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Is the following vector field conservative? A(T (y 4x3 z, 2z3y s, 3y2z2 sin x -...

Is the following vector field conservative? A(T (y 4x3 z, 2z3y s, 3y2z2 sin x - a) COS x _ If so, what is the potential ø(F)

Is the following vector field conservative? A(T (y 4x3 z, 2z3y s, 3y2z2 sin x - a) COS x _ If so, what is the potential ø(F) of that vector field A? (see worksheet 17)
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Dek Salution : ) conservative vector field. A rector field is called conservative F(x, y, z) = fit fait F₂ k els cul f = 0 Cwe find, curl à (8) = V Ã(8) cel ) Ý j to do zai2-4x2 27 มิก: 2 งมีก2 - -Boteīns - 24) - 2 (2z8ysinz)]: [*%8v?sinx-x4)- (092?15. RCF) = < 057), Qy (7), Þz (7) (y²² cost = 4x32 , 27² y sinx , 3y²z² sinx - 24)=<daily, de de = y²z3 cosx - 4x32 - © dyas CyMiz)= 0 Cly,z) : S Cycy, z)dy Sody =) (912) = otco (2) : Dom ean ④ $(8)= y2 z3 sinx-x4 2¢ ¢ (2) again diff. above eqn wo

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