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

Results 1 to 6 of 6

- May 2nd 2006, 11:00 AM #1

- Joined
- Sep 2005
- Posts
- 136

- May 2nd 2006, 11:11 AM #2

- Joined
- Jan 2006
- From
- Brussels, Belgium
- Posts
- 405
- Thanks
- 3

- May 2nd 2006, 01:13 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, 01:21 PM #4

- Joined
- Jan 2006
- From
- Brussels, Belgium
- Posts
- 405
- Thanks
- 3

- May 2nd 2006, 01:25 PM #5

- May 2nd 2006, 01:27 PM #6

- Joined
- Jan 2006
- From
- Brussels, Belgium
- Posts
- 405
- Thanks
- 3

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.