L'Hospital's Rule - Indeterminate Powers

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! L'Hospital's Rule - Indeterminate Powers.
In this video I discuss indeterminate powers and show how to compute them!
For more free math videos, visit PatrickJMT.com

[@travisfiedler4416]

"Tired of scrounging KZbin for math help?" This ad actually made me laugh because it's so easy to find what I'm looking for. Thanks!

[@patrickjmt]

infinity is not a number. if you treat it like a number, you are missing something conceptually

[@osq6415]

yes sir!

[@mtech1020]

1st semester calculus was easy for me but i got a new teacher for 2nd semester calculus and i've been struggling. i just found your youtube and your videos have helped so much! thank you!!

[@ellaweim]

I have been cramming for my final and without your help I would have spent many frustrating hours. It is 3 am and I have to get up for my exam in three hours. I am feeling so much more confident thanks to you. THANK YOU!

[@nood1le]

The hell dawg. You do know getting good rest is beneficial towards your exam and the opposite goes for not enough sleep.

[@nood1le]

Oh, Its been ten years since you commented... whatever.

[@sebasargent]

You're helping people from all over the world. Thank you from Argentina.

[@ElmoPansy]

Man, your videos are awesome. I can't even begin to tell you how much they've helped me out.

[@chiconium]

man......... thanks alot.............. it helped me... coz ur examples are the same as my teacher's example which i didn't understand......... it really amazed me the way u teach.. :)

[@1603stanley]

i am so feeling this guy..just 20 mins has helped me alot..hehe.thanks men.

[@WretchedM]

Patrick, I admire your humility.

[@ru7547]

it's 2021 and your video is still useful. thank u sir

[@coldfuse45]

THANK YOU!!!! My prof did a horrible job of explaining that, but you made it very clear.

[@patrickjmt]

@AceAites cause it is a limit... the value is getting close to 1 , but not necessarily equal.

[@patrickjmt]

@AceAites so when you raise that number to a large power, many things can happen.

[@Firebolt773]

Thank you SO much for making these videos!!!!!! I'm at a large university and my teacher's office hours are ALWAYS busy so I can't get as much help as I would want!

[@supermadcrazy]

hey thanks pattric u er really very great in teaching,this vidio of urs is like a magic wand which make solving limits easy.thanks a lot

[@msgabe112]

Fantastic tutorial, PatrickJMT. Thank you for going step by step.

[@dozentcare]

u r just straight up amazing! if i get through my college Cal 1 class because of u i'm gonna donate to ur website

[@Gixxiemoto]

Your work is so freaking beautiful,Thank God for creating you haha

[@paradiseheaven]

i actually have atest on this tomorrow and i'm watching this vid to help me haha. thx so much!!! it's a great refresher and helper

[@Arolbreaker]

@AirJordanXVIII I know this is four months old, but the reason that it's spelled in two different ways is because the french word Hospital was changed to Hôpital for faster pronounciation. Most words with an S that jus slowed down the pronounciation of the word had their S removed and a "circumflex" accent was added to the vowel closest to the S. Hospital ----> L'Hospital Hôpital-----> L'Hôpital Hostel Hôtel

[@Syruscleat]

Once again, great demonstration, PJMT.

[@chris2kgreat]

i worked it out slightly differently but I'm not sure if its right but here it is, after i reached ln(e^x + x) / x i worked out the brackets and got: lne^x + lnx / x i then used the property of logs and brought down the x in lne^x: xlne + lnx / x since we know that lne=1, we get: LIM x - infinity = x + lnx / x = infinity over infinity

[@patrickjmt]

@AirJordanXVIII actually, both spellings are common

[@CameronCope]

thank you - i'm studying for an analysis exam and this was very clear. I appreciate the upload!

[@kmed-7044]

Hope you did well:))

[@mgironda]

Great explanations, perfect in case my APC kids are tired of listening to me =] thanks!

[@patrickjmt]

@IGNsucks bernoulli rocks (which one though). those poor brothers fought. one day, when you all get rich, you can pay me to do some math research but you all get all the credit.

