# Taylor polynomial

• Apr 12th 2008, 01:30 PM
matty888
Taylor polynomial
Use the Taylor polynomial of order 3 for f(x) = e^x about x = 0 to

a calculator.
• Apr 12th 2008, 01:41 PM
o_O
Given $f(x) = e^{x}$:

$e^{x} \approx P_{3}(x) = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!}$

Note that $\sqrt{e} = e^{\frac{1}{2}}$

So simply plug 1/2 it in.
• Apr 12th 2008, 05:52 PM
ThePerfectHacker
Quote:

Originally Posted by matty888
Use the Taylor polynomial of order 3 for f(x) = e^x about x = 0 to

(Note $0).
$\frac{f^{(4)}(y)}{4!}(1/2)^4 = \frac{e^y}{384}\leq \frac{\sqrt{3}}{384}$.