Define f : 7. Let the power series -0 anc" have positive radius of convergence R. (-R, R) → R by f(r) = Eo anT". Suppose that there is a sequence (t;), in (–R, R) such that (i) lim; >0 ti = 0, (ii) ti 7 0 for all i, (iii) ƒ(t;) = 0 for all i. %3D Prove that f'(0) = 0.

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