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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)=(−4x+5y)i+(5x+16y)j
f(x,y)= ?

B. F(x,y)=−2yi−1xj
f(x,y)= ?

C. F(x,y,z)=−2xi−1yj+k
f(x,y,z)= ?

D. F(x,y)=(−2siny)i+(10y−2xcosy)j
f(x,y)= ?

E. F(x,y,z)=−2x2i+5y2j+8z2k
f(x,y,z)= ?

Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

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Expert Solution

milcah answered 2 years ago
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