Bounding the Error in Taylor Series Approximations for ln(1+x)

[francisg3]

Had a recent homework questions:
Find a bound for the error |f(x)-P3(x)| in using P3(x) to approximated f(x) on the interval [-1/2,1/2]
where f(x)=ln(1+x) abd P3(x) refers to the third-order Taylor polynomial.

I found the Taylor series of f(x) seen below:

x- x^2/2!+(2x^3)/3!

I know the Taylor series expression has a remainder which in this case would be the 4th order polynomial and beyond but I am completely lost beyond this. Any help would be greatly appreciated!

 

[LCKurtz]

Your formula for the remainder after n = 3 is

\frac{f^{(4)}(c)}{4!}(x-a)^4

Your a = 0. How large in absolute value can this be for x and c in your given interval?