The Taylor series of a polynomial is the polynomial itself!!

You can still write the summation and possibly verify this of course.

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- May 2nd 2006, 12:00 PM #1

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- May 2nd 2006, 12:11 PM #2

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- May 2nd 2006, 02:13 PM #3Originally Posted by
**TD!**

The Taylor series for a function f(x) about a point x = c is:

The notation is meant to represent the nth derivative of f evaluated at x = c. This form is only correct, of course, assuming the series converges for a given f(x) and c.

In this case your function is going to be:

-Dan

- May 2nd 2006, 02:21 PM #4

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- May 2nd 2006, 02:25 PM #5

- May 2nd 2006, 02:27 PM #6

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I see what you mean, but the 'form' doesn't matter since the functions (the original result and the simplification to g(x) again) are completely the same.

I don't really see the use of this question, unless its intention is that the student sees that the taylor series of a polynomial is the polynomial again; by experimentally finding this through the formula like you did.