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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online