July 2023
Beginner to intermediate
304 pages
6h 41m
English
Content preview from Calculus II Workbook For Dummies
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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 ...
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