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Using known Maclaurin series to approximate modification of original

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Recall that the Maclaurin series for sin(x) is [itex]\sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}[/itex].

    Use this formula to find the Maclaurin polynomial P5(x) for f(x)=xsin(x/2).

    2. Relevant equations



    3. The attempt at a solution

    I know that to approximate sin(x/2) with the Maclaurin polynomial for sinx, I just substitute x/2 for x. But for xsinx, since the Maclaurin series is approximating sinx, can I just substitute the series for sinx so that I get [itex]x\sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}[/itex]?
     
  2. jcsd
  3. Feb 20, 2013 #2
    Re: Using known Maclaurin series to approximate modification of origin

    yes you can :smile:
     
  4. Feb 20, 2013 #3

    CompuChip

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    Re: Using known Maclaurin series to approximate modification of origin

    Yes. You can make that better if you now sweep the x inside the sum. You may also want to include the summation bounds as you can sometimes simplify further by shifting them.
     
  5. Feb 20, 2013 #4
    Re: Using known Maclaurin series to approximate modification of origin

    Sorry, didn't see that I forgot the bounds. It's supposed to be from n=0 to infinity. Thanks for the help guys :)
     
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