Lesson 6.2: Tangent Planes and Linear Approximation

In this lesson, you will study tangent planes, linear approximation, differential and related applications.

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.

Lesson Objectives

Upon completion of the lesson 6.2, you will be able to:

• Find tangent planes

• Apply linear approximation

• Use differential to approximate change

• Model and solve applications

Lesson Content

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

1. Tangent Plane [10:08]

   1. Source: bullcleo1 from YouTube

1. Verifying the Equation of a Tangent Plane to a Surface [5:12]

   1. Source: bullcleo1 from YouTube

1. Tangent Plane Approximations [12:15]

   1. Source: patrickJMT from YouTube

1. Tangent Planes | MIT 18.02SC Multivariable Calculus, Fall 2010 [9:01]

   1. Source: MIT from YouTube

1. Tangent plane approximation | MIT 18.02SC Multivariable Calculus, Fall 2010 [6:55]

   1. Source: MIT from YouTube

1. Application of Tangent Plane Approximation [11:20]

   1. Source: DrChrisTisdell from YouTube

1. Differentials of Functions of Two Variables [8:37]

   1. Source: bullcleo1 from YouTube

1. Applications of Differentials of Functions of Several Variables [10:40]

   1. Source: bullcleo1 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. Tangent Planes and Linear Approximations

2. Paul’s Online Math Notes

3. Differentials

4. Paul’s Online Math Notes

5. Tangent Planes and Linear Approximations

6. The Multivariable Linear Approximation

7. Explore more using other links at the bottom of the page.

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. Tangent Planes and Linear Approximation in Two Variables

2. You may need to click on the button “3D Linear Approximation” to load the demo. It may take a few seconds.

3. Section 4: Tangent Planes and Linear Approximations

Additional Resources

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

1. Tangent Planes and Linear and Approximation

2. HCM Mathematics Online Tutorial

3. 3.5 Tangent Planes and Linear Approximations

4. 15.4 Tangent Planes and Linear Approximations

Homework Assignment

Do Homework 6.2 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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