(a) (5 points) What is the Taylor series of g(x) = centered at a = 0? (b) (5 points) Using (a), simply by replacing 2 wi

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A 5 Points What Is The Taylor Series Of G X Centered At A 0 B 5 Points Using A Simply By Replacing 2 Wi 1 (40.9 KiB) Viewed 41 times

(a) (5 points) What is the Taylor series of g(x) = centered at a = 0? (b) (5 points) Using (a), simply by replacing 2 with -26, derive the Taylor series of f(x) = 1 1+26 centered at a 0. (c) (5 points) Explain: f(x) is defined for all real numbers z. (d) (5 points) Explain: The Taylor series you derived in part (b) converges for x < 1 but diverges for x > 1, so the radius of convergence is 1. (e) (5 points) The radius of convergence you found in part (d) is not infinite because "something goes wrong with the function f(x) at distance 1 from the origin." Namely, there are complex numbers z with |z| = 1 for which f(z) is not defined. Give an example of such a complex number z.