AdrianPerry

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The CPU is most likely going to be the limiting factor. The GPU should be able to handle ULTRA settings (it certainly can when used with a better CPU), so it really depends to what extent that dual core bottle-necks your graphics card.

All you can really do is try it and see what happens :) I think it would be unlikely for someone else to be using the same CPU and GPU combo that's able to comment with a definitive answer.
 
You failed to mention your resolution which is the most important factor, However, the cpu will be a MAJOR bottleneck either way. You'll never see the capability of that video card with that cpu, and the cpu itself will not run the game well.

A E5200 with a HD6950 is like running a Nintendo Gamecube on a 60" HDTV.

 

loneninja

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BF3 is very cpu intensive online! Techspot, just like Tomshardware and every one else used part of a single player campaign to get consistency but it is very easy on the cpu. The benchmarks from BETA showed online was very cpu demanding, and here is a website that actually did ONLINE MULTIPLAYER for their testing. Note the single digit minimum FPS on a Phenom II X2.
http://www.sweclockers.com/artikel/14650-prestandaanalys-battlefield-3/5#pagehead

Overclocked E5200 will perform similar to a Phenom II X2.