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...

 

[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:

 

[lindsaygilber]

thank you!