1.1 Introduction to Limits and One-sided Limits

This lesson will provide you an intuitive understanding of limits and one-sided limits.

Lesson Objectives

Upon completion of the lesson 1.1, you will be able to:

• • Identify limits from graphs.

  • Identify limits from tables.

  • Visualize and understand one-sided limits.

Lesson Content

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

• 1. Brightstorm video: Limits – a numerical approach

• 1. Brightstorm video: One-sided and two sided limits

• 1. YouTube video: Finding limits from a graph

• 1. Brightstorm video: Limits – a graphical approach

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. Problems Leading to Limits [Paul's Online Math Notes]

2. The Limit [Paul's Online Math Notes]

3. One-sided Limits [Paul's Online Math Notes]

   1. Limits of Polynomial Functions [St. Charles College] (Please read pages 194 – 196.)

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. The Limit [Paul's Online Math Notes] (solutions provided

  2. One-Sided Limits [Paul's Online Math Notes] (solutions provided)

  3. Limits 1 [Khan Academy] (Checks your answer and also gives hints.) You must use Firefox, Chrome, Safari, or Internet Explorer 9. Graphical method.

Additional Resources

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

1. Chapter one: Limits and continuity [University of Houston]

   1. Please watch:

   2. - Lesson 1: What is a limit?

   3. - Lesson 2: When does a limit exist?

   4. YouTube video: Introduction to limits

• 1. YouTube video: Limit examples (part 1) – watch only until [6:30]

• 1. Limits and graphs [University of Houston], by [Selwyn Hollis from Department of Mathematics, University of Houston]

  2. The concept of limit from an intuitive, graphical point of view. Left and right-sided limits. Infinite one-sided limits and vertical asymptotes.