1.2 Calculating Limits

In this lesson, you will learn about the properties/rules for calculating limits including trigonometric limits. Please note that this lesson does not cover limits involving exponential and logarithmic functions.

Lesson Objectives

Upon completion of the lesson 1.2, you will be able to:

• • Apply basic limit laws (sum, difference, constant multiple, product, quotient, and power).

  • Evaluate limits of polynomial, rational, root, and trigonometric functions.

  • Apply the squeeze (pinching) theorem.

Lesson Content

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

• 1. Calculation of Limits [University of Houston] (Using "limit laws" to compute limits.)

  2. YouTube videos: Squeeze Theorem

  3. Example 1:

• 1. Example 2:

• 1. Example 3:

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.

• • Limit Properties [Paul's Online Math Notes]

  • Computing Limits [Paul's Online Math Notes']

• Limits of Polynomial Functions [St. Charles College]

  • Please read pages 199 - 201, beginning with Examining the Concept (some properties of limits involving polynomial functions: evaluating basic limits, applying the limit laws to a polynomial function, determining the limit of a polynomial function.)

• Putting the Squeeze on a Limit [Karl's Calculus Tutor]

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. Evaluating Limits [University of Tennessee] (solutions provided)

  2. Quiz - Limit Theorems [University of Tennessee] (solutions provided)

  3. Limit Properties [Paul's Online Math Notes] (solutions provided)

  4. Computing Limits [Paul's Online Math Notes] (solutions provided)

Additional Resources

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

• 1. YouTube videos: Calculating a Limit By factoring and cancelling:

• 1. By getting a common:

• 1. By expanding and simplifying:

• 1. By multiplying by a conjugate:

• 1. Involving absolute value:

• 1. YouTube video: Squeeze Theorem

• 1. How Do You Evaluate Limits [Calculus-Help.com] from Calculus-Help (Flash-based tutorials). Note: The sound is a little muffled.

  2. YouTube videos: Limits of Functions Part 1:

• 1. Part 2:

• 1. Part 3:

• 1. Part 4:

• 1. Part 5:

• 1. Part 10:

• 1. Part 11:

• 1. YouTube video: Common Trigonometric Limit Technique (2)

1. Introduction to Limits [University of Tennessee]

   1. The Vocabulary of Polynomial Functions [The Math Page] Review definitions and terminology.