Math 112 Calculus II Fall 2021 Homework #9 (Due: Wednesday, April 11} 1: Find the radius of convergence for each of the following power series {a} Z2119\" (b) 23391 (c) 237:3". \"=1 n=l 2 {15 points) . Let f(.r} = (1 f I}. (a) Express f(:r) as a power series on the interval (1, 1). 1 (b) Find a power series expression for f'(:r) = (1 _ I): on (1,1). (c) Use the result of (b) to nd the sum of the series m 1 go k!22k' 3. (15 points) (a) Find the radius, R, and interval of convergence for the power series co \"+1n_ E2 2334 E 2\": :r+4.r+3:r+l;r+ . (1)) Let f be the function dened by the series above on (R,R). Find a power series expansion in (R,R) for the unique an- tiderivatve F for f with FUD) = 1. (c) Determine the interval of convergence for F. (d) Extra Credit: Find elementary expressions for the functions f and F above. 4. Let HI) = 1:1212. (a) Find f's Taylor series about 0. (b) What is jimmy