[@chris2kgreat]

we now use l'hopital rule and get: 1 + 1/x / 1 = 1 + 1/x (only one "1" is over x) i then worked out the fraction and get: x + 1 / x ( both x and 1 is over x ) this still gives infinity over infinity so i use the rule again 1 / 1 = 1 therefore i still get the answer but i'm not sure if its right. can you please check Patrick

[@dvary89]

@hifhif123 take for example the limit of: (1+1/n)^n as n goes to infinity. this limit is a case of 1 raised to infinity,but the answer is actually the number e. this is one of the various definitions of e.

[@dmd70621]

@patrickJMT yeah im doin a research thing on him right now for my ap calc class, he studied under johann bernoulli and had his own findings as well. when this method was learned by others, it was believed that l'hopital had come up with it which was not l'hopital's intention, bernoulli was only a little upset with this. i guess there's reason to believe he either came up with it himself, or bernoulli did, or they both found it together lol, but later l'hopital had paid bernoulli off for credit

[@scatter47]

5/x where x approach 0 is undefined right? Since right side of the limit is positive infinity and the left side of the limit is negative infinity.

[@dapoochiman]

whoa that's crazy! what do you guys do instead of L'hop??

[@patrickjmt]

i am your teacher now! send me your tuition! i will print out a nice diploma from me!

[@patrickjmt]

thank ya mr. syrus

[@BlahLab]

thank u! i was so lost on this stuff. hopefully i'll pass that quiz tmrw

[@hussainalassaf1138]

its been 9 years . did you?

[@ewaschenko]

Thank You ! Your explanation is amazing compared to my Prof

[@Shkencetari]

This was very helpful.

[@Arycke]

Well, this is what I learned in high school, at least for the last two years of it.

[@Bakugantsuvai1]

Exactly what is an indeterminate power anyway? Would LH's rule help me simplify a cubic minus a constant type problems where the x approaches infinity?

[@patrickjmt]

@yoguely thanks!

[@MageMager-mm9ie]

So the letters are are they missing info or is it an equations that has a background and what is an on on the calculator

[@SATORvii]

as a number gets diveded by numbers betwin 0 and 1 they get larger as the numbers they are devided by get closer to 0. and so closer to infinite as x->0 we say 5/x-> infinite. I hope this is helpfull

[@sethyup]

Thanks, that was a great explaination

[@patrickjmt]

i love l'hospital!

[@skinnycarrotchan]

@akmcferran its supposed to be as it x approaches 0 then as x gets smaller 5/x goes to infinity

[@tao072002]

you saved me, love from a uoft student

[@pyarexxx]

great videos.thanks

[@patrickjmt]

@applesnnbananas 1^infinity only.

[@shogundapker]

I don't speak spanish extremely well, but a rough translation is: The truth is that the explanation was very well. And it is in english...???...but math doesn't have a set language! Did I translate that right? :O

[@MalakWafa]

Is this the way for all tricky questions?

[@SamNecktie]

Oh how I wish I found you earlier in the semester

[@12221bebe]

OMG this video is AWESOME! Thank you

[@Kevin93939]

For the second example, (5/x)(ln(cos3x)), don't you have to divide by (5/x)? So wouldn't it be [xln(cos3x)]/(5) ?

[@x0chick]

Your a great teacher!!! =D

[@n1g3l25]

you mean something like x^3-1 as x approaches infinity? you wouldn't need to use LH rule on that. just solve it normally. Indeterminate powers are powers that involve variables like 3^x-1 as x approaches infinity

[@ICOD73]

What about (∞+∞) and (-∞-∞)? Is it indeterminate too?

[@Epeetastic]

@shoaib21soccer He took the negative from the Sin, so that way he had -15, so that it was just sin/cos to give him tangent. rather than -sin.

[@bearrrr5846]

definitely helped me out! :)

[@Manole52]

Why are you not using the quotient rule in these equations? If the rule is followed (ln(e^x+x))/(x) should not equal (e^x+1)/(e^x+x).

[@alaajassar]

YOU ARE GREAT

[@mistersirisaacnewton]

@tifrogers44 5 is a constant, when you take a limit of a constant, it equals the constant

[@SBUDEX]

uhmm ThanK You very much 4 this.. but y do we use e^(0)? i mean y use e??

