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Solved: Power series for derivativesa. Differentiate the
Chapter 8, Problem 22E(choose chapter or problem)
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