Let (x4/3y5/3 + ix5/3y4/3)/(x² + y²) if z 0, if z = 0. f(z): >= {(x²4/ :{ 0 Show that the Cauchy-Riemann equations hold at z = 0 but that f is not differen- tiable at this point. [HINT: Consider the difference quotient f(Az)/Az for Az → 0 along the real axis and along the line y = x.]
Let (x4/3y5/3 + ix5/3y4/3)/(x² + y²) if z 0, if z = 0. f(z): >= {(x²4/ :{ 0 Show that the Cauchy-Riemann equations hold at z = 0 but that f is not differen- tiable at this point. [HINT: Consider the difference quotient f(Az)/Az for Az → 0 along the real axis and along the line y = x.]
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 48E
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![Let
ƒ (2) = { (x4/3y5/³ +ix5/³y4/3)/(x² + y²) ifz±0,
if z = 0.
Show that the Cauchy-Riemann equations hold at z = 0 but that ƒ is not differen-
tiable at this point. [HINT: Consider the difference quotient f(Az)/Az for Az → 0
along the real axis and along the line y = x.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2c1c8f6-d0e0-4f37-9b09-6d91c3c70800%2Faf2e2083-d2da-4efc-a8a6-6448980b4ca7%2F60pbdxm_processed.png&w=3840&q=75)
Transcribed Image Text:Let
ƒ (2) = { (x4/3y5/³ +ix5/³y4/3)/(x² + y²) ifz±0,
if z = 0.
Show that the Cauchy-Riemann equations hold at z = 0 but that ƒ is not differen-
tiable at this point. [HINT: Consider the difference quotient f(Az)/Az for Az → 0
along the real axis and along the line y = x.]
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