a) show that the vector field F= <siny, xcosy, -sinz> is conservative by finding a scalar...

a) show that the vector field F= <siny, xcosy, -sinz> is conservative by finding a scalar f such that ∇f=F.

b) use this fact to ecaluate ∫C F•dr along the given curve C where C is the line segment from (0,0,0) to (4, π/2, π/2).

Expert Solution

milcah answered 2 years ago

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Questions Determine whether or not the vector field is conservative. If it is conservative, find a...

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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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a) show that the vector field F= <siny, xcosy, -sinz> is conservative by finding a scalar...

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