[@MageMager-mm9ie]

It be fantastic if you could define the algorithm it's genetic coding it's structure it's placement. What's its value. It has an action I think you have to calibrate your calc30 to recognize your commands to understand the formula

[@spectralblue]

it's pronounced lawn for ln! do you spell out log or do you just say log?

[@EpicNostra]

So is infinity^0=1 let say a trillion a gazillion in power 0 makes 1 right ?

[@sushmad6051]

Very helpful

[@MageMager-mm9ie]

Or it already understands that's why it recorded interderminate. I looked it up and it's like having 2 structures or 2 weights of measurement and not understanding what to do with it what number in a contaminate container yard stands for hazardous or fuel in short ton measurements

[@patrickjmt]

i did that in calculus 0

[@mrproxj]

Hi PatrickJMT, please upgrade your microphones, the volume is a little bit low. Thanks.

[@oneinabillion654]

Is ln(infinity) = infinity? I thought it levels off?

[@jayakumarkumar9188]

THERE IS ALSO ANOYHER WAY-WITHOUT USING THE LOPITALS RULE,IT IS BY USING THE FORMULA.....e^limx-->0 or whatever of {f(x)-1}g(x)

[@sfrancisco18]

Why did you write y as e^ln(y)?

[@goaram]

love Barcelona!

[@ElifArslan-l9g]

thank you

[@WhatElseExceptNature]

Thank you very much

[@AceAites]

Why is 1^infinity indeterminate ? I thought that it would just be 1x1x1....=1. Can you explain that please ? :) Thanks. :D

[@freemkulima]

i thought 1/0 is undefined. How then does 5/0 equal to infinity?

[@leonardohernandez9804]

1/cos3x = tan 3x? Isn't sec 3x? What am I missing here.

[@leonardohernandez9804]

nevermind. figured it out. - sin 3x/ cos 3x = - tan 3x.

[@RadoAller]

Instead of using L'Hopital's Rule could i say that becuz it's ln|infinity| so it's 1....cuz that's when ln is infinity?????

[@michaelderaiche1609]

If infinity isnt a number than why is (infinity + infinity) = to infinity. How can you add an idea but you can't multiply an idea?

[@mandlacalvin6869]

wow THANKS!!!!!!!!!!!! SIR

[@Rocking3anu]

Hello!!!! Thank you...no words ! love you ! bye !

[@santiagoramirezacosta3799]

THANK YOUUUUU

[@michaelbarton7835]

"L'Hospital's" lol, nice

[@andranik70]

Discovered by Bernoulli

[@emmanuelwinston8817]

That is the more older spelling of this rule. Considering the fact that this video is more than 8 yrs old we can cut him some slack on this one.

[@AFIGHTCHANNEL]

Hmm, I understood some of those words.

[@n1g3l25]

definitely

[@patrickjmt]

ahhh, nothing like some good ole fashion racism.

[@ezalcinoryahoocom]

i have to learn all of this by tomorrow :(

[@YaadataKalid]

finna pass my calc final

[@RadoAller]

sorry i meant when ln|infinity| it's 0 ....nt 1

[@vishadmehta5952]

isn't infinity/infinity= 1 ?????

[@MohannadGoesRawr]

He did the algebra first before plugging in the limit.

[@MultiMoe91]

awesomastic.

[@minhtran3988]

Can anyone explain how the Lim y = Lim e^ln(y) x→∞ x→∞

[@abdirahmanali7230]

+Minh Tran e and ln cancel each other. Its one of the log properties.

[@patrickjmt]

@supermadcrazy haahahah! glad i can help

[@prohabetamu]

good job body i like the way u tutor your help me a lot I got A on calcules 1 class tank you body keep up the good work God bess you

[@doncprinc]

la verdad q muy bien explicado.y eso q esta en ingles je je je pero las matematicas no tienen idioma juaz!!!baez!

[@maccamracecar]

@Angelgrrl04 My professor said it has many spellings.

[@khidrrr]

wow... thanks!

[@AirJordanXVIII]

seriosuly you should be a teacher. btw its l'hopitals, not l'hospital haha. but your great man tahnks a ton

[@patrickjmt]

@IGNsucks and he really did not steal it, he paid for it!