Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 56, Problem 33AR
To determine

The Length 'x'.

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Classify the singularities for the following functions at the given point. at a = (a) f(z) = 1 (2 sin z-1)² (b) f(z) = exp(4)-1 at 0 and at a = (c) f(z) = 1-cosh z at a=0 2 In the case of a pole, indicate the order of the pole and its residue.
Determine all functions f analytic in the open unit disc || < 1 which satisfy in addition f(0) = 1 and |f(z)|≥ 1 whenever || < 1. Justify your answer.
Deduce the Laurent expansion for f(z) = 22(2-3)2 in the annulus 0 < |z3|< 3.

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