1. ## Taylor Polynomial

Spivak 4th Edition: Chapter 20, Problem 13
f(x) = ((e^x) - 1)/x , x not equal to 0
f(x) = 1, x = 0
a) Find the Taylor Polynomial of degree n for f at 0, compute f^(k)(0) [f differentiated k times at 0], and give an estimate for the remainder term Rn,0,f.
b) compute integral from 0 to 1 of f with error of less than 10^-4.
I haven't worked with any questions like this before so I'm unable to get started. Seeing this example worked fully would be enough to understand the topic.
~Many Thanks

2. ## Re: Taylor Polynomial

Any help would be appreciated.

3. ## Re: Taylor Polynomial

Look up the MacLaurin Series (Taylor Series centred at x=0) for \displaystyle \begin{align*} e^x \end{align*}, use this to get a series for \displaystyle \begin{align*} \frac{e^x - 1}{x} \end{align*}.