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Math Help - Taylor Polynomial for e^x

  1. #1
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    Taylor Polynomial for e^x

    I could really use some help with the following...Any guidance or hints are appreciated.

    Let f(x) := e^x.
    Show that the nth Taylor polynomial for f at 0 is
    T_nf(x) =\sum_{k=0}^{n}\frac{x^k}{k!}
    and the Lagrange Remainder is
    R_nf(x) = e^c\frac{x^{n+1}}{(n + 1)!} for some c between 0 and x.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    This is just a straightforward application of Taylor's theorem, using the fact that (e^x)'=e^x and e^0=1.
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