Hello. I just bought a 2002 audi a4 1.8t quattro 5 speed manual a couple days ago. And today on my way home from work I noticed when I was getting on the highway that the engine cuts out at around 3 grand rpm for a few times and then seems to go away until I shift into a different gear and hit 3 grand in that gear. Any help is much appreciated

 

i had a similar issue with a 2007 A4 - took forever to diagnose because it did not throw a check engine light. It ended up being the torque converter going bad - I hope that's not your problem because it costs like 4K to replace.

 

Since you've got a manual, can't be the torque converter.
Off the top of my head I'd start with checking the fuel pressure WHEN THE SYMPTOM OCCURS. You'll have to hook up a pressure gauge and tape it to the windshield and go for a drive. Yeah, you get weird looks from people but that's the way it goes. See if it drops off. I can't recall off hand what the fuel pressure spec is right now (believe it's 35-40 psi?) At any rate, it shouldn't drop on hard accel. If it does, first try a new filter. Sometimes you get lucky. Otherwise replace the pump. Not too bad a job, panel under the rear seat for access. Just have less than 1/2 tank of fuel at the time.

If the fuel pressure is good then it should be driven with a scanner attached to watch the input/output data for anything abnormal.