Let fsxd H e21yx 2 0 if x 0 if x 0 (a) Use the definition of derivative to compute

Chapter 4, Problem 91

(choose chapter or problem)

Let fsxd H e21yx 2 0 if x 0 if x 0 (a) Use the definition of derivative to compute f9s0d. (b) Show that f has derivatives of all orders that are defined on R. [Hint: First show by induction that there is a polynomial pnsxd and a nonnegative integer kn such that f snd sxd pnsxdfsxdyxkn for x 0.]

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