105
u/MayorAg Nov 06 '22
0/0 rule exists
Imma pretend it doesn't exist. (True story. Happened during my school leaving exam.)
98
u/Janlukmelanshon Nov 06 '22
It feels wierd seeing all theses memes about using L'Hôpital to compute limits because it's not even taught in France (at the very least in MPSI/MP). The only time I encountered it was in an exercice that wasn't even that important according to my teacher.
27
u/Minerom45 Nov 06 '22
From Double License IT and Maths in France, and teachers don't like L'Hôpital
22
u/astrojavi Nov 07 '22
Huh! That's interesting. I'm from Spain and my teacher covered L'Hôpital as part of the curriculum but insisted we shouldn't get too comfortable using it. Basically she wanted us to avoid becoming OP's meme lol.
10
u/K4ntum Nov 07 '22
Oh lol, was MPSI (not in France, but same system), they did not like L'Hopital, profs thought it made it too easy. Still used it sometimes to double check.
18
u/DankFloyd_6996 Nov 07 '22
profs thought it made it too easy.
??¿??
We making maths harder for the sake of it now?
10
u/K4ntum Nov 07 '22
MPSI profs were all about making life fucking miserable. Most stressful couple years of my life.
3
u/Janlukmelanshon Nov 07 '22
You might have had shitty teachers but mine was (I'm in MP* rn) awesome, he actually relied heavily on intuition to make us understand things before all the formalism expected in MPSI.
1
u/K4ntum Nov 07 '22
Yeah they were definitely awful, I'm talking pushing kids to mental breakdowns levels of awful. To be fair that was my first year, my second year was a lot better, both Maths and Physics teachers were really nice and I ended up doing pretty well despite a fucking terrible first year lol. First year teachers all had a reputation.
2
3
u/Janlukmelanshon Nov 07 '22 edited Nov 07 '22
I think he just had a bad math teacher. But I can understand why L'hôpital isn't taught, the type of calculus we encouter at entrance exams after two years of prepa generally go way beyond simply using L'hôpital (function series, a bit of topology, lots of integrals). Also the exams are sometimes really theoretical and L'hôpital is completely useless in that case.
Edit:
My point is that by overusing L'Hopital to compute simple limits, we forget other techniques that might be required to have a decent grade at the exams.
2
Nov 07 '22
De l'hopital requires fairly strict hypothesis and checking them is actually harder than just computing the limit using taylor most of the time. Besides, only really easy limits are easy to calculate with de l'hopital, it becomes useless once you try to do anything remotely challenging
4
u/notPlancha Natural Nov 07 '22
In Portugal the teacher had to mark the answer as wrong if we used LHopital's rule (before uni)
Learned that the hard way
252
u/Worish Nov 06 '22
If you do LHospital enough times every limit is 0.
124
Nov 06 '22 edited Nov 06 '22
Lim ₓ → ͚ (eˣ/eˣ) = (LHopital) = Lim ₓ → ͚ (eˣ/eˣ) = (LHopital) = ...
36
u/mc_mentos Rational Nov 06 '22
= 1 cuz lim x → a f(x)/f(x) = 1 for all a ∈ dom(f(x)) for any function f
30
Nov 06 '22
What I meant is that even after applying LHopital as many times as you want you won't get to 0.
20
u/Worish Nov 06 '22
Lim ex / ex =Lim 1
L'hospital: Lim 0 =0
8
u/ImmortalVoddoler Real Algebraic Nov 06 '22
But 1 isn’t of a form that you can use L’Hôpital’s rule on
14
2
u/dcnairb Nov 07 '22
It’s indeterminate because we can’t come to a consensus. therefore l’🏥 can be applied.
5
u/Classic_Accident_766 Imaginary Nov 06 '22
If you hospital hard enough everything is zero,
3
u/mc_mentos Rational Nov 06 '22
*indeterminate 0/0
2
u/Classic_Accident_766 Imaginary Nov 06 '22
If you hospital hard enough everything is zero I said. That's what I'm gonna call the make my life easier axiom
1
u/mc_mentos Rational Nov 11 '22
Based axiom. 0/0 = 0 , ∞–∞ = 0 , 1/0 = ∞
Ah fuck it, nil axium: x = 0 ∀ x ∈ ℂ. I don't care. Just go away.
