What is the Correct Pronunciation of L'Hospital's Rule?

  • Thread starter vsage
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Johann, he did, at a very young age, write a commentary on l'Hospital's text, which was used in Daniel's father's class to teach calculus. In summary, L'Hospital's rule, also known as L'Hopital's rule, is a mathematical rule used in calculus to evaluate limits involving indeterminate forms. It is often mistakenly referred to as "The Hospital Rule" or "L'Hospitaling". The rule was named after its discoverer, Marquis Guillaume de l'Hospital, a French mathematician who lived in the 17th century. Despite its French origin, the rule is commonly spelled with a circumflex in English, due to the influence of the French Academy. It is worth noting that
  • #1
vsage
"L'Hospital's Rule"

Back when I took calculus for the first time and we learned about L'Hopital's rule, roughly half the class lazily read it as "L'Hospital's Rule", and some even weeks after the idea was introduced, would refer to it as "the hospital rule". I always thought this was pretty funny, but people on this very board use "L'Hospital's Rule" all the time when referring to it! Is this some sort of ongoing PF joke, that there has been such a mass misinterpretation of the word that it has been assimilated into the language? I must know, because it is very funny seeing it
 
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  • #2
I think it is considered OK usage, and not some inside joke. When I tutored math last semester people would always come up with some weird way of saying it, commonly, as you said, they would use Hosiptal. I would always try to say it with a strong French accent, but people would think I was joking, which I somewhat tried to do. Poisson is another fun one, to say that is.
 
  • #3
the use of the circumflex above the o in the 'correct' spelling usually indicates an s that has been dropped from the word. in this case, "hôpital" would be from "hospital".

this would imply that "l'hospital's rule" is equally valid..
 
  • #4
rhj23 said:
the use of the circumflex above the o in the 'correct' spelling usually indicates an s that has been dropped from the word. in this case, "hôpital" would be from "hospital".

this would imply that "l'hospital's rule" is equally valid..

That nuance I was not aware about the french language. I mistakedly equated "L'Hospital's Rule" with the kids in my class saying "The Hospital Rule", whose misinterpretation where I come from is so common that I just assume it's like confusing your and you're, which is also very common in my circle. Thank you for this information.
 
  • #5
rhj23 said:
the use of the circumflex above the o in the 'correct' spelling usually indicates an s that has been dropped from the word. in this case, "hôpital" would be from "hospital".

this would imply that "l'hospital's rule" is equally valid..

Most certainly not! Please feel free to refer to wikipedia's seven-page long article on the circumflex in French.

It often indicates the historical presence of a letter (commonly s) that has, over the course of linguistic evolution, become silent and fallen away in orthography.
 
  • #6
"L'Hospital" is most certainly accpeptable, and is probably the more common usage in mathematical communication. I've confirmed this among three different math texts, and Mathworld.

Note that l'Hospital's name is commonly seen spelled both "l'Hospital" (e.g., Maurer 1981, p. 426; Arfken 1985, p. 310) and "l'Hôpital" (e.g., Maurer 1981, p. 426; Gray 1997, p. 529)

http://mathworld.wolfram.com/LHospitalsRule.html
 
  • #7
Why would anyone write a letter that isn't pronounced?
 
  • #8
Rach3 said:
Why would anyone write a letter that isn't pronounced?
Indeed, why would they? :biggrin:
 
  • #9
Behold the perils of not drinking coffee...
 
  • #10
In the 17th century when l'Hospital lived, the s was still used but not pronounced (it had been of course, once upon a time, but the French pronunciation changed just as English has). So he spelled it l'Hospital (pronounced LOW pee tall). But the French academy decreed the circonflex and French math and hisotry books used it and texts of other nations copied them.

l'Hospital was a student of Liebniz, and wrote the first textbook on calculus.
 
  • #11
How soon is l'Hospital rule taught in current first year calculus classes these days? It was one of the significant differences between two textbooks available back when I was in high school, (1969->1970). Crowell and Slesnick (not a popular text) introduced the rule early on to assist with explanation of the derivative. Thomas's text only includes it in an appendix.
 
  • #12
I don't think we did any "L'Hopitaling" (my teacher used it as a verb - I thought that was cute) until the second half of my single var. calc class.
I just think of it as Bernoulli's Thingy and don't trouble myself with French name spelling. :smile:
 
  • #13
Any calculus class with say, 40 or more students, will have someone calling it "the hospital rule" either as a joke or by accident. The joke/error stops being amusing sometime before the 5121st time you hear it.

