1. ## Taylor polynomial

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

a calculator.

2. Given $\displaystyle f(x) = e^{x}$:

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

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

So simply plug 1/2 it in.

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

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