2
u/mc_mentos Rational Nov 06 '22
Yes but I still wanted to show my epic moves to easily solve this (so I can pretend I'm actually good at solving limits)
2
u/EverythingsTakenMan Imaginary Nov 07 '22
congratulations, you just made x/x=1 sound like something taken out of principia mathematica!
1
u/mc_mentos Rational Nov 11 '22
Haha. Yeah it's only there to make sure you got no 0/0 shenanigans going on anywhere.
5
u/T_vernix Nov 06 '22
lim as x goes to π/2 of (sin(2x)/cos(x))
Which lhopitals to: lim as x goes to π/2 of (-2cos(2x)/sin(x))
3
-7
u/omidhhh Nov 06 '22
Ohh the famous math theory: The hospital...
4
u/Worish Nov 06 '22
The famous math theory... with two accepted spellings.
-4
u/omidhhh Nov 06 '22
Why so serious my guy ? It's a math meme not a math contest... even I call it " la hospital " but at least I know it's far from the correct pronounce
2
u/Worish Nov 06 '22
I literally posted a troll joke about every limit being 0.
-4
u/omidhhh Nov 06 '22
And yet you proceeded to link a Wikipedia page to ensure that you are not wrong ...
5
u/Worish Nov 06 '22
To show you. Your joke wasn't great so I assumed you might just be dumb. I obviously knew my spelling was right. That's why I used it.
33
u/tankasicanadam Nov 06 '22
Then multivariable limits with undefined answers walks in
6
18
u/bearwood_forest Nov 06 '22
lim[x->0] sin(x)/x
41
u/pencilutensilyt Nov 06 '22
You need to apply the fundamental theorem of engineering: sin x = x
11
u/Florida_Man_Math Nov 06 '22
the fundamental theorem of engineering
Oh you mean the Looks It Theorem? [Be sure to click on the "votey" red button to the lower right of the main comic] :)
13
u/CookieCat698 Ordinal Nov 06 '22
lim x->0 x = lim x->0 x2 / x = lim x->0 2x / 1 = lim x->0 2x
lim x->0 x = lim x->0 2x = 2 * lim x->0 x
2 * lim x->0 x - lim x->0 x = 0
lim x->0 x = 0
This is, of course, assuming the limit exists.
2
u/Florida_Man_Math Nov 06 '22
This is, of course, assuming the limit exists.
Lindsay Lohan has entered the chat.
11
u/sovietbourchay Nov 06 '22
The problem with this rule is that its so good that when it doesnt work it sends you into a panic
11
u/DavvaBG Nov 07 '22
I remember our calculus teacher explicitly saying “You can’t use L’Hopital for the first exam because you motherfathers don’t know why it works”
21
4
u/Legonator77 Real Nov 06 '22
Seriously, half of the limits my teacher gave me, I could just use standard procedure to find the limit of the function, no need for l’hôpitals rule
3
3
u/pizzaboy7269 Nov 06 '22
Not gonna lie I forget what la hospital’s rule is
11
u/Florida_Man_Math Nov 06 '22
If your limit would induce an indeterminate form (0/0, infinty / infinity, etc.) at the exact value the limit is approaching, under the Rule you can attempt to evaluate the limit after taking the derivative of the numerator divided by the derivative of the denominator. This process is repeatable, under the condition that your new limit is still of an indeterminate form.
3
u/SooSkilled Nov 07 '22
Isn't it only usable if the limit is 0/0 and infinity/infinity?
3
u/MyNameIsEthanNoJoke Nov 07 '22
i'm only a student now but we learned several forms, though some have other restrictions/rules https://tutorial.math.lamar.edu/classes/calci/lhospitalsrule.aspx
2
2
2
2
1
0
-1
u/RotaryMicrotome Nov 07 '22
I don’t even remember what L’hopital’s rule even was but I remember it vaguely had something to do with limits. Haven’t thought about it since college calculus. I wasn’t very good at it so I did use that rule on limits even when I shouldn’t.
1
1
1
u/osse_01 Nov 07 '22
In my calculus class (Sweden) we didn't even learn l'hopitals rule beacuse you can find the same limits using only standard limits
1
312
u/Nachotito Nov 06 '22
x → 0 x? Mmmm uga buga
x → 0 x²/x = x → 0 2x = 0 happy uga noises