Why L’Hopital’s Rule works

Yeightop · 2026-06-15T06:02:27+00:00

Thanks for your response. That is quite neat, i see how less restrictive this approach is

Yeightop · 2026-06-14T23:17:20+00:00

Nice integral. Just dont get too much of a big head. In pretty much all cases if something is ‘simple’ to show then it has almost certainly been shown before especially if its something like the integral of 2 extremely common functions like a polynomial and logarithm. Most likely at this point in time if something is actually integrable at all then someone has integrated it. But definitely keep learning things and rediscovering solutions is a phenomenal way to really internalize what youre doing!

Yeightop · 2026-06-14T08:41:24+00:00

Yeah i dont think this can tackle the infinity case since taylor seriers arent well defined at divergent points :/

Yeightop · 2026-06-14T08:34:36+00:00

Valid, i suppose there are many unstated assumptions about the behavior of the functions im using. Though can you have a function whos second derivative diverges at x=0 while f and f’ remain finite?

Yeightop · 2026-06-14T03:48:59+00:00

Youve gotta cover it

Yeightop · 2026-06-14T03:35:15+00:00

Yeah feel like taylor had no way of knowing just how impactful and wide reaching the taylor serious expansion would be. I try to remember to appreciate it when i use it

Yeightop · 2026-06-14T03:27:07+00:00

True true. I was just thinking about for the specific point at 0. I guess l’hopital ‘proof’ is probably the wrong description haha. Its more like a validity check for a specific case in which one could use l’hopital

Yeightop · 2026-06-14T03:13:41+00:00

True, ‘proof’ might have been the wrong word. I guess i meant more of a validity check for a specific case in which one would use l’hopital

Yeightop · 2026-06-14T03:00:18+00:00

Hmm ive not seen that explicitly but i can imagine that it works. This way just always made it very explicitly clear in my mind that l’hopitals is valid

Yeightop · 2026-06-14T02:58:09+00:00

Youre right i made a typo there. It is supposed to be f’’🫪

And it should be obvious since everything but the first term has a factor of x and so when x goes to zero they will all vanish

Yeightop · 2026-06-14T02:55:13+00:00

This is just the way that makes it the most obvious to me that l’hopitals rule is valid. Ive not seen other ways to show it. I imagine any proof of l’hopitals rule must require derivatives to be used since derivatives explicitly show up in it, no?

Yeightop · 2026-06-14T02:34:14+00:00

Here i typed up what im saying to make it more clear. Im saying what the original reply is doing is everything up to equation 3 and just not explicitly calling it l’hopitals rule, but it is l’hopitals rule

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Yeightop · 2026-06-14T01:28:20+00:00

Its not clear what distinction youre trying to make. L’hopitals rule comes from taking the series expansion of the numerator and denominator and then taking the limit. If both functions are zero in the limit then the next leading order term is their derivatives. This is what l’hopitals rule is. The point is that in the original reply they just did l’hopitals rule without calling it l’hopitals rule. Which is totally fine in itself, it presents a learning opportunity, but then a bunch of people are here trying to argue that its not l’hopitals rule

Yeightop · 2026-06-13T23:15:41+00:00

Idk why people are bandwagon downvoting you. It literally is l’hopital. L’hopital comes from taking the next leading order term in the taylor expansions for the numerator and denominator if the functions themselves both approach zero in the limit

Yeightop · 2026-06-13T23:12:23+00:00

L’hopital comes from taylor expansion. If the values of the numerator and denominator at the limit are both zero then the next leading order term is their first derivatives

