L'Hospital's Rule and Indeterminate Quotients

[banananana99]

Thank you sooo much! you have helped save my ass

[otownfever]

When I get a job after graduation, I'm giving you a portion of my paycheck. From the bottom of my heart, thank you. You made me ace Algebra, Trigonometry, Calculus 1 and 2.

[Lulita38]

Ahh, I have to remember this -> l'hospital, simplify,,l'hospital, simplify,,l'hospital, simplify.......

Thanks to infinity Mr.Patrick !

[patrickJMT]

@Lulita38 yes, people forget to simplify (that is, do the algebra!) - you are very welcome : )

[QuaziGNRLNose]

Passed with an 88 final grade, top of the class, studying only by watching your videos.

instead of buying a textbook next semester i should just donate you 20$

[patrickJMT]

@QuaziGNRLNose better than that, tell EVERYONE about the vids! that is better than $20 for me. : ) glad the class turned out well for you.

[bwp2bruce]

Patrick > Khan

[hilbug93]

I go to an Ivy League school where tuition is $40000, and I have to watch these videos because my Calc prof is that terrible. Columbia needs to hire Patrick!

[TheRussianGlory]

Why aren't you my prof... why...

[lordkhalloody]

thx alot for wt u done

[FenixEven]

Rate my professor rated my teacher as 2.5. Patrick would most definitely be 5/5

[QuaziGNRLNose]

i should of went to college of JMT

[patrickJMT]

@QuaziGNRLNose send me your tuition and i will print out a diploma for you

[bling6]

@QuaziGNRLNose amen, 5-10 minutes of these videos i learned more than i did sitting for an hour in class :S

[Rahfulz]

6:20 is it okay to just divide before using l'hopitals rule again to get (1/2e^x)+1 as x->inf = 1?

[thatchickslara]

Thank you soo much! This so much more helpful then my actual discussion class! :)

[rsgirl10]

I think I could literally learn more from YouTube than from a first year calc course because of videos like these.

[AliveDog]

If I wasn't in debt from tuition right now I'd donate so much money.

Just you wait till I get my degree good sir :D

[AdamarRamada]

Take my calc midterm this friday for me haha

[ineedaname0608]

This man is amazing and is completely responsible for my A

[FireInTheCockPit]

Lol on that last question I was like "WTF this isn't working, you'll just keep on getting the same thing if you take successive derivatives", then he said "remember to simplify algebraically", and I was like "HOLY SHIT THIS MAN IS THE CHOSEN ONE"

[patrickJMT]

@FireInTheCockPit plug and chug, l'hospital, simplify, plug and chug (and repeat if necessary)!

[tina0595]

where have you been all my life!? ...i mean all semester...

[patrickJMT]

@tina0595 right here! where have you been?

[zguitarmaster]

Doesn't anyone else find it cool that he's a lefty?

[thatchickslara]

@zguitarmaster I seriously thought I was the only one thinking that lol

[shanniechen]

thank you so much for posting these! I hated my calculus course until my coursemate told me about your videos :)))

[Angelgrrl04]

This guy is great. Too bad there's not more of him in real life LOL.

[0505881328]

thank you very much patrick

I really do not know to to thank you

I wish if you are a teacher in my

university

[biancanatt2]

you're an amazing human being! thanks! :)

[djbluelive]

This is really childish: hehe you say L'Hospital in a very funny manner. Which means I haven't head it pronounced that way before. Very insightful though, my thanks you good sir.

[witpc]

thanks! i watch your videos a couple times everyday! :)

[cabz654]

Thanks to your videos, I passed my exam. Thank you :)

[charlesbene]

imba!

[halflife1994]

patrick, who is your math teacher when you are still in college? Cause ur soo good in teaching.

[psychoanalyst]

I purposely went from the website to the youtube page to make a comment, THANK YOU for being someone who KNOWS the rule is french and pronouncing it correctly. If I hear another "le" hospital, -.-

[TheHypaLink]

4 people couldn't solve indeterminate limits.

[paagera]

@TheHypaLink u came here to joke around and people are coming here after getting raped in classes D:<

[dcapacitor]

@paagera Ha ha maybe that's the problem, I'm here to avoid getting raped in class not the other way around

[paagera]

@TheHypaLink thumbs up btw *O*

[ilyahali]

@Bludgeoned2DEATH2 actually, it's either L'Hospital or L'Hôpital :p

[jrtavarez]

Thank YOU!!



