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13 Nov 2019
0O 1. (45 points) Determine the radius of convergence and the interval of convergence of 2n +1 Fully justify your answer, showing all your work, using proper notation, and citing any tests used and all their necessary conditions. Clearly state in your conclusion the radius of convergence and the interval of convergence 2. (30 points total) Clearly state your answers and show all your work. Parts c and d should be based on your answers to parts a and b. a. Find a power series representation for f(z) cent ered at 0 2r 3 b. Determine the radius of convergence of the power series in part a without applying the Ratio or Root test and give a reason for your answer. c. Based on your answers to parts a and b, find a power series representation for g(r)- and state its radius of convergence. (Hint: How does g(r) relate to f(r)?) (2r +3)2 In(2r 3) d. Based on your answers to parts a and b, find a power series representation for h(z) = and state its radius of convergence. (Hint: How does h() relate to f(r)?)
0O 1. (45 points) Determine the radius of convergence and the interval of convergence of 2n +1 Fully justify your answer, showing all your work, using proper notation, and citing any tests used and all their necessary conditions. Clearly state in your conclusion the radius of convergence and the interval of convergence 2. (30 points total) Clearly state your answers and show all your work. Parts c and d should be based on your answers to parts a and b. a. Find a power series representation for f(z) cent ered at 0 2r 3 b. Determine the radius of convergence of the power series in part a without applying the Ratio or Root test and give a reason for your answer. c. Based on your answers to parts a and b, find a power series representation for g(r)- and state its radius of convergence. (Hint: How does g(r) relate to f(r)?) (2r +3)2 In(2r 3) d. Based on your answers to parts a and b, find a power series representation for h(z) = and state its radius of convergence. (Hint: How does h() relate to f(r)?)
Hubert KochLv2
6 Feb 2019