Using a power series to estimate a function

[lindsaygilber]

I'm having a problem with estimating a function using a power series... the problem is

Use the power series for f(x)= (5+x)^(1/3) to estimate 5.08^(1/3) correct to four decimal places.


I found all the derivatives of f(x) but i'm not sure how to make it into a power series or what form to use for a cubic root...
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Durden]

I believe if you use a Taylor Series expansion(which I believe is a power series), you should be able to approximate it using this formula:

http://upload.wikimedia.org/math/6/c/8/6c81bd7e1ffe0d67ce7a348f7fec25ea.png

[lindsaygilber]

thank you!