Corrig Quizz
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M J M A U D ℓℓ ℓ L S B ℓ A F ℓ S ℓI A L M D S T X A M N D T. D. E f (x, y ) = e x 2 −y 2 sin(2xy). f f ′ x (x, y ) = (2x sin(2xy) + 2 y cos(2xy)) e x 2 −y 2 , f ′′ x 2 (x, y ) = (4x 2 − 4y 2 + 2) si n(2 xy) + 8xy cos(2xy) e x 2 −y 2 . f ′ y (x, y ) = (−2y sin(2xy) + 2x cos(2 xy)) e x 2 −y 2 , f ′′ y 2 (x, y ) = (−4x 2 + 4y 2 − 2) sin(2 xy) − 8xy cos(2xy) e x 2 −y 2 . ∆f (x, y ) = f ′′ x 2 (x, y ) + f ′′ y 2 (x, y ) = 0 f R 2 . E C C (z = x + iy x y f (z ) = (2x 2 − 3x − 3iy) + i(4xy + 2 iy 2 ). f (z ) = (2x 2 − 3x − 3iy) + i(4xy + 2iy 2 ) = (2x 2 − 3x − 2y 2 ) + i(4xy − 3y ) = P (x, y ) + iQ(x, y ). f P Q P ′ x (x, y ) = Q ′ y (x, y ), P ′ y (x, y ) = −Q ′ x (x, y ). P ′ x (x, y ) = (2x 2 − 3x − 2y 2 ) ′ x = 4x − 3, Q ′ y (x, y ) = (4xy − 3y ) ′ y = 4x − 3, P ′ y (x, y ) = (2x 2 − 3x − 2y 2 ) ′ y = −4y, Q ′ x (x, y ) = (4xy − 3y ) ′ y = 4y, f C. f (z ) = 2z 2 − 3z M
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7/21/2019 Corrig Quizz
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