Find the first three terms of the Maclaurin series for `xe^(-x)` Consider that it is centered at x = 0. 



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Posted on (Answer #1)

Maclaurin series of infinitely differentiable function `f` is defined as

`f(x)=sum_(n=0)^infty(f^((n))(0))/(n!)x^n=f(0)+(f'(0))/(1!)x+(f''(0))/(2!)x^2+cdots`` `

1st term

`f(0)=0e^0=0` <-- First term

2nd term



`1/(1!)x=x`  <-- Second term

3rd term



`-2/(2!)x^2=-x^2`  <-- Third term

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