Calculus II Workbook For Dummies

Chapter 17

Taylor and Maclaurin Series

IN THIS CHAPTER

Estimating functions using Maclaurin series

Improving estimates using Taylor series

I have to admit that, even as a math teacher, rewriting functions as infinite series seems magical to me. In this chapter, you get to see how some of this magic happens.

To begin, you discover how to express functions as Maclaurin series, which is a power series that’s a limited form of the more versatile but more complex Taylor series. Then, you proceed to the main event, which is expressing functions as Taylor series.

Expressing Functions as Maclaurin Series

You can express any infinitely differentiable function as a Maclaurin series using the following formula:

The notation means “the nth derivative of f.” To help make sense of this notation, here’s the expanded version of the Maclaurin series:

Q. Express the function sin x as a Maclaurin ...