15_2_2 - C 2 ( z ) ⇒ C 2 ( z ) = z 3 3 . Thus φ( x , y ,...

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2. F = y i + x j + z 2 k , F 1 = y , F 2 = x , F 3 = z 2 . We have F 1 y = 1 = F 2 x , F 1 z = 0 = F 3 x , F 2 z = 0 = F 3 y . Therefore, F may be conservative. If F = φ , then ∂φ x = y , ∂φ y = x , ∂φ z = z 2 . Therefore, φ( x , y , z ) = Z y dx = xy + C 1 ( y , z ) x = ∂φ y = x + C 1 y C 1 y = 0 C 1 ( y , z ) = C 2 ( z ), φ( x , y , z ) = xy + C 2 ( z ) z 2 = ∂φ z =
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Unformatted text preview: C 2 ( z ) ⇒ C 2 ( z ) = z 3 3 . Thus φ( x , y , z ) = xy + z 3 3 is a potential for F , and F is conservative on 3 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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