= Finding the residue with Laurent series expansion for two of the following functions:(1) (2²-2z+2)/(z-2) in the domain |z - 1| < 1.(2) 1) in the domain 0 < |z − 1| < 1.(3) (2-1) sinaround z = -2.

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Answered: = Finding the residue with Laurent…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5
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e(x-3)* - 1 (x-3)² 1) The continuous function fis defined by f(x) = of all orders at x = 3. = 3. (a) Write the first four nonzero terms and the general term of the Taylor series for g(x) = e(x-3)* about x = (Hint: Use the Maclaurin series for e.) for x3 and f(3) = 0. The function fhas derivatives (b) Use the Taylor series found in part (a) to write the first four nonzero terms and the general term of the Taylor series for fabout x = 3. (c) Use the ratio test to find the interval of convergence for the Taylor series found in part (b). (d) Use the Taylor series for fabout x = 3 to determine whether the graph of fhas any points of inflection.

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= Finding the residue with Laurent series expansion for two of the following functions: (1) (2²-2z+2)/(z-2) in the dómain |2 - 1| < 1. (2) (1) in the domain 0 < 2 - 1|< 1. (3) (z-1) sin around z = -2. +2