Question: 4. (15-20 points) (Note corrections!) (a) Find the radius, R, and interval of convergence for the power series n+1 5 . . 2n 16 n=1

4. (15-20 points) (Note corrections!) (a) Find the radius, R, and interval of convergence for the power series n+1 5 . . 2n 16 n=1 (b) Let f be the function defined by the series above on (- R, R). Find a power series expansion in (-R, R) for the unique an- tiderivatve F for f with F(0) = -1. (c) Determine the interval of convergence for F. (d) Extra Credit: Find elementary expressions for the functions f and F above. 4. Let f(x) = xe-2 (a) Find f's Taylor series about 0. (b) What is f(10) (0)

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