L'Hôpital or L'Hospital? This may be a stupid question but I just want clarification about the use of the name of this rule. Well, most of the time what I see is L'Hospital's Rule, like in Baby Rudin and many other places. Occasionally, though, I do see what seems to be the "more correct" form L'Hôpital's Rule (like in Wikipedia). I believe the latter is the correct version, because the rule was indeed named after Guillaume de l'Hôpital. (see the wikipedia link). 
But why is the former version so commonly used (much more than the latter I think)?  The only reason I can imagine is the popularity of the English language. However, though hôpital does mean hospital in English, isn't it totally ridiculous to translate Règle de L'Hôpital into L'Hospital's Rule (just because the corresponding English word hospital happens to make sense)? What's more, how are we supposed to pronounce L'Hospital? In an English way or in a French way? In the first place, I think it is confusing to combine a French article with an English word, and in the second, it is even more confusing to use l' in place of le/la since in English the h in hospital isn't even mute. Anyway L'Hospital makes little sense to me..
 A: In the 17th and 18th centuries, the name was commonly spelled l'Hospital, and, as far as I learned when I was a student, even himself used to spell his name that way. However, with time going, many French spellings have been altered: in particular, the silent s has been removed and replaced with the circumflex over the preceding o making l'Hôpital. The former spelling is still used in English with no circumflex.
A: I know you problem! I live in a city where English is popular, but people are not so good at it. I know for sure that it is pronounced without the 's', (L'Hôpital's Rule). But whenever I ask a question related to it to my teacher, instead of saying "lop-it-als" I say "eL-Hos-pi-tals", and then only he understands. So I don't think it will be a problem, just ensure that when you are speaking in front of knowledgeable mathematicians, speak the right way. But if you encounter a situation like mine, the shorter way is better! (y) 
Those who are saying that in English you have to pronounce is like "L Hospital", I don't think it is legitimate, because suppose you were born in Spain, and (just for an example), your name was "Jalapeno", then in England, if people call you "Jai-le-peeno", will it seem good? Now rest is in your hands.
