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.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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.]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
