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Well, how do you figure? I'm saying that with the type of driving I do, which is a good mix of city and hwy (city is everyday, guaranteed), with rush hour traffic and the whole stop and go thing, a 3,000 mile interval is a good thing. I'm just a weekend warrior though when it comes to matters of the garage...am I missing something?
Now, just so we don't stray, if my owner's manual said 5,000 miles, and I owned my car since 1999, I'd be going 5,000 increments. I wouldn't take a chance with voiding my warranty, and as far as dealer versus handbook, I'd go with what the manufacturer printed in the handbook...who else would know best other than the people who built it, right?
The book says 3750. By some mathematical formula, you arrived at 3000. I really don't understand what equation you used to get from 3750 to 3000, but it's your engine.