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Math Help - Need help with approximation using Taylor's Theorem

  1. #1
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    Need help with approximation using Taylor's Theorem

    Please help with the following:

    Determine the accuracy of the following approximation, using Taylor's Theorem. There can be more than one correct answer depending on your value for M, but use a reasonably small M.

    e = 1+1+1/2!+1/3!+1/4!+1/5!
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  2. #2
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    Re: Need help with approximation using Taylor's Theorem

    Do you know what "Taylor's theorem" is?
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  3. #3
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    Re: Need help with approximation using Taylor's Theorem

    Yes, I need help applying it with the M value from the remainder estimation theorem.
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  4. #4
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    Re: Need help with approximation using Taylor's Theorem

    Hi kimsanders82,

    I think HallsofIvy is just trying to figure out where you're stuck, and the place to start with this problem is Taylor's theorem.

    Here's what the first step looks like: You want to estimate the value of the function e^x. Taylor's theorem gives:

    e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!} +\frac{x^4}{4!}+\frac{x^5}{5!}+R(x)

    where R(x)=...

    If you understand how to get from the general form of Taylor's theorem to this expression, you should be able to say what R(x) is. The M comes in when you try to estimate what R(x) is (when x=1, of course).

    Hope this helps.

    - Hollywood
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