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Calculus analysis problem

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1. Show that u (x, y) is harmonic in some domain and find a harmonic conjugate v (x, y) when

(a) u (x, y) = 2x (1 - y)
(b) u (x, y) = 2x - x3 + 3xy2
(c) u (x, y) = sinh x?sin y
(d) u (x, y) = y / (x2 + y2)

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