Question: consider the vector field F(x,y,z)= (e 3z , 2yz+1, 3xe 3z +y 2 +5z 4 ) show that F(x,y,z) is conservative find the potential function

consider the vector field F(x,y,z)= (e3z , 2yz+1, 3xe3z+y2+5z4)

  1. show that F(x,y,z) is conservative
  2. find the potential function f(x,y,z) of the vector field F(x,y,z) such that f(2,2,0) = 1
  3. evaluate Ic F.dr , where c is the curve r(t)= (t,1-t, t2-2t) 0

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