Find the Taylor series (write a summation if possible) about the indicated center and determine the interval of convergence.

g(x)= x^3-x+1 c=1

Printable View

- May 2nd 2006, 11:00 AMbobby77need help!
Find the Taylor series (write a summation if possible) about the indicated center and determine the interval of convergence.

g(x)= x^3-x+1 c=1 - May 2nd 2006, 11:11 AMTD!
The Taylor series of a polynomial is the polynomial itself!!

You can still write the summation and possibly verify this of course. - May 2nd 2006, 01:13 PMtopsquarkQuote:

Originally 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, 01:21 PMTD!Quote:

Originally Posted by**topsquark**

So we find the same after all. This will always be the case for polynomials. - May 2nd 2006, 01:25 PMtopsquarkQuote:

Originally Posted by**TD!**

-Dan - May 2nd 2006, 01:27 PMTD!
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.