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Find the Taylor series for $ f(x) $ centered at the given value of $ a. $ [Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0.$] Also find the associated radius of convergence.

$ f(x) = x^5 + 2x^3 + x, $ $a = 2 $

$f(x)=50+105(x-2)+92(x-2)^{2}+42(x-2)^{3}+10(x-2)^{4}+(x-2)^{5},$ $R=\infty$

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Campbell University

University of Nottingham

Idaho State University

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