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Math 2260 HW #13 Due 10:10 AM Friday, April 12 Reading: Hass §9.8–9.9 Problems: Do the assignment “HW13” on WebWork. In addition, write up solutions to the following problems and hand in your solutions in class on Friday. 1. Consider the power series ∞ X 4n+1 (x − 2)n . n=0 (a) What is the interval of convergence of this series? (b) On this interval of convergence, what does the series converge to? 2. The 0th order Bessel Function is defined to be J0 (x) = ∞ X (−1)k x2k k=0 22k (k!)2 . (a) For what values of x is this function defined? (In other words, where does the series converge?) (b) Show that the series is a solution to the differential equation x2 J000 + xJ00 + x2 J0 = 0. 3. Find the Taylor series centered at x = π/4 of the function f (x) = cos x. 1