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Math Help - Taylor Polynomial

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    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.
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    Re: Taylor Polynomial

    Any help would be appreciated.
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    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*}.
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