Suppose that a function f has a power series expansion centered at x = 0, of the form f(x) = Σoana", with positive radius of convergence R > 0. Explain why, necessarily, the coefficients in this expansion are given by an = f(n) (0) n! 7 n = 0, 1, 2, ....

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A: Note: As per our guidelines, we can solve first three subparts. Please repost remaining parts.

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Q: 3. Without examining the convergence, find a power series generated by 1 f(x) =-at c = 5

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