Use the following form of the error term

$\displaystyle

R_{n+1}(x) = \frac{f^{n+1}(c)}{(n+1)!} x^{n+1}

$

where c is between 0 and x, to determine in advance the degree of Taylor polynomial at a = 0 that would achieve the indicated accuracy in the interval [0,x] for...

... $\displaystyle

f(x) = e^x, x = 2, error < 10^{-3}

$

(Do not compute Taylor polynomial.)

Thanks for the help!