations
      • 5.4.1 Quiz 9.4
    • 5.5 Supplement:Systems of Equations and Phase Planes
    • 5.6 Test-Ch9 First-Order Differential Equations
    • 5.7 Light your way
  • 6 Chapter 10 Infinite Sequences and Series
    • 6.1 Sequence
      • 6.1.1 Quiz 10.1
    • 6.2 Infinite Series
      • 6.2.1 Quiz 10.2
    • 6.3 The Integral Test
      • 6.3.1 Quiz 10.3
    • 6.4 Comparison Tests
      • 6.4.1 Quiz 10.4
    • 6.5 Absolute Convergence；The Ratio and Root Tests
      • 6.5.1 Quiz 10.5
    • 6.6 Alternating Series and Conditional Converge
      • 6.6.1 Quiz 10.6
    • 6.7 Power Series
      • 6.7.1 Quiz 10.7
    • 6.8 Taylor and Maclaurin Series;Application
      • 6.8.1 Quiz 10.8
    • 6.9 Test-Ch10 Infinite Sequences and Series
    • 6.10 Light your way
  • 7 问卷调查
    • 7.1 问卷调查
Sequence
  • 1 学习目标
  • 2 学习视频

1. What is an infinite sequence? What does it mean for such a sequence to converge? To diverge?

 Give examples.

2. What is a monotonic sequence? Under what circumstances does such a sequence have a limit? 

Give examples.

3. What theorems are available for calculating limits of sequences?

 Give examples.

4. What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? 

Give an example.

5. What are the six commonly occurring limits in Theorem 5 that arise frequently when you work with sequences and series?