- 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
multiplying Taylor
polynomials for and
?

2006-04-10