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Chapter 8: Power Series

Expert-verified
Calculus
Pages: 659 - 706
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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359 Questions for Chapter 8: Power Series

  1. Read the section and make your own summary of the material.

    Found on Page 679

  2. Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition or description with a graph or an algebraic example.

    Found on Page 703

  3. The Calculus of Power Series: Let \(\sum_{k=0}^{\infty }a_{k}\left ( x-x_{0} \right )^{k}\) be a power series in \(x-x_{0}\) that converges to a function \(f(x)\) on an interval \(I\).

    Found on Page 703

  4. Interval of convergence and radius of convergence: Find the interval of convergence and radius of convergence for each of the given power series. If the interval of convergence is finite, test the series for convergence at each of the endpoints of the interval.

    Found on Page 703

  5. Interval of convergence and radius of convergence: Find the interval of convergence and radius of convergence for each of the given power series. If the interval of convergence is finite, test the series for convergence at each of the endpoints of the interval.

    Found on Page 703

  6. Find third-order Maclaurin or Taylor polynomial for the given function about the indicated point.

    Found on Page 704

  7. If fis a function such that f(0)=−3and localid="1650438953513" role="math" f'(x)=2f(x)every value of x, find the Maclaurin series for f

    Found on Page 659

  8. Show that the power series ∑k=0∞ (−1)k2k+1x2k+1converges conditionally when x=1and when x=-1. What does this behavior tell you about the interval of convergence for the series?

    Found on Page 669

  9. What is the relationship between a Maclaurin series and a power series in x?

    Found on Page 679

  10. If f(x) is an nth-degree polynomial and Pn(x) is the nth Taylor polynomial for fat x0, what is the nth remainder Rn(x)? What is Rn+1(x)?

    Found on Page 692

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