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
Actually, no it isn't quite the same.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:
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.