Question

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∇f=F ). If it is not conservative, type N.

A. F(x,y)=(−10x+3y)i+(3x+10y)jF(x,y)=(−10x+3y)i+(3x+10y)j
f(x,y)=f(x,y)=

B. F(x,y)=−5yi−4xjF(x,y)=−5yi−4xj
f(x,y)=f(x,y)=

C. F(x,y,z)=−5xi−4yj+kF(x,y,z)=−5xi−4yj+k
f(x,y,z)=f(x,y,z)=

D. F(x,y)=(−5siny)i+(6y−5xcosy)jF(x,y)=(−5sin⁡y)i+(6y−5xcos⁡y)j
f(x,y)=f(x,y)=

E. F(x,y,z)=−5x2i+3y2j+5z2kF(x,y,z)=−5x2i+3y2j+5z2k
f(x,y,z)=f(x,y,z)=

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

Answer 1

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