For each of the following vector fields F , decide whether it is conservative or not...

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)=(5sin⁡y)i+(14y+5xcos⁡y)j
f(x,y)=f(x,y)=

E. F(x,y,z)=5x2i+7y2j+5z2k

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milcah answered 1 year ago

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