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Math Help - Using the Taylor Series of expansion and finding the radius of convergence

  1. #1
    Newbie andvaka's Avatar
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    Using the Taylor Series of expansion and finding the radius of convergence

    How do I go about solving this?

    Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that R(x) → 0.] f(x) = 6 cos x, a = 7π



    f(x) =



    Find the associated radius of convergence R.
    R =
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  2. #2
    MHF Contributor
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    Re: Using the Taylor Series of expansion and finding the radius of convergence

    Hint: 6cos(7π + x) = -6cos(x).
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    Re: Using the Taylor Series of expansion and finding the radius of convergence

    Quote Originally Posted by emakarov View Post
    Hint: 6cos(7π + x) = -6cos(x).
    Except that centring at \displaystyle \begin{align*} a = 7\pi \end{align*} means you are expanding \displaystyle \begin{align*} f(x - 7\pi) \end{align*}, not \displaystyle \begin{align*} f(x + 7\pi) \end{align*}. Won't make any difference though
    Thanks from emakarov
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