The formual for this type of thing isQuote:

Use taylor's theorem to bound the error in approximating the function f(x) = e^x with the maclaurin series M_6(x) on the interval [-1,1]

$\displaystyle |f(x) - P_n(x)| \leq \frac {K_{n + 1}} {(n + 1)!}|x - x_0|^{n + 1}$

the max bound is $\displaystyle K_{n + 1} = e^1$ $\displaystyle x_0 =0, n = 6$

$\displaystyle \frac {e^1} {7!} |-1|^7 \approx 5.39 * 10^-4$

is this correct?