1.3 Limits Involving Infinity

In this lesson, you will learn about limits at infinity.

Lesson Objectives

Upon completion of the lesson 1.3, you will be able to:

• • Identify any infinite limit from graphs or tables.

  • Find infinite limits analytically.

  • Identify a limit as x goes to positive or negative infinity from graphs or tables.

  • Find the limit as x goes to positive or negative infinity analytically.

  • Find horizontal or vertical asymptotes by using limits.

Lesson Content

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

• 1. Brightstorm videos: Infinite Limits and Vertical Asymptotes

• 1. Brightstorm videos: Limits and End Behavior

• 1. YouTube video: Calculating a Limit at Infinity with a Radical in the Expression

• 1. Some Trigonometric Limits [University of Houston] - Limits involving sine and cosine. Vertical asymptotes of tan, cot, sec, csc. View only pages 1 - 5.

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. Infinite Limits [Paul's Online Math Notes] (infinite limits and vertical asymptotes)

  2. Limits at Infinity, Part 1 [Paul's Online Math Notes] (limits at infinity and horizontal asymtotes)

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. Infinite limits [Paul's Online Math Notes]

  2. Limits at Infinity - Part 1 [Paul's Online Math Notes]

  3. Drill- Horizontal Asymptotes [University of Tennessee]

  4. Note: Only do problems #2, 4, 6, and 7.

  5. Vertical Asymptotes [University of Tennessee]Note: Disregard finding discontinuities and removable discontinuities. Just find the vertical asymptote(s) by finding appropriate limits

Additional Resources

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

• 1. YouTube video: Limits at infinity: Basic idea and shortcuts!

• 1. Limits Involving Infinity. Only view slides 1 - 7

  2. YouTube video: Calculus - Infinite limits

• 1. Lesson 7.1 - Vertical and Horizontal Asymptotes [Texas Instruments] (Vertical/horizontal asymptote definitions, comparing vertical and horizontal asymptotes, vertical/horizontal asymptotes from a table of values, finding a vertical asymptote analytically)