Let .
Find the MacLaurin polynomial of degree 5 for .
Use this polynomial to estimate the value of .
I don't understand this. For the MacLaurin polynomial do I take derivative until the 5th derivative?
Should be $\displaystyle 1+(-4x^4)+\frac{(-4x^4)^2}{2!}+\frac{(-4x^4)^3}{3!}...$
Then integrate to find the series for $\displaystyle F(x)$, just like Skeeter said. Note that you only need the first two terms of this sequence, since all the rest have $\displaystyle \text{deg}\geq5$.
$\displaystyle \int 1-4x^4\,dx=x-\frac{4x^5}{4}$