Math Is Hard said:
I just think of it as Bernoulli's Thingy and don't trouble myself with French name spelling. :smile:

Go Bernoulli! :smile:
 
  • #14
shmoe said:
Go Bernoulli! :smile:
Which one?
 
  • #15
Gokul43201 said:
Which one?

Isn't that kinda like asking which Bach? Its understood.
 
  • #16
Rach3 said:
Most certainly not! Please feel free to refer to wikipedia's seven-page long article on the circumflex in French.

please feel free to be less condescending in future, especially when you are mistaken
 
  • #17
As far as I now, in Medieval times copyists would put a small lowercase s above the o. This has became the circumflex.
I was told that the reason he was called this was because he was left by his parents on the doorstep of a "hospital". The people taking him in thus assigned him this name, as they had no idea what his real name was.
 
  • #18
You christen someone "The Hospital" ?!
Oh those French !
 
  • #19
"de l'Hôpital", meaning of or from the hospital. :smile:
 
  • #20
selfAdjoint said:
In the 17th century when l'Hospital lived, the s was still used but not pronounced (it had been of course, once upon a time, but the French pronunciation changed just as English has). So he spelled it l'Hospital (pronounced LOW pee tall). But the French academy decreed the circonflex and French math and hisotry books used it and texts of other nations copied them.

l'Hospital was a student of Liebniz, and wrote the first textbook on calculus.
Hmm..I think L'Hopital was a student of J. Bernoulli.
 
  • #21
Gokul43201 said:
Which one?

J. Bernoulli of course :wink:
 
  • #22
shmoe said:
J. Bernoulli of course :wink:
You got that one from me. :approve:

You should be grateful I hindered you from referring to Daniel.
 
  • #23
Yuck! :yuck:

By "J." I guess you mean Johann (not Jakob), the jealous father of Daniel, also the man who plagiarized essentially all of Daniel's work on Hydrodynamics (with the help of none other than Daniel's close friend and Johann's former and grateful pupil, Euler).

And while Johann was not really tutored by Leibniz, he and his brother Jakob, did exchange letters with Leibniz. And incidentally, it was Jakob, who first understood what Leibniz's calculus of infinitesimals was all about and explained it to Johann. Johann's fame grew in no small part due to the public brawl between Leibniz and Newton, and because Johann had jumped both feet in, into the fray, in support of Leibniz.

And finally, L'Hospital wasn't exactly Johann's student. Marquis G. de l'Hospital commissioned Johann, at a handsome price, to teach him everything he had learned about the calculus of Leibniz...and to promise to never teach it to anyone else.
 
  • #24
I thought you were talking about dextercioby! :redface:
 
  • #25
Yes of course I meant Johann. Nice chap, by all accounts.
 
  • #26
Draw your sword (the metallic one) arildno; we duel to the death!
 
  • #27
Gokul43201 said:
Draw your sword (the metallic one) arildno; we duel to the death!

I'm glad that was specified :tongue2:
 
  • #28
LoppyTAL.

I've never heard it said any differently.

But then again, everybody here has to take french for a certain length of time and understands rundimentary french language rules.
 
  • #29
Gokul43201 said:
Draw your sword (the metallic one) arildno; we duel to the death!
I concede; I melted it down, so it is rather flaccid at the moment.
 

What is the correct pronunciation of L'Hospital's Rule?

The correct pronunciation of L'Hospital's Rule is "law-pee-tahlz rule."

Who is L'Hospital and why is this rule named after him?

L'Hospital's Rule is named after Guillaume de l'Hôpital, a French mathematician who first published the rule in his book "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes" in 1696.

What is the purpose of L'Hospital's Rule?

The purpose of L'Hospital's Rule is to evaluate limits of indeterminate forms, which are expressions that cannot be solved using basic algebraic techniques.

What are the indeterminate forms that L'Hospital's Rule can be applied to?

L'Hospital's Rule can be applied to the following indeterminate forms: 0/0, ∞/∞, 0*∞, ∞-∞, 1^∞, and ∞^0.

What are the steps for using L'Hospital's Rule to evaluate a limit?

The steps for using L'Hospital's Rule to evaluate a limit are as follows:

  1. Simplify the expression so that it is in an indeterminate form.
  2. Take the derivative of the numerator and denominator separately.
  3. Evaluate the limit of the derivative of the numerator and denominator separately.
  4. If the limit is still in an indeterminate form, repeat steps 2 and 3 until the limit can be evaluated.
  5. The limit of the original expression is equal to the limit of the derivatives.

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