I ain't need all that yapping. Desist. L + ratio + pi = 3 = e¹ = sqrt(g) + sin(x) = cos(x) = tg(x) = x + I assume thin layers + I assume negation of air resistency + I assume adiabatic container + I assume you have no bitches
Actually the engineering part is actually pretty valid as that’s what the intermediate value theorem (IVT) states. But again, you don’t really know if the value of x at 0+ is the same as the value of sinx at 0+ just by IVT. So if you want to technical, you’d still want to use squeeze theorem in order to make the confirmation and thus get an accurate answer.
Can' l'hôpital's rule here because that limit is needed to find the derivative of sin x so we cant say d/dx sin x = cos x without prooving that limit approaches 1 using another method (squeeze theorm)
Both ways are wrong for subjective reasoning. This limit can be solved by geometry by comparing sector and triangle and then make theta approach 0 to make sector area equal to triangle area.
@@GockBlock64 Again, we're *defining* them in this way, not deriving the taylor series and then using them. It works because the taylor series definition is equivalent to the more "standard" definition using triangles. It's something that I realize feels a little odd, but it's perfectly mathematically valid and actually fairly common practice.
sin(x)=x for small values of x is derived from this limit, also you can’t use l’hospitals rule because d/dx sin(x) requires the computation of this limit to calculate. Taylor expansion is also not allowed as it requires the derivative of sin(x) to be known which requires you to know the value of this limit. The only true method is using geometric arguments, proof by definition, or epsilon delta limits.
I mean shouldnt it be the other way around LHospital Rule used by engineer and Squeeze theorem used by math student, because to actually calculate the derivative of sinx using first principle you use the result of sin(h/2)/(h/2) = 1.
hold on for Taylor series expansion wouldn't you also need to define the derivative of sin(x) and take its derivative an nth number of times? In reality the only way to do this would be squeeze theorem since L 'Hopital's rule also uses circular reasoning.
I'm in second year engineering and tbh only the basic derivatives integrals and differential equations are used. Study math but study your engineering classes more
You can't use l'hopital's rule to calculate sinx/x as this limit is used to calculate the derivative of sinx and that would be a circular argument, same with Taylor expansion
Those are not the only way to calculte the limit... You american always forgot the simplest thing, pretty sure no american can prove the Hospital Rule ...
Yeah, just ignore the fact that many of the greatest modern mathematicians are American. I am pretty sure that most undergraduate math students could prove l'Höpital's rule in a few minutes.
The Hospital’s Rule 💀💀
that's its true name btw (no cap)
@@ivoturi It's not pronounced like english "hospital" tho, thats why he (and me, and many others) cringed
@@Matthias-Shaw ah yeah well i didnt know that because im not from england so thanks
Im also not from england, thats why I know its not pronounced "hospital" but instead "delopi'tal"@@ivoturi
Biblically accurate math term (totally correct spelling) 💀
my humor is broken
us bro us
Nahhhh its fineeeee
But sinx = x for small x values comes from expanding the Taylor series of sinx so the math student was right all along
_"Just because you are right doesn't mean you are correct"_
~ Maths Teacher☕
are you a nerd because you like math or do you like math because you're a nerd
I ain't need all that yapping. Desist. L + ratio + pi = 3 = e¹ = sqrt(g) + sin(x) = cos(x) = tg(x) = x + I assume thin layers + I assume negation of air resistency + I assume adiabatic container + I assume you have no bitches
🤓🤓🤓🤓☝️☝️☝️☝️
Bro the point was that both were right, engi just did it the simpler way
I pretend to understand
Or do i understand to pretend
Are you @insane7718 because you pretend to understand?
Or do you understand to pretend you are @insane7718?
do you pretend to understand or to understand do you pretend?
@@aquilonthepro8319
Stand proud, you are strong but nah, I’d understand
When you understand, always bet on iq @@samblackstone3400
@@samblackstone3400 I'm you.
These deaths really driving the fandom insane.
The way the ai actually says "hospitals"😂
With the power of a graphing calculator
Actually the engineering part is actually pretty valid as that’s what the intermediate value theorem (IVT) states. But again, you don’t really know if the value of x at 0+ is the same as the value of sinx at 0+ just by IVT. So if you want to technical, you’d still want to use squeeze theorem in order to make the confirmation and thus get an accurate answer.
