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MATH 1320 : Spring 2014 Lab 5 Lab Instructor : Kurt VanNess Name: Score: Write all your solutions on a separate sheet of paper. 1. Give an example of power series with the following radius of convergence respectively: (a) R = 0 (b) R = 1 (c) R = ∞ 2. A function f is defined by f (x) = 1 + 2x + x2 + 2x3 + x4 + · · · i.e. the coefficients are c2n = 1 and c2n+1 = 2 for n ≥ 0. Determine the interval of convergence of the series and find an explicit formula for f (x) using geometric series. 3. (a) Show that the fucntion ∞ X xn g(x) = n! n=0 is a solution of the differential equation f 0 (x) = f (x). (b) Find the general solution to the differential equation f 0 (x) = f (x). Find g(0). Can we conclude g(x) = ex ? Page 1 of 1