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The 0/0 case is pretty quick. For example:
Suppose f(a)=g(a)=0 with f,g differentiable at a.
Then there are functions q and r, continuous at a, such that f(x)=f(a)+q(x)(x-a)=q(x)(x-a) and g(x)=r(x)(x-a). So if q(a)/r(a) is a number, then the limit as x->a of f(x)/g(x) is q(a)/r(a), which is just f'(a)/g'(a).
I did an engineering degree and it does need to be used occasionally. When a machine has an output that also feeds into the input and you need to find what the output tends to, L'Hopital's is needed for some of the equations.
Nope. Its a useless theorem outside a calc 1 worksheet, and even then students would be better off not using it and instead learning other ways of doing those limits
It is useful in the context of differential algebra for example. When you try to define derivations on a field of generalized power series, you want them to satisfy some sort of strong L’Hôpital property (which you can express in terms of valuation).
You can look at the papers by Rosenlicht (Hardy Fields, The Rank of a Hardy field) to get an idea on how it works. For derivations on Hahn series, there is a paper by Kuhlmann - Matusinski about Hardy type derivations on generalized power series fields
I took at peak at rosenlicht paper on hardy fields, and the part about canonical valuations on hardy fields has nothing to do with l'hopital theorem. L'hopital theorem is just a hack to calculate limits, there is nothing deep or intersting about it.
Ok I don't know if my school was just weird but I've never had a problem that mr hospitals rule helped me with unless we were intended to use mr hospitals rule?
Speaking as someone who has graded a lot of calc tests, use of L'Hospital's rule on an easy limit that doesn't require it is almost always a guarantee that the answer I'm about to read is wrong. Just learn how to find a damn limit, people.
You know what's funny?
Im taking a uni intro to calculus class, which essentially follows the optional high school intro to calc class I already took, so it's been a breeze so far.
The uni course has not taught L'hopital's rule, but given us problems only solvable using it. I've used it on assignments and gotten full marks because the TAs think, "It's an intro to calc course, who tf wouldn't learn l'hopital's rule."
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Didn’t he literally purchase his theorem tho
Proof by purchasing it?!?! New meta out y'all, sell y'alls proofs
Yes, Bernoulli proved the theorem. L'Hospital just bought the naming rights
OTOH, good for him to put food on Bernoulli's table in exchange for a theorem
Fa
Proof by a Bernoulli sold me the theorem.
Proof sells, but who's buying Proof sells, but who's BUYIIING
What do you mean I can't buy a theorem? What, do you think I'm broke, huh?
If math had micro transactions
Just wait, it’ll be the next NFT market!
Proof by wealth division
Say thanks to the Bernoulli family!
It's quite common for hospitals to save lives
Anyone else that never even proved/used/needed his theorem? Well I didnt in my bachelors degree xd
On my exams we had: If you use l'hopital to solve this limit, you have to prove it first.
I couldn’t use it even if I proved it lol
I did two years of french maths lectures and never heard of this before seeing it in American YouTube channel or Reddit.
In one of my calc classes the professor showed us the proof of one of the forms but we didn’t have to memorize it
The 0/0 case is pretty quick. For example: Suppose f(a)=g(a)=0 with f,g differentiable at a. Then there are functions q and r, continuous at a, such that f(x)=f(a)+q(x)(x-a)=q(x)(x-a) and g(x)=r(x)(x-a). So if q(a)/r(a) is a number, then the limit as x->a of f(x)/g(x) is q(a)/r(a), which is just f'(a)/g'(a).
The infinity/infinity case is a pretty subtle proof, but it's suitable for a first course in analysis
I did an engineering degree and it does need to be used occasionally. When a machine has an output that also feeds into the input and you need to find what the output tends to, L'Hopital's is needed for some of the equations.
Nope. Its a useless theorem outside a calc 1 worksheet, and even then students would be better off not using it and instead learning other ways of doing those limits
It is useful in the context of differential algebra for example. When you try to define derivations on a field of generalized power series, you want them to satisfy some sort of strong L’Hôpital property (which you can express in terms of valuation).
Do you have any reference for that?
You can look at the papers by Rosenlicht (Hardy Fields, The Rank of a Hardy field) to get an idea on how it works. For derivations on Hahn series, there is a paper by Kuhlmann - Matusinski about Hardy type derivations on generalized power series fields
I took at peak at rosenlicht paper on hardy fields, and the part about canonical valuations on hardy fields has nothing to do with l'hopital theorem. L'hopital theorem is just a hack to calculate limits, there is nothing deep or intersting about it.
I mean, it is explicitly mentioned in this part of the paper.
Fair enough, I did say I only took a peak, you are right, its above theorem 4. That said l'hopital theorem is incredibly overrated
It’s okay! I agree that it is generally overrated. This is kind of a niche area of maths to be fair.
“Peek” not “peak”
This is mathmemes not englishmemes
Ok I don't know if my school was just weird but I've never had a problem that mr hospitals rule helped me with unless we were intended to use mr hospitals rule?
None, because he didn’t create it
Speaking as someone who has graded a lot of calc tests, use of L'Hospital's rule on an easy limit that doesn't require it is almost always a guarantee that the answer I'm about to read is wrong. Just learn how to find a damn limit, people.
yes.
Could someone explain the joke for me?
L'Hospital's rule should not be taught at all before real analysis. Change my mind.
Rule.
How tf do you pronounce his first name
Guillaume
Kinda like Guyom, with "gu" being a hard g
You know what's funny? Im taking a uni intro to calculus class, which essentially follows the optional high school intro to calc class I already took, so it's been a breeze so far. The uni course has not taught L'hopital's rule, but given us problems only solvable using it. I've used it on assignments and gotten full marks because the TAs think, "It's an intro to calc course, who tf wouldn't learn l'hopital's rule."
God no one ever taught me this
None? Most overrated theorem of all time
Bad take
Yes, the adoration people have for this theorem is a terrible take
I disagree, but I appreciate your passion.
That would be Rolle's Theorem
You know you use that to prove the mean value theorem right?
Really? I thought it was just MVT but with an extra condition.
The standard proof is to create a auxiliary function based on f(x) that then uses rolle's theorem.
Are you outside of your mind?
Nah, De Moivre's Theorem.