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(1 point)
Find a potential function for the following conservative vector fields. Use +C in your answers.
1. Vector Field \(\vec{F}(x, y, z) = (\cos z, 6y^2, -x \sin z)\) with potential function \(f(x, y, z) =\)
2. Vector Field \(\vec{F}(x, y, z) = (10xyz + 6 \sin x, 5x^2z, 5x^2y)\) with potential function \(f(x, y, z) =\)
Find the specific potential function for each of the above vector fields given the initial conditions:
1. If \(f(1, 0, 0) = 5\) then \(f(x, y, z) =\)
2. If \(f(0, 0, 0) = 0\) then \(f(x, y, z) =\)