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The Calculus Lifesaver by Adrian Banner

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CHAPTER 26 _____________________________

Taylor and Power Series: How to Solve Problems

In this chapter, we’ll look at how to solve four different classes of problems involving Taylor series, Taylor polynomials and power series:

• how to find where power series converge or diverge;

• how to manipulate Taylor series to get other Taylor series or Taylor polynomials;

• using Taylor series or Taylor polynomials to find derivatives; and

• using Maclaurin series to find limits.

26.1 Convergence of Power Series

Let’s say we have a power series about x = a:

Images

As we saw in the case of geometric series, a power series might converge for some x and diverge ...

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