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- Verify that substitution and multiplication work as described
above to generate Taylor series (with base point a=0) for the
following functions. That is,
compare the Taylor polynomials for various orders obtained directly
with those obtained by substitution, multiplication, or division.
- Use substitution followed by integration to generate the first
three terms in the Taylor series with base point for
. Start with the series for .
- Can you find the sum of the following series?
(Hint - differentiate the series for , then multiply by a
power of .)
- In the background section we only considered multiplication of
series by polynomials. Suppose you wanted to generate the Taylor
polynomial of order ten with base point for the function
. Can you do this by
polynomials for and
William W. Farr