Can' l'hôpital's rule here because that limit is needed to find the derivative of sin x so we cant say d/dx sin x = cos x without prooving that limit approaches 1 using another method (squeeze theorm)
Wow, great vid!! I love Gojo and Jujstu Kaisen DATTEBAYO!!!!!!!✊✊✊
Both ways are wrong for subjective reasoning. This limit can be solved by geometry by comparing sector and triangle and then make theta approach 0 to make sector area equal to triangle area.
Are you a nerd because you're a maths student, or are you a maths student because you're a nerd?
I mught need to start prepping for college entrance exams if i still don't know this
@@Blade.5786xDDDDDD
just dont use lhopital rule in your exam for limx->0+ sinx/x because its circular reasoning
True
We could say the same for cosx -1/x and tan x/x
Not inherently, if you define sin and cos in terms of their Taylor series then you can freely take a derivative to see that one grants the other
but to find the taylor series in the first place you would need to repeatedly differentiate
@@GockBlock64 Again, we're *defining* them in this way, not deriving the taylor series and then using them. It works because the taylor series definition is equivalent to the more "standard" definition using triangles.
It's something that I realize feels a little odd, but it's perfectly mathematically valid and actually fairly common practice.
i love taylor swift expansion series🥰
what the
"Teach me magic" i said
"I ain't no magician, but i can teach you some mathematics" he said
i can't believe this is actually funny
but small values of sin x is x is derived using taylors series so techincally the math student won
You have my greatest respect i.e I will be ur subscriber.
this series is peak
sin(x)=x for small values of x is derived from this limit, also you can’t use l’hospitals rule because d/dx sin(x) requires the computation of this limit to calculate. Taylor expansion is also not allowed as it requires the derivative of sin(x) to be known which requires you to know the value of this limit. The only true method is using geometric arguments, proof by definition, or epsilon delta limits.
Finally my calculus class is useful. By helping me understand jjk shitposts
I'm gonna be taking calc next year. God help me.
Domain Expansion: Taylor's Series
The fact that sin(x) ≈ x for small values of x follows from this limit, so you cannot use it here.
I mean shouldnt it be the other way around LHospital Rule used by engineer and Squeeze theorem used by math student, because to actually calculate the derivative of sinx using first principle you use the result of sin(h/2)/(h/2) = 1.
Hospital’s Rule? Math stuudent? Nah, That's wrong. Math students calculate by definition bro
omg sinc(x) my beloved
Coseen x😭
Sandwich theorem
It's funny af also because I'm a math student😂
there is a geometric proof of this
Squeeze theorem clears
Taylor Swift and the Hospital's Rule
As an engineer I have seen people sub sinx for x 😭
hell naw im dying ☠️💀☠️💀
hold on for Taylor series expansion wouldn't you also need to define the derivative of sin(x) and take its derivative an nth number of times? In reality the only way to do this would be squeeze theorem since L 'Hopital's rule also uses circular reasoning.
Yeah, bprp actually made a video about this
I'm studying engineering, should I also study the math student's books and classes to completely comprehend my maths???
I'm in second year engineering and tbh only the basic derivatives integrals and differential equations are used. Study math but study your engineering classes more
Hop-a-lol rule amiright ladyyys?
More videos required. Those are meth
i feel like such a goddamn nerd for finding this funny
tho l'hopital's rule cant be applied here, proove it via ST or taylor series
insanity
Cap4 plis
0/0 = 1
1/1 = 1
WHAT'S THE DIFFERENCE?
Comment section full of nerds
I agree . "Uhm actually that is mathematically incorrect 🤓🤓"
Are you gay because you like jujutsu kaisen or do you like jujutsu kaisen because you are gay?
N TANKO LFMAO
isn't lim x->0 sinx/x = 1?
You can't use l'hopital's rule to calculate sinx/x as this limit is used to calculate the derivative of sinx and that would be a circular argument, same with Taylor expansion
But wait, that's illegal.
Engineers are nerds tho. As a matter of fact all stem majors are nerds
Agreed
Those are not the only way to calculte the limit... You american always forgot the simplest thing, pretty sure no american can prove the Hospital Rule ...
Im not even american and this is a satire video btw
Plus im in engineering why do I need math proofs 😂
What type of engineering?
Yeah, just ignore the fact that many of the greatest modern mathematicians are American. I am pretty sure that most undergraduate math students could prove l'Höpital's rule in a few minutes.
@@ethanbottomley-mason8447I think it's a joke about healthcare...