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Homework Help: Please help me with this Taylor series!

  1. Nov 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the Maclaurin series of the function f(x) = 5(x^2)sin(5x)

    2. Relevant equations


    3. The attempt at a solution
    I'm supposed to enter in c3-c7
    I already know that c4 and c6 are 0 because the derivative is something*sin(0)=0

    but for the odd numbered c's I am having problems...
    i know that the taylor series for sinx = [tex]\sum[/tex]((-1^n)*x^(2n+1))/(2n+1)!
    so i just substituted in 5x and multiplied by 5x^2 and got
    5 [tex]\sum[/tex] ((-1^n)*(5^(2n+1)*x^(2n+3))/(2n+1)!

    so for c3 i got 5(-1^3)(5^7)/(7)! = -5^8/7!
    but I am not getting the answer right for this. Can someone please explain what I am doing wrong.
  2. jcsd
  3. Nov 30, 2007 #2


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    Science Advisor

    c3 corresponds to n=0 in your series, not n=3 (because you have x^(2n+3), not x^n).
  4. Nov 30, 2007 #3


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    Homework Helper

    Putting n=3 in your formula does not give you c3. It gives you c9. If you want to find ck then the power of x in the formula should be k. The power of x in the formula is 2n+3. So if you want to find c3 set 2n+3=3. You want n=0.
  5. Nov 30, 2007 #4
    Wow, thank you guys! That actually makes sense. I asked my teacher and he wasn't much help, but I guess he didn't know that I was plugging in the wrong n's. I have the right answers now. Thanks again :)
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