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solve For each of the following vector fields F, decide whether it is conservati

ID: 3342006 • Letter: S

Question

solve

For each of the following vector fields F, decide whether it is conservative or not. Type in a potential function f (that is, f = F). If it is not conservative, type N. F (x, y) = (-8x - 5y)i + (-5x + 8y) j f (x, y) = F (x, y) = -4yi - 3xj f (x, y) = F (x, y, z) = -4xi - 3yj + k f(x, y, z) = F (x, y) = (-4 sin y)i + (-10_y - 4x cos y)j f (x, y) = F (x, y, z) = -4x2i - 5y2j + 4z2k f(x, y, z) = Note: Your answers should be cither expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

Explanation / Answer

E. (-4/3)x^3 -(5/3) y^3 +(4/3)z^3