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Extra Credit Homework 11: Convergence of Power Series in Math 116 - Prof. Jeff Mermin, Assignments of Calculus

Information about the extra credit homework assignment for math 116, specifically section jeff mermin's assignment on the convergence of power series for various functions such as ex, sin x, cos x, ln(1 + x), 1 + x, and 1 + x^2, as well as arctan x. Students are required to have completed satisfactorily extra credit homework 9 and 10 and are encouraged to use the ratio test or the root test to determine the intervals of convergence for each power series.

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Pre 2010

Uploaded on 09/17/2009

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Math 116
Jeff Mermin’s section
Extra Credit homework 11: Convergence of Power Series
To have this assignment graded, you must have done a satisfactory job on
Extra Credit homework 9 and 10.
You can use the ratio test or the root test to answer all of these questions.
You may also be able to identify a metatheorem or two. Your answer should be
an interval.
1. At what xdoes the power series for exconverge?
2. At what xdoes the power series for sinxconverge?
3. At what xdoes the power series for cosxconverge?
4. At what xdoes the power series for ln(1 + x) converge?
5. At what xdoes the power series for 1
1+xconverge?
6. At what xdoes the power series for 1
1+x2converge?
7. At what xdoes the power series for arctanxconverge?

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Extra Credit homework 11: Convergence of Power Series^ Jeff Mermin’s sectionMath 116

To have this assignment graded, you must have done a satisfactory job onYou can use the ratio testExtra Credit homework 9 and 10. or the root test to answer all of these questions. You may also be able to identify a metatheorem or two. Your answer should bean interval.1. At what x does the power series for exconverge?

  1. At what x does the power series for sin x converge?
  2. At what x does the power series for cos x converge?
  3. At what x does the power series for ln(1 + x) converge?
  4. At what x does the power series for (^) 1+^1 x converge?
  5. At what x does the power series for (^) 1+^1 x 2 converge?
  6. At what x does the power series for arctan x converge?