the COOLEST limit on YouTube! (limit of ln(x)/W(x) as x goes to infinity)

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We will evaluate the limit of ln(x)/W(x) as x goes to infinity. This will add one more nice connection between the natural log function and the production function. To see a crash course on the Lambert W function, check out: • Lambert W Function (do...
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Опубликовано:

27 сен 2024

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Комментарии : 52

@Getsomewaterplease 3 часа назад

I substituted x with ue^u so I will get (u+ln(u)) /u which its limit goes to 1

@blackpenredpen 3 часа назад

That’s an extremely smart way to do it!!!

@patricklelu6975 2 часа назад

that's what I did too !

@chaosredefined3834 2 часа назад

It genuinely threw me off that he didn't do that. We have a W(x), we probably will make life easier by getting rid of it.

@sajuvasu 4 часа назад

Where is thr fish?

@heinrich.hitzinger 3 часа назад

The fish: 🐟

@donwald3436 3 часа назад

my reply got deleted lol, google free speech platform.

@donwald3436 3 часа назад

google deleted both my fish lol, frxe-spexch = orangeman? lol.

@kaisteinsiek6946 3 часа назад

We got green pen on bprp before GTA6 release

@donwald3436 3 часа назад

Imagine how fun GTA6 will be after SweatBabbyInk "fixes" it! lolfml.

@donwald3436 3 часа назад

ohhhh google canceled facts again lol.

@Mediterranean81 Час назад

Nah his old vids had green pen

@alexdefoc6919 3 часа назад

Yooo we need more "FISH" vids. (the w function)

@umutgokce3185 3 часа назад

GREEN PENCIL???

@Arycke 2 часа назад

I was shocked also lol

@blackpenredpen 3 часа назад

if x+y=8, find the max of x^y (Lambert W function) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zdAJXil-NvA.html

@TheBoeingCompany-h9z 2 часа назад

bprp should change his name to bprpgp 😂

@DiggOlive 3 часа назад

oh yeah baby show me the limit

@donwald3436 4 часа назад

It's 4am why am I watching this lol. Notification gang?

@Naman_shukla410 3 часа назад

Are you at US?

@Arycke 2 часа назад

@Naman_shukla410 probably central US, maybe Mexico or Central America. Most likely US though.

@craftcrewtv8094 Час назад

It was 10am here when he posted the video.

@ingobojak5666 Час назад

While the limit is correct, these functions do not really become the same at large x. For large x, W(x)=ln(x)-ln(ln(x)+O(1). Hence as x->Infinity, W(x)/ln(x) ->1 because ln(x) grows faster than ln(ln(x)). However, as x-> infinity also ln(x)-W(x) -> ln(ln(x)) -> Infinity. Thus the difference between log and product log becomes infinite at large x. It's just that this difference grows slower than the functions themselves, so the result of dividing them tends to 1 at large x...

@ingobojak5666 Час назад

Fun challenge: what's the minimum of W(x)/ln(x)? Yes, it has a "nice" answer.

@Wielorybkek Час назад

I was curious and checked inverses of x^n*exp(x) and apparently all of them also behave like ln(x)

@bunga0911 4 часа назад

@craftcrewtv8094 Час назад

Now I just need to see THE PURPLE PEN!

@trwn87 27 минут назад

The 🐟 Function is here!

@PhilosophicalNonsense-wy9gy 2 часа назад

Limits can never be cool!

@cheeseparis1 3 часа назад

This is really really cool.

@RB_Universe_TV 6 минут назад

Where's your *"PurplePen"* from the old videos? XD

@olivarra1 Час назад

Nothing better than a fresh limit on a Saturday morning

@craftcrewtv8094 Час назад

Yes!!!

@i_am_anxious0247 4 часа назад

Woag

@RB_Universe_TV 7 минут назад

Ahh yes! Welcome to another very cool video of *"BlackpenRedpenBluepenGreenpen"* litterelly

@e6a4 6 минут назад

Can you show please how to compare W(W(1)) and (W(1))^2 without calculator?

@cdkw2 3 часа назад

Lets go, comeback of the lambert W function

@ItsMeTheUser 23 минуты назад

9:18 missaying: he want to say 1/W(x) goes to zero as z goes to inf.

@asparkdeity8717 2 часа назад

My thought before substituting is to just let x -> xe^x. Then we have lim x->inf (lnx + x)/x = 1

@authorttaelias4483 3 часа назад

You’re the goat BPRP

@muditY0 3 часа назад

who is that in the photo kept behind?

@guillaumeprudhomme4181 2 часа назад

How gosh he got a green one ! 😮

@ByRoadPrim 2 часа назад

I tried and done in 2nd try ❤

@Jack_Callcott_AU Час назад

So good to know this, because the Lambert W() function has been mysterious to me.

@AmmoGus1 Час назад

Why is the domain [-1,inf)? xe^x accepts any number as input. Maybe i just dont kniw what "to have inverse" means exactly

@ConManAU 24 секунды назад

A function f has an inverse if for every x there is a unique y so that f(y) = x. For that to happen, it has to be bijective - one-to-one and onto. The function x e^x can be defined for all real x, but you’ll find that there are values of x less than -1 and values greater than -1 that give the same value of the function, meaning you can’t pick a unique inverse across that domain. By restricting the domain of the function to [-1,infinity), you force it so that there’s only one value in the domain that corresponds to each value in its range.