# Taylor's Inequality

• Apr 15th 2009, 02:34 PM
ahawk1
Taylor's Inequality
ok i dont know how to find the error bound plz help?
http://www.webassign.net/www32/symIm...7edd1305a2.gif

(a) Approximate f by a Taylor polynomial with degree n at the number a.
T2(x) = Enter a mathematical expression.
12+(1/4)*(x-4)-(1/64)*(x-4)^2

(b) Use Taylor's Inequality to estimate the accuracy of the approximation f http://www.webassign.net/images/apx.gif Tn(x) when x lies in the given interval. (Round the answer to six decimal places.)

i think i find M to be .001953125 to use in the formula (M/(n+1)!)|x-a|^n+1 but i dont know what to do on this anyone help? THANKS!
• Apr 15th 2009, 02:46 PM
icemanfan
Quote:

Originally Posted by ahawk1
ok i dont know how to find the error bound plz help?
http://www.webassign.net/www32/symIm...7edd1305a2.gif

(a) Approximate f by a Taylor polynomial with degree n at the number a.
T2(x) = Enter a mathematical expression.
12+(1/4)*(x-4)-(1/64)*(x-4)^2

(b) Use Taylor's Inequality to estimate the accuracy of the approximation f http://www.webassign.net/images/apx.gif Tn(x) when x lies in the given interval. (Round the answer to six decimal places.)

i think i find M to be .001953125 to use in the formula (M/(n+1)!)|x-a|^n+1 but i dont know what to do on this anyone help? THANKS!

I believe the approximation of the function using a Taylor polynomial of degree 2 should be:

$\displaystyle 2 + \frac{x - 4}{4} - \frac{(x-4)^2}{64}$
• Apr 15th 2009, 02:53 PM
ahawk1
Quote:

Originally Posted by icemanfan
I believe the approximation of the function using a Taylor polynomial of degree 2 should be:

$\displaystyle 2 + \frac{x - 4}{4} - \frac{(x-4)^2}{64}$

i already had that in my answer up top but i need to know the error bound not that actual polynomial but thanks!