5. Use Cauchy-Riemann conditions to determine which of the following functions are differentiable and evaluate the derivatives if they exist. (a) a3 – 3x2 – 3ry² + 3y? + i(3x²y – 6xy – y³). (b) [z – (2 + i)]².
5. Use Cauchy-Riemann conditions to determine which of the following functions are differentiable and evaluate the derivatives if they exist. (a) a3 – 3x2 – 3ry² + 3y? + i(3x²y – 6xy – y³). (b) [z – (2 + i)]².
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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![5. Use Cauchy-Riemann conditions to determine which of the following functions are differentiable and
evaluate the derivatives if they exist.
(a) a³ – 3a? – 3ry? + 3y? + i(3x²y – 6xy – y³).
(b) [z – (2+ i)]².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9c4eba8-6404-4f66-8deb-9e8cf1f0b54c%2F3c30e050-a782-42b1-9cb9-13f9ca3127be%2Fgrlhhss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Use Cauchy-Riemann conditions to determine which of the following functions are differentiable and
evaluate the derivatives if they exist.
(a) a³ – 3a? – 3ry? + 3y? + i(3x²y – 6xy – y³).
(b) [z – (2+ i)]².
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Transcribed Image Text:The average production cost for major movies is 66 million dollars and the standard deviation is 18 million
dollars. Assume the production cost distribution is normal. Suppose that 50 randomly selected major
movies are researched. Answer the following questions. Give your answers in millions of dollars, not
dollars. Round all answers to 4 decimal places where possible.
Transcribed Image Text:b. What is the distribution of ? ~ N
c. For a single randomly selected movie, find the probability that this movie's production cost is
between 67 and 71 million dollars.
d. For the group of 50 movies, find the probability that the average production cost is between 67 and
71 million dollars.
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