QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) +iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(z) 2. Find f'(2) at these points. Show all working. Hence, determine where f is analytic.

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.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 45E
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QUESTION 3
(3.1) Find the analytic function f(z) = u(x, y) + iv(x, y) given that u(x, y) = sin x coshy and
z = x+iy.
(3.2) Let f(2)=Ln(z), where -π/2 < Arg(2) < π/2. Find f'(z) at these points. Show all
working. Hence, determine where f is analytic.
Transcribed Image Text:QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) + iv(x, y) given that u(x, y) = sin x coshy and z = x+iy. (3.2) Let f(2)=Ln(z), where -π/2 < Arg(2) < π/2. Find f'(z) at these points. Show all working. Hence, determine where f is analytic.
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