# error bound taylor polynomial

• May 2nd 2009, 10:57 PM
diroga
error bound taylor polynomial
Quote:

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]
The formual for this type of thing is
$|f(x) - P_n(x)| \leq \frac {K_{n + 1}} {(n + 1)!}|x - x_0|^{n + 1}$

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

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

is this correct?
• May 3rd 2009, 12:35 AM
CaptainBlack
Quote:

Originally Posted by diroga
The formual for this type of thing is
$|f(x) - P_n(x)| \leq \frac {K_{n + 1}} {(n + 1)!}|x - x_0|^{n + 1}$

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

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

is this correct?

More or less, but you need to improve your notation and explain what things are.

CB