6. Consider the function f: R → R defined by 0 if x = 0, if x = 0. f(x) = { e x2 Show that this function is infinitely f(n) (0) = 0 differentiable on R and for all n ≥ 1. Deduce that the Taylor series of f at 0 converge for all x E R. Show that the sum of the Taylor series is only equal to f(x) when x = = 0.

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