5. Given examples of f, g and h satisfying the following properties: f (z) is continuous at z = 0 but not differentiable at z = 0, • g(z) satisfies Cauchy-Riemann equations at z = 0 but not differentiable at z = 0, • h(z) is differentiable at z = 0 but not analytic at z = 0. To get the full credit, you should verify that your example satisfies the given properties.

5. Given examples of f, g and h satisfying the following properties: f (z) is continuous at z = 0 but not differentiable at z = 0, • g(z) satisfies Cauchy-Riemann equations at z = 0 but not differentiable at z = 0, • h(z) is differentiable at z = 0 but not analytic at z = 0. To get the full credit, you should verify that your example satisfies the given properties.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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