Find the Maclaurin series for f(x) = e^(-x^2)
Note:
I don't know how to solve or work out so show all your work. And give the answer in EXACT FORM example 3pi, sqrt(2), ln(2) not decimal approximations like 9.424,1.4242,1232
surely you can do this one. Show some effort!
f = e^-x^2
f' = -2x e^(-x^2)
f" = (4x^2-2)e^(-x^2)
f"' = -x(2x^2-3)e^(-x^2)
and so on.
All the odd-order terms contain an x factor, so they go away, leaving
e^(-x^2) =∑ (-x^2)^k/k!
makes sense, since e^x = ∑x^k/k!