# determination of vector field conservative, find those that are

• Dec 6th 2009, 05:21 PM
determination of vector field conservative, find those that are
Hello everyone

This is another one of my really hard homework problems. I'm not sure if anybody will be able to answer this, but any help whatsoever will be very very much appreciated.

Question:

Determine whether each of the vector fields below is conservative, and find potential functions for those that are.

a) e^(2x) * cos(2y)i + e^(2x) * sin(2y)j

b) [y/(1+x^2 * y^2)] i + [x/(1+x^2 * y^2)] j

c) [6/(6x+3y^2+2z^3)] i + [6y/(6x+3y^2+2z^3)] j + [6z^2/(6x+3y^2+2z^3)] k

Thanks in advance everybody, thank God for forums :)
• Dec 6th 2009, 06:57 PM
mr fantastic
Quote:

Hello everyone

This is another one of my really hard homework problems. I'm not sure if anybody will be able to answer this, but any help whatsoever will be very very much appreciated.

Question:

Determine whether each of the vector fields below is conservative, and find potential functions for those that are.

a) e^(2x) * cos(2y)i + e^(2x) * sin(2y)j

b) [y/(1+x^2 * y^2)] i + [x/(1+x^2 * y^2)] j

c) [6/(6x+3y^2+2z^3)] i + [6y/(6x+3y^2+2z^3)] j + [6z^2/(6x+3y^2+2z^3)] k

Thanks in advance everybody, thank God for forums :)

F is conservative if $\displaystyle \nabla \times F = 0$.