[AMARTYA7]

good video!! :-)

[mathewrokz]

thanks :D

[sustantivo1espritu]

l'hopital's rule or l'hospital's rule? but wither way i always call the latter. very nice video man

[NorthernMonologue]

I have never watched a video of yours that hasn't helped. thanks so much :)

[iagopb]

If only math lessons at school were awesumly clear like yours, math would be more fascinating.

[23youwatch]

q: i was watching one of your videos: on solving improper integrals. I i noticed that u carried out L'Hospital's rule in a case where u had (infinity)*(0).

But in this video u said that L'hospitals rule could only be applied when u have (inf / inf) or (0/0).

i may be misunderstanding something, but even so could u put me on the right track

[ckala13]

@23youwatch L'Hopital's rule can be used when dealing with limits that produce indeterminate forms. 0 x infinity is an indeterminate, so you're able to apply L'Hopital's rule.

[ssibalgeseki]

for your last question: (1+2e^x)/2e^x you can simply separate it into 1/2e^x + 2e^x/2e^x and finding this limit of 1/2e^x + 1 is equal to 1. Therefore you don't necessarily have to find the last derivative.

[23youwatch]

@ssibalgeseki i thought that too... but would that give u just Zero?

coz Patrick managed to get 1 :S

[ssibalgeseki]

@23youwatch No, because finding the limit of 1/2e^x + 1, there is only an x value in the first term (1/2e^x). the limit of this term is zero, therefore the limit is 0+1 = 1.

[23youwatch]

@ssibalgeseki

true... damn... im not thinkin today! this rain weather has got me down :(

tht was really stupid :P thnx any way ;)

[humanityexists]

good thing you exist.

my cal teacher knows she cant teach, so she just tells us to look on youtube to learn.

[13xxxbigboyxxx13]

keep doing what you're doing Patrick. Don't stop, this is a great thing man, thanks!

[nbhav1992]

you are the man... i cant understand a word my professor says.. i hope you get paid a lot for your work becasue this is amazing

[ches92]

Seriously why are 90% of all math profs shit at teaching.. I wish my school would hire you, I bet our classes average would go up

[krolarthur]

Man, this is great. Do work.

[TehThreeMusketeers]

You don't understand how much I love you.

Marry me.

[gljma4ever]

Thank you.

[MahadCh33ma]

which book do you use to get questions?

[hyorkim11]

4:33 awkward silence...... LOL

[CharlieTan84]

Thanks for this great lecture!

[pimpmymail]

The number of views shows how many teachers LACK THE ART OF PRESENTATION in their classes. Just a report card they could hand on their wall, or plug it in their **** . Why ? cuz my math "teacher" is a sleepy effed up one

[chenwei1996]

loving this video, the exam questin sloved finally  :))

[LilyMuve1]

Dude you're awesome  O.O

[Blasterfi9]

Damn man thanx, my textbook is completely useless for this section... but yah if possible i think u should maybe improve the indeterminate powers video, the examples r good, but some more variety would be more helpful. BUT STILL THANKYOU

[kpxflameboy]

i always say it like "el hospital (like a real hospital)" xD it sounds spanish..lol

[metallicawtf]

lol my man

[metallicawtf]

lol

[MrAsh2222]

you are so much better than my prof at western...thank you to the power of infinite :D

[antiherodarkmatter]

How is your camera mounted??

[SZS0001]

How can you dislike this video?

[noobguitar321]

@SZS0001 dislike button :D JK

[pheni0x]

thank you very much this cleared up some confusion

[zainabbeans]

wow u are genius.

[N0NA09]

Thank you so much, sir. Greatly appreciated.

[19bng]

I was looking for the explanation of the problem on 3:09 all over books and I could never find it!

million thanks! your tutorials are the key to understanding math!

[dez3192]

Can you take the double derivative or even tripple derivative of each one, anyone comment if you know the answere, on one hand i would assume so because you can just apply the rule again if you have not changed the limit, but on the other hand if you derive the top and bottom of a fumction, that derivative is not equivalent to the function you derived obvously, and maybe the rule no longer applies

[aimoo220]

@dez3192 i guess if even after taking the first derivative you're getting the indeterminant form then only you can apply 2nd derivative...

[Danasqu]

thanx very helpful ! 5*

[zaraki1080]

dude your online tutorials are the best, why cant there be more profs like u !!!

