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.]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.]
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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