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Finding the MacLaurin Series of a function

  1. Sep 23, 2012 #1
    I have to find the Maclaurin series of:
    (1) f(x)=cos(x)+x,
    (2) g(x)= cos(x^2)+x^2
    (3) h(x)=x*sin(2x).


    I'm stuck at the first one, I kind of understand the concept of how P(0)=f(0)+f'(0)x+(f''(0)x^2)/2+. . .
    What it gave me when I started calculating the value of the fn was this:
    f(0)=cos(0)+0=1
    f'(0)=-sin(0)=0
    f''(0)=-cos(0)=0

    And the pattern kept repeating as follows: 1,0,-1,0,1,0,-1,0.

    So when I want to write the mclaurin series, should it come out as?
    P(x)=Ʃ(x2n(-1)n)/n!

    As for the other problems, I really don't know how to start
     
  2. jcsd
  3. Sep 23, 2012 #2
    You mean -cos(0) = -1.

    Yes, you should get somewhat that pattern. Actually, you are close with the answers you have. It's not x^(2n)(-1)ⁿ/n! since x^(2n) doesn't occur in (cos(x) + x) altogether! You can only express cos(x) as the Maclaurin series.

    See: http://www.wolframalpha.com/input/?i=cos(x)

    You should get the answer.
     
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