[patrickJMT]

@zaraki1080 tell your math department to hire me

[STEFIzeADVENTURER]

@patrickJMT i sooo would!...i had a precal prof last semester and man was she awful. i didnt learn jack squat in that class (of course i didnt know about you videos back then, but now i do! and i am doing great in calc thanks to you!)

[alexmusicgraffity]

@zaraki1080 , there's no more profs like him cuz he's da best!

[anhhai2000]

thanks for the video dude

[Hackiesacker007]

patrickJMT for President!!!

[patrickJMT]

@Hackiesacker007 i would be vice vice president

[Hackiesacker007]

@patrickJMT

Ron Paul / PatrickJMT 2012!!!!

[ThePinkFlamingo305]

@patrickJMT Patrick do you know any good calculus textbooks for a BC student? Also I never took AB but I know some calculus (almost up to integrals) thanks to your videos. I'm in BC but i still need to learn some of AB material because I never took the AB class (they skipped me) so that's why i'm asking you this. Should I worry about being in BC?

[patrickJMT]

@ThePinkFlamingo305 well, i used books by stewart. the books by larson are also good i think. as for being worried, i really can not say at all. best to talk to your instructor / teacher and let them assess the situation.

[MrPlender]

I just love you Patrick. You cover stuff (like this and Lagrange Multipliers) that no one else covers or covers in the same way (even places like Khan Academy don't have some of the more advanced stuff you do). What you do is GREATLY appreciated. One day, when I am a distinguished thinker and poet I shall publish and dedicate to you a laudatory poem commemorating your deeds.

[patrickJMT]

@MrPlender ha, sweet! an epic poem!

[evenness]

@patrickJMT thanks mate, your videos going to save my ass , my teacher is called The Titanic, i mean you don't need to see the the movie to know what it means XDXDXDX

[crudster]

V helpful.

[Cybernetic]

what if you have something like lim n-->infinity (ln n)^2/n?

[sikera182]

@Cybernetic you have to do the chain rule (I think that's the name in english) and after L'H you will have lim n--> infinity 2(ln n) (1/x) / 1. Then you have to do L'H again, but that is on the video[around 2:40], so you get 0 as answer :)

well if I didn't mess up the chain rule, i guess it's right

[anebg]

Thanks man, I appreciate it. (Getting ready for finals xD)

[ravi487]

Hey patrick JMT...thanks a ton for all the videos...very helpful!!!

can u post some videos doing kind of like a review for all the tests...like one video for series and one video for sequences.... We went through a couple tests in my calc class regarding the regular limit test and the ratio test....when to use which?/

Also, our teacher gave us a problem of alternating sequence...like 5,-1. 5, -1.....

and we had to find the nth term...can u go over this??

thanks and sorry for the long comment!

[Postscript624]

Alright, so that's L'Hopital's Rule then. You basically just taught me what a full semester could not, thanks.

[WeSparkAndFade]

i love your writing lol

[blindskater99]

Thank you very much! You helped me a lot. In 7:25 min I've learned more with you than I learned in my 2 hours math class on L'Hoputals Rule.

[username14657]

Thanks!!

[00oNotAnyMoreo00]

thank you!

[headachehd]

I was given a problem in my calculus class and it deals with L'Hopital rule. The instructor ask us to tell him why you cannot use the rule on The lim sin[x]/x. And he pointed out that if the rule is used there isn't any mathematics problem or anything but there is a fallacy if used based off the definition of the sin derivative

[miinibee]

so that's how you pronounce it lol. I always pronounce it like "hospital" like the hospital where sick people are. Awesome explanation

[heyyhowyadoin]

i love ya man

[dnanalahcnap]

great explanation mate

[bobbylee08]

Great video! I also have the same book. And i need help with a couple of probs. chapter 7.8- #'s 9, 13, and 15.

Your awesome! =]

[Osiyor]

u are simply the best bro!!!

[achironis10]

what happened to ln at 5:30, don't you have to take the derivitive of that?

[H4NN]

The derivative of a natural log (ln) is just 1 divided by whatever was inside the natural log, times the derivative of whatever was in the natural log. Which he did.

[manson666korn]

Lmao!!! He must have written it without even realizing he spelled it wrong but im sure he knows because I tend to right L'HOSPITALS even though i clearly know its l'hopitals rule. Its funny how the mind can play tricks on you :D

[blueboyEXE]

Its funny how you dont get the point of the whole video.

[irfaanfr1]

Nice!

