Good afternoon,

I think I can finally wrap my head around Taylor (& Maclaurin) polynomials. However, I seem to really be struggling with the error bounds. I am looking for an error bound of $\displaystyle <10^{-4}$ for the $\displaystyle n^{th}$ Maclaurin polynomial of $\displaystyle f(x)=e^x$ for $\displaystyle x=2$.

I'm not even sure I know how to set this up. Should it be simply:

$\displaystyle

\frac{|2|^{n+1}}{(n+1)!}<10^{-4}

$

If this is what it should be, can someone explain why (or point me to some "easy to digest" reading)?