Conservative Vector Fields

snakefashion

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Joined
Apr 9, 2016
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1
I had a homework problem that asked if
8b153caec7c1cb1259b8ae3f3fe5fc1.png
was conservative. The partial derivatives are the same, and I got that part of the problem right, but it is not a conservative function. If C is the circle
c96182283d1b0b1d003b2340e014951.png
,
a5be77ad8145fe650e6d714d2e5c9c1.png
., then
5782267662cc42eb81942071e19a621.png
= 2*pi, not 0, like it would if the vector field was conservative (as t = 0 and t = 2*pi are at the same point). Can anyone explain why this vector field isn't conservative? How can its partial derivatives be the same if it's not a conservative function?
 
I had a homework problem that asked if
8b153caec7c1cb1259b8ae3f3fe5fc1.png
was conservative. The partial derivatives are the same, and I got that part of the problem right, but it is not a conservative function. If C is the circle
c96182283d1b0b1d003b2340e014951.png
,
a5be77ad8145fe650e6d714d2e5c9c1.png
., then
5782267662cc42eb81942071e19a621.png
= 2*pi, not 0, like it would if the vector field was conservative (as t = 0 and t = 2*pi are at the same point). Can anyone explain why this vector field isn't conservative? How can its partial derivatives be the same if it's not a conservative function?

Your graphics are not being displayed properly on my screen.
 
I had a homework problem that asked if

http://webwork.wheatoncollege.edu/w...ations/34/8b153caec7c1cb1259b8ae3f3fe5fc1.png

was conservative. The partial derivatives are the same, and I got that part of the problem right, but it is not a conservative function. If C is the circle

http://webwork.wheatoncollege.edu/w...ations/87/c96182283d1b0b1d003b2340e014951.png

http://webwork.wheatoncollege.edu/w...ations/45/a5be77ad8145fe650e6d714d2e5c9c1.png

then

http://webwork.wheatoncollege.edu/w...ations/d6/5782267662cc42eb81942071e19a621.png

= 2*pi, not 0, like it would if the vector field was conservative (as t = 0 and t = 2*pi are at the same point). Can anyone explain why this vector field isn't conservative? How can its partial derivatives be the same if it's not a conservative function?
We're not in your class at Wheaton College, so we can't see your classroom files. Attempting to view them first displays a message that starts:

Webwork is not accessible off campus. For off campus access, please use VPN.

Then we're redirected to a page with instructions for installing your school's VPN software.

Please reply with the typed-out text of the exercise(s), the full instructions, and a detailed description of (or link to an off-campus, web-viewable version of) any required images or other supplemental material. Thank you! ;)
 
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