[Naminator99]

It's not Hospitals, it's L'hopital

[silvergodofgold]

@Naminator99 No, that's actually right. See my comment above. The 'ô' is a contraction of 'os', so his spelling is more correct than yours. Originally Guillaume de l'Hôpital, for whom this rule is named, spelled his name l'Hospital before the French changed all their 'os' spellings into 'ô' spellings etc.

[drcraptainfraction]

On the example of x approaching 0 from the right, why is negative infinity divided by 0 negative infinity, and not DNE?

[Ambarenya13]

Because its coming from the right side. The limit as x->0 diverges and if you think about it like an asymptote, one side goes down to negative infinity and the other side goes up to positive infinity, thus as x approaches 0 from the right side it goes down to negative infinity. Hope that helped. =)

[sMaRtiEs1202]

thanks fr explaining @ambarenya13

[gobitz]

dude..all of my dumb PhD professors are just simply Idiots, you make math easier than those with PhD's...

[heydeniseison]

your writing is a lot nicer than my professors haha

[aaronchesterD]

thanks, i have my midterm 2 exams tomorrow.. technical maths - limit, differentiation and intergration.. my notes all suck and i found this youtube link that helped me out so much, thanks again!

[dannyboy12357]

i could watch these all day. good refresher of the fundamentals

[patrickJMT]

sounds like a good (but tough) teacher to me!

[InfernoX17]

shut up

[niccetta]

you are doing a great service to aspiring mathmeticians out there, you just explain the concepts so clearly

[MetallicaFTW7]

omg wtf this is EASY! my math teacher really sucks ... lol

[unholyftw]

wow these really help and brought me back into math, thanks man.

[bestkiteboarder27]

figures...he's left handed

[patrickJMT]

i do things with my right hand too

[bestkiteboarder27]

I know ;) You're just a smart kid. I like how you teach while you're learning and do a better job of it than

lim x

x→100-

teacher's out there. Well done, and thank you!

[bestkiteboarder27]

There was supposed to be a % symbol in there...

[ericasaidso]

ow OW!

[surfinmaniac]

@patrickJMT thats what she said!

[Zhangsiping]

Amazing！！！

[xxotmshankxx69]

tnx alot

[sniper200110]

well lots of ppl had thanked u but i thank you more than all people did =]

[randomUserPR27]

Thanks for the video... I mean VIDEOS. They are really really helpful, thanks a million!

[carzy999]

I feel like I am in class, except for the fact that I am actually learning here :P

[patrickJMT]

u paying attention now : )

[setz0010]

I have to write a term paper on l'hopitals rule. Do you know of any good sources for proofs?

[3BNole]

thank you thank you thank you thank you thank you thank you thank you! :D

[patrickJMT]

hahah! no problem!

[3BNole]

This has been such a great help, my Calc final is in 2 hours, so I've been studying a lot the past couple of days. Every once and a while, I'll come across something that the book and my notes don't explain well, and it's so nice to know that I have another resource to consul and figure out what I'm doing wrong. It's been a huge help! I know comments are only worth so much, but seeing how many you have on your various videos, it doesn't take a lot to see how many people you've helped.

[patrickJMT]

good luck on your final : )

[ibdrumn]

thanks bro this helped a lot

[MiyukiYuki]

Thanks! I have a cal. exam today and needed some review!!

[hbquanie]

lol hey, 1st i thought u were shit! bcuz u spelled l'hopital wrong lol, but after i watched the whole thing!!.....2 words for you! THANK YOU!

[patrickJMT]

In calculus, l'Hôpital's rule (also called Bernoulli's rule; and which is sometimes spelled l'Hospital due to the rule for ô in French writing)

[hbquanie]

ohhhh!! lol learn something new everyday! my bad then! oh snap, u posted this on my bday! thanks again!

[sameasurz]

What if the equation is not a division type..? how do we transform into a division way so we can use the hopital rule..(ax)/(bx)

[driftx2]

good job.. really good explaining!

[patrickJMT]

thanks!!

[jessy0516]

dude ur awesome! im passing calculus because of you.

thanks

:)

[patrickJMT]

you are welcome : )

[bangalirussian]

oh shit i never knew that , the other guys right aur a legend

[magic100172]

i passed math test buy watching your videos the night before.. man ur fuckin legend.. for real

[vaccarovj]

Instead of using L'Hopital's rule a second time, you can also factor out an e^x in the numerator so you'll have:

[e^x(1/e^x + 2)/2e^x)] and the e^x factors will "cancel" and you'll end up with 2/2 = 1 after you take the limit.