3.05.4.Literacy

# 3.05.4.Literacy - L.7 Write down the number that is 1 I 1 M...

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Approximation Authors: Bill Davis, Horacio Porta and Jerry Uhl ©1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 3.05 Barriers to Convergence LITERACY · L.1) At what point on the x-axis are the convergence intervals of expansions in powers of H x - 1 L centered? At what point on the x-axis are the convergence intervals of expansions in powers of H x + 5 L centered? · L.2) Use complex numbers and singularities to explain why, when you expand f @ x D = 1 I 1 + x 2 M in powers of x, you run into barriers at x = - 1 and x = 1. · L.3) Use complex numbers and singularities to explain why, when you expand f @ x D = ArcTan @ x D in powers of x, you run into barriers at x = - 1 and x = 1. Confused? Look at the tip below: D @ ArcTan @ x D , x D 1 1 + x 2 · L.4) Use complex numbers and singularities to explain why, when you try to expand f @ x D = x H 5 ê 2 L in powers of x, you must fail. · L.5) Give the convergence interval for the expansions of the following functions f @ x D in powers of H x - a L for the given choices of a : Ø f @ x D = 1 1 - x with a = 0 , Ø f @ x D = 1 1 - x with a = 4 , Ø f @ x D = e x with a = 0 , Ø f @ x D = Sin @ x D with a = 0 , Ø f @ x D = Sin @ x D with a = p , Ø f @ x D = Cos @ x D with a = 0 , Ø f @ x D = 1 + x with a = 0 , Ø f @ x D = x I 5 3 M with a = 1 , Ø f @ x D = ArcTan @ x D with a = 0 , and Ø f @ x D = 1 1 + x 2 with a = 1 . · L.6)

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3.05.4.Literacy - L.7 Write down the number that is 1 I 1 M...

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