Lesson 5.2: Limits and Continuity

In this lesson, you will study limits and continuity of functions of two or more variables.

View all of the instructional videos, read the provided readings, and practice exercises/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided. It helps to review some of the techniques that you learned in Calculus I about evaluating limits.

Lesson Objectives

Upon completion of lesson 5.2, you will be able to:

• Evaluate limits of functions of several variables

• Determine continuity of functions of several variables

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

1. Limits of Functions of Two Variables [11:18]

   1. Source: bullcleo1 from YouTube

1. Multivariable Calculus: Showing a Limit Does NOT Exist [8:39]

   1. Source: patrickJMT from YouTube

1. Showing a Limit Does Not Exist [3:54]

   1. Source: MathDoctorBob from YouTube

   2. Similar to the previous example, but the presenter also does it in polar coordinates.

1. Multivariable Calculus – Showing a Limit DOES Exist Using Algebra (Conjugate) [5:01]

   1. Source: patrickJMT from YouTube

1. Limits in polar co-ordinates example [3:23]

   1. Source: DrChrisTisdell from YouTube

1. Limits doesn't exist 2 variable example [4:26]

   1. Source: DrChrisTisdell from YouTube

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

1. Limits

2. Paul’s Online Math Notes

3. 6. Limits and Continuity of Functions of Two Variables

4. Dr. Marcel B. Finan

5. Functions of Several Variables

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

1. Section 11.2: Limits and Continuity

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Functions of Several Variables: Limits and Continuity

2. Phillippe B. Laval

3. Math 53: Multivariable Calculus Worksheets

4. This set of worksheets doesn’t include solutions, but you can use it for both Calc 3 and 4 if you wanted some extra practice. It’s from UC Berkeley.

Homework Assignment

Do Homework 5.2 on MyMathLab.

Show Your Work Assignment

Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.

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