Prove that the function f(z2) defined by x*(1+ i) – y°(1 – 1) , (z ± 0) x² + y? f(z) = [0, (z = 0) is continuous and the Cauchy-Riemann equations are satisfied at the origin, yet f'(0) does not exist.
Prove that the function f(z2) defined by x*(1+ i) – y°(1 – 1) , (z ± 0) x² + y? f(z) = [0, (z = 0) is continuous and the Cauchy-Riemann equations are satisfied at the origin, yet f'(0) does not exist.
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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![Prove that the function f(z) defined by
x*(1 + i) – y°(1 – 1)
, (z ± 0)
f(z) =
x? + y?
[0, (z = 0)
is continuous and the Cauchy-Riemann equations are
satisfied at the origin, yet f'(0) does not exist.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfd6dbcc-5499-4ca1-984b-36a9c6624471%2F93e2d897-400a-438d-917c-6cf7c3d5e1c7%2Fmcovh8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove that the function f(z) defined by
x*(1 + i) – y°(1 – 1)
, (z ± 0)
f(z) =
x? + y?
[0, (z = 0)
is continuous and the Cauchy-Riemann equations are
satisfied at the origin, yet f'(0) does not exist.
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