Question

(1 point) In each case, if the vector field is conservative, give the potential function whose...

(1 point) In each case, if the vector field is conservative, give the potential function whose value at the origin is zero; otherwise answer NA.

(1) 〈4yz(xyz)^3,4xz(xyz)^3,4xy(xyz)^3〉

(2) 〈−ysin(x)z,zcos(x),ycos(x)〉

(3) 〈y,x+z,y〉

(4) 〈−y,x〉

(5) 〈3y−3z,3z,−(3y+3x)

(6) 〈exp(x)cos(y),−(exp(x))sin(y),4(z^3)〉

Please show all steps when finding potential functions.

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