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). If it is not conservative, type N.
A. F(x,y)=(10x+7y)i+(7x+10y)jF(x,y)=(10x+7y)i+(7x+10y)j
f(x,y)=f(x,y)=
B. F(x,y)=5yi+6xjF(x,y)=5yi+6xj
f(x,y)=f(x,y)=
C. F(x,y,z)=5xi+6yj+kF(x,y,z)=5xi+6yj+k
f(x,y,z)=f(x,y,z)=
D.
F(x,y)=(5siny)i+(14y+5xcosy)jF(x,y)=(5siny)i+(14y+5xcosy)j
f(x,y)=f(x,y)=
E. F(x,y,z)=5x2i+7y2j+5z2k