15_4_10 - C 2 ( z ) = z 2 + C . Thus φ = x 2 y + xz + z 2...

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10. F = ( axy + z ) i + x 2 j + ( bx + 2 z ) k is conservative if F 1 y = F 2 x a = 2 F 1 z = F 3 x b = 1 F 2 z = F 3 y 0 = 0 . If a = 2 and b = 1, then F = φ where φ = Z ( 2 xy + z ) dx = x 2 y + xz + C 2 ( y , z ) C 1 y + x 2 = F 2 = x 2 C 1 ( y , z ) = C 2 ( z ) dC 2 dz + x = F 3 = x + 2 z
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Unformatted text preview: C 2 ( z ) = z 2 + C . Thus φ = x 2 y + xz + z 2 + C is a potential for F ....
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