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Show in two ways that the function ln(x2 + y 2 ) is

Complex Variables and Applications | 9th Edition | ISBN: 9780073383170 | Authors: James Ward Brown ISBN: 9780073383170 169

Solution for problem 3.30 Chapter Chapter 3

Complex Variables and Applications | 9th Edition

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Complex Variables and Applications | 9th Edition | ISBN: 9780073383170 | Authors: James Ward Brown

Complex Variables and Applications | 9th Edition

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Problem 3.30

Show in two ways that the function ln(x2 + y 2 ) is harmonic in every domain that docs not contain the origin.

Step-by-Step Solution:
Step 1 of 3

4.2 What Derivatives T ells Us I. What first derivatives tells us Increasing/Decreasing Test (I/D Test)  If f ‘ > 0 on interval  f is increasing on the interval  If f ‘ < 0 on interval  f is decreasing on the interval  F is decreasing on (-5,-2) (0,5)  F ‘ < 0  F is increasing on (-2,0)  F ‘ > 0  Corner points f ‘ DNE o F ‘ (-2) DNE, F ‘ (0) DNE  F is increasing on (-4,-3) (-1,1)  f ‘ < 0  F is decreasing on (-3,-1) (2,2)  f ‘ > 0  F ‘ (-3) = f ‘ (-1) = f ‘ (1) = 0 EXAMPLE 1: Sketching a function f(x) continuous on its domain (- ,) satisfying the following conditions. (1) F ‘ > 0 on (- , 0), (4,6) and (6, )  [ f increasing on (- , 0), (4,6) and (6, ) ] (2) f ‘

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Chapter Chapter 3, Problem 3.30 is Solved
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Textbook: Complex Variables and Applications
Edition: 9
Author: James Ward Brown
ISBN: 9780073383170

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Show in two ways that the function ln(x2 + y 2 ) is