(Calculus 3) (Please Clear hand writing)
1. Find the gradient field for the potential function Ï(x, y, z) = x + e y + xyz
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(Calculus 3) (Please CLEAR hand writing)
1. Consider the conservative vector field F¯ = h2xy, 2yz + x 2 , 2z + y 2 ion R 3 . Find a potential function for this field.
(Calculus 3)(Please CLEAR hand writing)
1. Calculate the line integral Z C âÏ. dr, where Ï(x, y, z) = âxy + yz + zx, and C is the curve ¯r(t) = hsin t, cost,sin tifor 0 ⤠t ⤠2Ï.
1. Determine if the vector field F¯ = hy â z, x â z, x â yiis conservative. After showing all your work, give a clear YES/NO conclusion.