For each of the following vector fields f, decide whether it is conservative or not by computing curl f. type in a potential function f (that is, ∇f=f). assume the potential function has a value of zero at the origin. if the vector field is not conservative, type n.1. f(x, y)=(-6x+5y)i+(5x+10y)j
2. f(x, y,z)=-3xi-2yj+k
3. f(x, y)=(-siny)i+(10y-3xcosy)j
4. f(x, y,z)=-3x^2i+5y^2j+5z^2k

1,2 and 4 are conservatives

3 is not conservative

Step-by-step explanation:

We calculate  the Curl F

Remember that:

        Curl F = <>

1. Curl F = <0,0,5-5> = <0,0,0>

  The potential function f so that  ∇f=F

  f(x,y,z) =

  Then F is conservative

2. Curl F = < 0, 0 ,0>

  The potential function f so that  ∇f=F

  f(x,y,z) =

  Then F is conservative

3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>

              = <0 ,0 , 10 +3xsin(y) + cos(y)<

 How the field's divergence is not zero the vector field is not conservative

4. Curl F = <0, 0, 0>  

  The potential function f so that  ∇f=F

  f(x,y,z) =    

   Then F is conservative

answer is more than one

step-by-step explanation: