anonymous
  • anonymous
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion.] f(x)=x*e^(9x). Steps would be greatly appreciated
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
The maclaurin series for e^u is 1+x+[(u^2}/(2!)]+[(u^3}/(3!)]+[(u^4}/(4!)]... Now, let u=9x. Substitute it in. Then multiply the entire series by x (distribute). Err, wait. Using the defenition. I would parenthesis the x out and find the series for e^(9x). The formula for a maclaurin series is here:http://mathworld.wolfram.com/MaclaurinSeries.html So find the successive derivatives of e^(9x) and evaluate them at 0. Then substitute them in into the formula. x(Maclaurin series for e^(9x)). Then multiply though by x.

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