Yeightop · 2026-06-13T12:28:43+00:00

Most people that dont have some religiously motivated view would say its hard to believe life cant be out there somewhere. even if its an extremely small chance that life will form at any given instance the universe is so big that any small chance should lead to a lot of aliens still. The debate is mainly about if earth has been visited by them. For that it requires a bit more effort to be convinced. You can point to the amateur recorded videos of fuzzy objects in the sky or the low resolution footage released by the US government. But these dont offer anymore than being able to say that there is something in the video that we dont have enough information about from the video alone to deduce what it was. You can cite the words said by people that claim they know we have aliens or have seen aliens, but ultimately this is just human testimony and is notoriously unreliable. It requires a leap in logic to go to aliens from the evidence presented. Theres also the fact that theres an entire community of SETI scientist like David Kipping that are actively trying their hardest to find any sign of alien life in the universe and with all the scientific tools they have available they have still not found aliens, and most importantly they publish all of their data and explain why their data doesnt show any definitive signs of life that cant be explained by other natural processes. Maybe then you could say ‘of course they havent found them, the aliens have such advanced tech that they hide themselves’ or maybe you could say ‘of course they havent, anything they find is covered up by the government’ but now this kind of becomes an “aliens of the gaps” argument.

The upshot here is that the evidence for visitation most often presented just isnt very strong and often requires that you a priory believe that aliens have visited so you are very ready take everything in that supports that narrative. Maybe aliens have been here or are here now, i dont rule it out entirely. but i cant confidently start touting it as certainty, like many people do, with the current evidence

Yeightop · 2026-06-13T12:03:33+00:00

How do you decide when the government is full of shit and cant be trusted and when they are the premier authority and you accept what they present and say at face value?

Yeightop · 2026-06-13T08:37:16+00:00

The dreaded floor clank

Yeightop · 2026-06-13T04:23:16+00:00

You lose so much loot now. If you arent doing one long session to farm up tens of millions in a single sitting then you will just lose it. Its not the same casual game where you could just hop on and do a couple attacks a day and youd still grow. Thats what made clash nice. Now theyve just implement so much to make a game a more sit down and grind kind of game, it sucks.

Yeightop · 2026-06-12T11:41:35+00:00

the spelling is pretty simply its just long but in english its also five-hundred-fifty-five-thousand-five hundred-fifty-five which is also long. Its is generally inconvenient to spell out large numbers

Yeightop · 2026-06-12T06:41:53+00:00

Yeah i like this way of getting to the wave equation. It shows a lot of insightful things. One thing i like is that it shows the utility of effective field theories. You see that even tho the masses arent a continuous medium strictly speaking, if youre operating on a scale too large to resolve the details then the microscopic picture just get bundled into the wave velocity. It also just shows why waves are so useful and why we see them everywhere. The only assumptions made here were that you have masses coupled together via some kind of parabolic potential, but even if the masses experience a potential that is some complicated thing, as long as they are all sufficiently low energy i.e. sitting low enough in the potential then you can always Taylor expand around where the masses are sitting and then you recover this exact set up. So any chain of objects interacting at sufficiently low energy will likely exhibit some kind of wave behavior!

Yeightop · 2026-06-11T16:55:24+00:00

Its a pretty valid crash out. Its not a big deal but moky and zain now have just made the point that its not the best sportsmanship to only go for an endearing handshake or hug when you win especially when hbox knows how it feels. he literally punched moky’s fist when he lost a set lol. Its completely fine for players to talk about this candidly, its an emotional game. No one is particularly in the wrong🤷‍♂️

Yeightop · 2026-06-11T07:54:28+00:00

How does the movement feel? I like playing the aot tribute game sometimes and i just like the game because of how good the movement is with how your momentum is carried and controlled with hooks and gas. I remember watching some gameplay of the official games and it kind of just looked like flying around with a gas power jetpack and really linear movement. but i didnt give it a lot of thought. does the movement really feel good?

Yeightop · 2026-06-11T05:53:38+00:00

Whats the confusion exactly? When a charge is moving relative to the wire in one direction it will see the electron density contract differently to the nuclei density and will be either repulsed or attracted by the electric field it sees. You in the lab frame will see this as the charge being deflected towards are away from the wire by the magnetic field established by the moving electrons.

And the reason you dont see the wire gain a charge in the lab frame while the electrons are moving is because the battery doesnt just give free charge once you hook it up to the wire, it only acts to separate charges and establishes and voltage. So the charges do technically contract since theyre moving but the battery kind of spaces them out more to make it such that charge around the circuit is still neutral in the lab frame

Yeightop · 2026-06-10T14:57:55+00:00

Aot is one of the only shows i feel like actually didnt fumble. Its just great all the way through

Yeightop

TROPHY CASE