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Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $

$ f(x) = xe^{-x} $

$$\sum_{n=1}^{\infty}(-1)^{n-1} \frac{x^{n}}{(n-1) !}$$

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Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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