1. Consider the function f(z) = 3z? a. Determine u(x, y)

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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Please answer 1a, 1b, and 1c with details on how to do it. 

It will be in the image. Make hand writing legible please. 

 

Thank you. 

Cauchy Riemann: Show u, = vy, & – uy = v, are satisfied so that f can be concluded to be analytic
(0, 1)
90°
30
of
0, 2n
0이 (1,0)
f (z)
9 Tz- zo)m+1
2πί
dz =
f(m) (zo)
т!
1. Consider the function f (z) = 3z?
a. Determine u(x, y)
b. Determine v(x,y)
c. Determine ux
d. Determine Uy
e. Determine vx
f. Determine
Vy
g. Finally, is f(z) is analytic?
Transcribed Image Text:Cauchy Riemann: Show u, = vy, & – uy = v, are satisfied so that f can be concluded to be analytic (0, 1) 90° 30 of 0, 2n 0이 (1,0) f (z) 9 Tz- zo)m+1 2πί dz = f(m) (zo) т! 1. Consider the function f (z) = 3z? a. Determine u(x, y) b. Determine v(x,y) c. Determine ux d. Determine Uy e. Determine vx f. Determine Vy g. Finally, is f(z) is analytic?
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