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Math Help - Expanding Sine cardinal with Taylor Series

  1. #1
    Junior Member
    Joined
    May 2010
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    Expanding Sine cardinal with Taylor Series

    Hi,
    I am trying to expand the sine cardinal (sin(x)/x) using the Taylor series around x=PI. Then I need to show that when x is near PI, the result is approx 0.0525.

    My problem is when working out the derivatives. f(0)=1 but f'(0) leads to cos(0)/0 which is infinity.

    Any hints please? thanks
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  2. #2
    Newbie
    Joined
    Apr 2012
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    london
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    Re: Expanding Sine cardinal with Taylor Series

    hmm, a few questions for you first.
    f = sin(x) / x
    then
    1. f(pi) = 0 surely? What do you mean you want to show its 0.0525?
    2. you are expanding around pi, why do you need f(0)?
    3. f'(0) = f'(x) at 0, and have you worked out f'(x)?
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