Hello, will a Nvidia GeForce GT 640 work in my dell studio XPS 8100
More aboutupgrading graphics card
It should work fine as long as your power supply is over 300 watts.
It should work fine. Your PSU is 350W and Dell usually doesn't use terrible PSUs, but you may want to check the amps available on the 12V rail. A decent 350W PSU should have at least 25A on the 12V rail(s) which is enough to drive a 95W CPU and a fairly powerful GPU.
However, gt640 is only 5670/6670 ddr5 territory at best. I mean you're looking at BARELY playable in BF3. I'd step up to a 7750 -- the lowest entry-level card I'd recommend-- which is going to be nearly two times as fast. I don't know your budget, but there are three cards on newegg for less than $100 after shipping and before rebates.