Bobby Guzzler makes a good point.
There are three types of crosswind limits. The manufacturer's "demonstrated" limit, the company's limit, and the limit of what the aircraft can actually handle.
I don't know the PA38, but 11kt sounds a little low to me, so I'd guess it's probably a company (i.e. school or club) limit? I would guess that the number in the POH is a little higher (please correct me if I'm wrong) - this will be the "demonstrated" limit, and is often limited simply by how much crosswind the test pilot could find on the day he was doing his crosswind tests.
The actual limit in some cases will be very close to the demonstrated limit, and in other cases will be much higher. I've landed a PA18 (demonstrated limit, if I remember correctly, is 12kt, but I may be wrong - it's been a couple of years since I last flew one) in a gusty 25kt crosswind without any sweat at all. (Doubt I could do it now - I was much more current at the time than I am now.)
In the world of commercial transport, though, I suspect that the aircraft's actual limit is pretty unimportant, because the pilots won't be allowed to exceed the company's limit in any case?
FFF
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