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The Calculus Lifesaver by Adrian Banner

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CHAPTER 24 _____________________________

Introduction to Taylor Polynomials, Taylor Series, and Power Series

We now come to the important topics of power series and Taylor polynomials and series. In this chapter, we’ll see a general overview of these topics. The following two chapters will deal with problem-solving techniques in the context of the material in this chapter. Here’s what we’ll look at first:

• approximations, Taylor polynomials, and a Taylor approximation theorem;

• how good our approximations are, and the full Taylor Theorem;

• the definition of power series;

• the definition of Taylor series and Maclaurin series; and

• convergence issues involving Taylor series.

24.1 Approximations and Taylor Polynomials

Here’s a nice fact: for ...

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