L'Hopital's Rule Example 1

[tireironman]

great example

[g2k25d94]

You know this guy is something special when he gets the same thing 3 times in a row yet still trudges on!

[milroxsox]

Why didn't my calculus teacher show us this on the first day?!

[DavidsonLoops]

Did Sal just prove that infinity equals 6?

[OldRsPk]

@DavidsonLoops no rofl

[MementoMario]

In 02:18, why does it say, "So that's the derivative of our numerator, maria, and [...]" in the subtitles? He doesn't say MARIA? Surreal moment there... since that's my name. Am I going crazy?

[kingkarl12341]

this is awesome i love the colors

[MegaZambam]

L'Hopital's rule is essentially useless.

[TuMadreCon]

L'Hopital's Rule in a nutshell: We must go deeper.

[MrTakeUrBitch95]

thny sal

[fishboneisredhot]

after how many attempts do we give up on L`hopoital`s rule? I can`t imagine a problem in a test requiring a 10 fold L`Hopital`s rule solution

[MrMetacognition]

"Woman Orgasms 300 Times a Day"... What are you trying to suggest here Sal?

[nddung92]

Thanks you very much, my 2nd best teacher (after my parents). Your lectures are always interesting.

[randomdd123]

I don't know if anyone else has mentioned this, but an alternative is to use L'Hopital's rule backwards and use the antiderivative. This would give you lim x->0 = (-2cosx + .5cos2x)/(.5x^2 + cosx) = (-2+5)/.5 = 6.

[JMRostropovich]

@randomdd123 wrong. calculation error. have to prove that (-2ccosx+.5cos2x)/(.5x^2+cosx) is 0/0 or infinity/infinity before using L'Hôpital's Rule

[knobbyno8]

Ok quick question, At what point do you stop using L'hopital's rule, and just expect that the limit does infact equal zero??

[ranmanxd]

@knobbyno8 U just go on using L 'hopital's rule till you get indefinite form.

No Indefinite form, U put the value to calculate the limit no matter the limit is zero or whatever

[shobhan126]

we could have simplified (-2sinx+4sin2x)/sinx = [-2 + 4(sin2x/sinx)]

which would further simplify as 8cosx - 2

and then take the lim of this expression

then we wouldn't have to apply L'hopital's rule again......

[ParanormalEnities]

This is great!! I wish their was also an engineering or computer programming section that would be amazing Thumbs up if you agree!

[CluckCluckBoomz]

Theres no way you can write that well with a mouse?

[supercalifragilismic]

@CluckCluckBoomz yes because he actually uses a pen tablet

[Br3nD0g]

@CluckCluckBoomz he's a ninja

[navataru]

@CluckCluckBoomz he's using a tablet

[mathewheffley121]

@CluckCluckBoomz hes prob on a tablet

[yamenhawit]

@CluckCluckBoomz Definitely a tablet.

[CreeBrother]

@CluckCluckBoomz tablet

[plostellum]

thanks so much!

[Charddy]

Khan.. please stop repeating yourself.. Driving me nutts.... I can rewind the vid here..if i need to hear it again. (P.S. not just this vid.. all of them)

[Ganondorfothraccount]

@Charddy I find it very helpful because it reinforces his previous statements, and becomes more concrete in my mind. That being said, everyone is entitled to their own opinions.

[Charddy]

@Ganondorfothraccount .... Thats.. cool maybe its just me then.

[hedonism13]

Am I the only one who think Sal would make great gaming walkthrough videos?

[tIs4gatorbait]

@hedonism13

I don't know, it took him a while to get mspaint down lol

[mdwael]

@hedonism13 There are plenty of good gaming walkthroughs all over youtube, but it's not often you find a good person like Sal who posts good educational videos.

[hedonism13]

@mdwael

haha, I know, I was just saying I thought that Sal's voice doing a gaming walkthrough was a funny concept.

I wasn't making a request or anything.

[hadesbearer]

Hey man, thanks for all your help this exam season... I never knew about iterating l'hopitals rule like that! Useful

[piggygobyebye]

Why didn't you use the quotient rule when evaluating the derivatives? I thought you had to when taking the derivative of a fraction...

[theavantika31415]

@piggygobyebye I'm not exactly sure here, but I think it's because it's fprime(x)/gprime(x)

soooo that's two separate functions. it's not the derivative of one function, it's the derivative of two separate functions (top and bottom). if that makes any sense... i'm not sure if that's right

[wlnstontang]

@piggygobyebye I'm not sure if he explained in this video, but using L'hospital's rule, you evaluate the derivatives of the numerator and denominator separately. I know this is 3months late, but hopefully this explains this question to other viewers. MaTh RuUuLeZzZ!!

[chrisrock1990]

@piggygobyebye i don't know if i am right or not but i believe its because we are NOT taking the derivative of the whole function. we are only taking the derivatives of the numerator and denominator separately. Because that is what l'hopital's rule tells us to do.

so what im trying to say is we are NOT finding f'(x) of the function f(x) = ( 2 sin x - sin 2x ) / (x - sin x)

if we were we would use the quotient rule

[tIs4gatorbait]

@chrisrock1990

yeah i was thinking the same thing. going to have to remember to derive numerator and denominator independently

[KISHAsodmg]

OMG thanks you

[alkalait]

Brilliant, but why did L'Hopital use the slopes of the functions to find the limit of their ratio? What is a good geometric explanation that the ratio of derivatives is the same as the ratio of the anti-derivatives? ... Oh wait.

[alkalait]

I think I get the intuition now. By taking derivatives we basically get a ratio of the "speeds" at which each function approaches 0 or +-infinity. No matter how small or big I get, the rate at which I get to next largest or smallest number implies how much larger or smaller I am going to be than my denominator-function. Correct me if I'm wrong of course.

[faustrecht]

<-- likes that

[adkinsjr]

Pretty straight forward stuff. This rule gets tricky when the indeterminate form is 0^0 or infinity-infinity.

[andreiduffy]

This is my favorite rule. Totally saves me from making careless mistakes using limits.

[Abdelati786]

nice