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Example 7. Show that the function f(z) = u + iv, where f(2)= x³(1+i)-y³(1 - i) x² + y² is continuous and that Cauchy-Riemann equations are satisfited at the origin, yet f'(0) does not exist. ,2 #0 and f(0) = 0

Example 7. Show that the function f(z) = u + iv, where f(2)= x³(1+i)-y³(1 - i) x² + y² is continuous and that Cauchy-Riemann equations are satisfited at the origin, yet f'(0) does not exist. ,2 #0 and f(0) = 0

Advanced Engineering Mathematics
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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Example 7. Show that the function f(2)= u + iv, where 1 - f(z) = x³(1 + i) − y³(1 − i) x² + y² ,20 and f(0) = 0 is continuous and that Cauchy-Riemann equations are satisfited at the origin, yet f'(0) does not exist.
Transcribed Image Text:Example 7. Show that the function f(2)= u + iv, where 1 - f(z) = x³(1 + i) − y³(1 − i) x² + y² ,20 and f(0) = 0 is continuous and that Cauchy-Riemann equations are satisfited at the origin, yet f'(0) does not exist.
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