# 7.3 Taylor Series

In this lesson, you will learn about Taylor series.

### Lesson Objectives

• Construct the Taylor (or Maclaurin) series for a differentiable function.
• Determine the radius and interval of convergence of a constructed Taylor (or Maclaurin) series.
• Derive the formula for the Binomial Series using the Taylor (Maclaurin) process.
• Establish convergence of a Taylor (or Maclaurin) Series.
• Estimate remainders for Taylor (or Maclaurin) Series.

### Lesson Content

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

1. YouTube video: Maclauren and Taylor Series Intuition
2. YouTube video: Deriving the Taylor Series Expansion
3. YouTube videos: Taylor and Maclaurin Series
Example 1:

Example 2:

4. YouTube videos: The Binomial Series
Example 1:

Example 2:

5. YouTube videos: Taylor’s Remainder Theorem – Finding the Remainder
Example 1:

Example 2:

Example 3:

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.

### 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. Maclaurin and Taylor Series
2. Exercises for Taylor Series and Laurent Series
Note: do problems 1, 2, and 3.