Solved: Power series for derivativesa. Differentiate the

Chapter 8, Problem 22E

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QUESTION:

Power series for derivatives

a. Differentiate the Taylor series about 0 for the following functions.

b. Identify the function represented by the differentiated series.

c. Give the interval of convergence of the power series for the derivative.

f(x) = cos x

Questions & Answers

QUESTION:

Power series for derivatives

a. Differentiate the Taylor series about 0 for the following functions.

b. Identify the function represented by the differentiated series.

c. Give the interval of convergence of the power series for the derivative.

f(x) = cos x

ANSWER:

Solution 22E

Step 1:

In this problem we have to find the power series for derivatives.

a. Differentiate the Taylor series about 0 for the following functions.

We have

The taylor series for with center 0 is

Differentiate, we get

         

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