Determine whether each of the following vector fields F is path independent (conservative) or not. If it is path indepen

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Determine Whether Each Of The Following Vector Fields F Is Path Independent Conservative Or Not If It Is Path Indepen 1 (39.29 KiB) Viewed 35 times

Determine whether each of the following vector fields F is path independent (conservative) or not. If it is path independent, enter a potential function for it, that is, a function f(x,y) so that ∇f=F. If it is path dependent, enter NONE. (a) If F(x,y)=(x+6)i+(6y+3)j​, then f(x,y)= (b) If F(x,y)=(2x+2y)i+(2x+3y)j​, then f(x,y)= (c) If F(x,y)=⟨−3y,3x⟩, then f(x,y)= (d) If F(x,y)=⟨5x2−y2,−2xy⟩, then f(x,y)= (e) If F(x,y)=x+26y​i+6ln(x+2)j​, then f(x,y)= (f) If F(x,y)=3ysin(xy)i+3xsin(xy)j​, then f(x,y)=