In problem 1-4 determine whether the given field F is conservative. Is so, find f so that

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In problem 1-4 determine whether the given field F is conservative. Is so, find f so that F = ∇f; if not, state that F is not conservative.
1. F(x, y) = (10x - 7y) i - (7x - 2y)j
2. F(x, y) = (12x2 + 3y2 + 5y)i + (6xy - 3y2 + 5x)j
3. F(x, y) = (45x4y2 - 6y6 + 3)i + (18x5y - 12xy5 + 7)j
4. F(x, y) = (35x4 - 3x2y4 + y9)i + (4x3y3 - 9xy8)j
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Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

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