Question
Asked Dec 8, 2019
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Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)

F(x, y, z) = 3y2z3 i + 6xyz3 j + 9xy2z2 k

f(xyz) =

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Expert Answer

Step 1

To determine if the given field is conservative and find the potential function f(x,y,z).

Step 2

Given:

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F(x, y,z) = 3y²z'i+ 6xyz’ j +9.xy°z*k

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Step 3

Compute the curl of the vector field to det...

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V ×F = ôy ÔZ 3y°z 6.xyz 9.xy z| (6xyz³ ôy = (18xyz – 18.tyz" )i-(9y°z² -9y°z°)j+(6yz² -6yz' )k %3D = Oi – 0 j + Ok ince, the curl of the field is zero hence F is conservative.

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Math

Calculus

Derivative

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