Consider the function f: R→ R given by 0 if x ≤0 ) = { 2 - 11/2² e-1/² if x > 0 f(x) is infinitely-differentiable function. Explain why the infinitely-differentiable function f Σ E ax" 11 n=0 cannot have a power series expansion centered at x = 0 of the form f(x) with positive radius of convergence R > 0. =

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