MTHSC 208 (Differential Equations)Dr. Matthew MacauleyHW 16Due Monday March 23rd, 2009(1) Use the ratio test to find the radius of convergence of the following power series:a.∞n=0(-1)nxn,b.∞n=01n+ 1(x-π)n,c.∞n=03n+ 1(x-2)n,d.∞n=012n(x-π)n,e.∞n=0(5x-10)n,f.∞n=01n!(3x-6)n.(2) Use the comparison test to find an estimate for the radius of convergence of each of thefollowing power series:a.∞n=01(2n)!x2n,b.∞n=0(-1)nx2n,c.∞n=112n(x-4)2n,d.∞n=0122n(x-π)2n.(3) Find the radius of convergence of the power series∞n=0(-1)n1(n!)2x22n.(4) The differential equation(1-x2)d2ydx2-xdydx+p2y= 0,wherepis a constant, is known as Chebyshev’s equation. It can be rewritten in the form
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