Let f(x) = x ex 1 + x 2 . Although the formula for f is not defined at x = 0, we can
Chapter 0, Problem 63(choose chapter or problem)
Let f(x) = x ex 1 + x 2 . Although the formula for f is not defined at x = 0, we can make f continuous by setting f(0) = 1. If we do this, f has a Taylor series about x = 0. (a) Use a computer algebra system to find P10(x), the Taylor polynomial of degree 10 about x = 0 for f. (b) What do you notice about the degrees of the terms in the polynomial? What property of f does this suggest? (c) Prove that f has the property suggested by part (b).
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