There are some older threads about this exact topic here. Lot's of good detail info if you use the search function.
In short, the Honda ue2000i will run every thing in a 30 amp trailer except the air conditioning and the electric hot water element.
It's not the current draw while running, it is the surge draw when start up the AC. Depending on the specific current requirements of the AC unit, a 2000 watt genny may or may not start it up.
There are some conflict issues, too. Don't use the hair dryer while running the microwave, etc. Even with a 3000 watt genny, you'll have problems if you try to use too many appliances at the same time.
The Honda eu2000i is the predominant choice of trailer folk because it is VERY quiet and weighs only about 46#. The Honda eu3000 is much heavier (78#) for only 1000 more watts of power.
There was talk at one time of Honda and Yamaha coming out with 2,600 watt gennies specifically for the RV'ers to run their AC's. Honda advertised one for a while, but it's not in their current product list. Check Yamaha's website.
The big deal with quiet generators is that they are QUIET. Some of the less expensive generators out there are darned noisy, and if you neighbor sets his generator near your campsite, it can ruin your day.
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