Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007

[GuitarShredda99]

the limit of the log is the log of the lim

[AntoMelta]

Good, I like that you share this video, I wish success always Exponential and log

[willamricard]

Nice Video Logarithmic differentiation hyperbolic functions That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Exponential and log From Your

[bundawartini]

Your Video Is Very Useful Sharing differentiation hyperbolic functions

[stavrospod]

at the end he says that the limit is equal "1" so how that equials to e^1 !? doesn't it supposed to be e^0 ?

[rydvalj]

great video, you're one of the best lecturers i've found on youtube!

[mdgreg]

Is Saying: "the Square Root of Two", Redundant?

[mdgreg]

@mdgreg , Looked At What I Said, Pretty Stupid.

[agapitoflores001]

This is very useful. Very relevant to students like me.

[channeling1]

at 18:37 he says that b = e if k =1 / M(2) and then moves on without explaining what he means by that. so if you take the equation kfprime (0) = kM(2) , it becomes kfprime = 1/M(2) x M(2), which is kfprime = 1. i don't really get what this accomplishes in terms of defining e. definitely agree with the other commenter that this is an extremely confusing way of explaining it.

[treeandplant]

Guys I beg you that you help me out with this lecture.This is the 10th time i'am watching this.I understood only the first 4 steps.

[toxzen]

dat chain rule....

[joy2000cyber]

This guy screwed up at 26:27 by by using d(e^w)/dw = e^w, which is the exact conclusion he needs to prove. He should've calculated derivative of ln(x) using definition of derivative. Then he can find derivative of e^x using inverse function derivative property. Can't believe this is MIT.

[tikilikiboomboom93]

i so badly want to write on that board with that piece of chalk :P it looks so nice to write with

[rockandswing1]

@tikilikiboomboom93

I so badly want to write on that blackboard only to erase using that amazing "eraser" (am I correct calling that an "eraser"? My english is prety poor). I've never seen these things SO large. I'm going to get one of them for my own teaching.

[santiagogcastro]

I think he got lost in this lesson, he should have use the propiertes of ln and make the equation lny=lna^x and then use the chain rule and implicit diferentiation and he would have finish right away

[santiagogcastro]

I love mathematics, because I like true reasoning, the problem seems to be the language, I told my friends that I saw more truth in 3dMax of Autodesk because its language is perfect, they use objects, transformation, parameters, functions... but all these words are always in the right place, here I have no problems understanding, geometry, algebra, arithmetic, the problem arises when different variables come into the ecuation and notations are not rigurous such as confusing a line with a plane

[santiagogcastro]

God I don't know if I am crazy, but when he goes around with a demonstration which takes hours and he pases over a figure such as saying :"the slope of a exp to x where x=0 and we know that a exp 0 is equal to 1. right there what could it be easier.

[ScoNate]

I like his bigass chalk.

[amapmwt]

i enjoyed this seminar very much. from the very beginning there was a crescendo building towards the end where the climax had arrived and the meaning of e and ln were understood.

[Osman9100]

To Keep straight :

If w=lnx then e^w =w. And then w=lnx and e^ln x=x

[MargusMartsepp]

@blakescello If you use iPhone, then open a browser and go to wolframalpha and search for Limit[(1 + 1/n)^n, x -> Infinity] or just lim_(x->infinity) (1+1/n)^n.

[izadk]

The natural log explanation (21-27:~) was absolutely fantastic!!!

[coolboy93smokingeyy]

nerds

[Muffinfordinner]

He's an ok teacher. He certainly doesn't hold your hand with this shit.

[MrHinderance]

I hate how he ends everything with a period. You're not writing sentences, prof.

[KwameNewton]

@MrHinderance Math is the universal language!!! :D

[EdwardCurrent]

I've been watching these lectures and this is my favorite so far. To finish with the numerical calculation of the "mystery number" e was brilliant.

[baaroodii]

black boards are beautiful

[rune500125]

you write faster than i can type

[sandi0688]

thata was great video!!!!!!! you are awesome!! thanks very much

[comecra85]

This is the best explanation of e that I have ever met.

[kauboibiboppu]

did he even prove the derivative of e^x ?

[evox1991]

the way he solved that limit at the end by using the derivative was absolutely brilliant : ) thx : D

[Lithiumz]

My native language isn't English, but this prof explains things so well that I feel like he's from my country.

[suinthemat]

Diffrerentiation of logarithmic and exponential functions.

[DBangaDon]

I <3 MIT

[dmokhtar]

Great series and lecturer. Only thing that bothers me is how math instruction always insists on teaching the general abstract proofs at the VERY BEGINNING of the lecture which makes everything so confusing. It's a logically correct method but on a practical level silly.

It would be much easier for the iniate to first be presented straight with the equation, practice a couple of exercises first, and then afterwards show how it's proof is derived.

[Mzimzim]

I like this guy.

[payroll6278]

This is very informative!! It makes me eager to go to class again tomorrow!!

[pcarron2]

Someone message me if they want to work through some of these problem sets. OCW >= College

[Vegasred125]

I took Calculus some 20 years ago !! Young people today have it made. Once you went home with your textbook in the old days you were on your own to figure things out.

I also like this teacher. I am listening to these lectures for the fun of it given my math is very rusty. I want to get back into physics ... so I need to polish up my math.

[humper3000]

For some of us this isnt enough =/. I actually have to sit in the library for hours to figure things out not all of us have it made ... Sadly

[floppyorange]

@Vegasred125 I am so sick of hearing about how the youth of today have it made. Boo hoo, did you walk both ways to school uphill too? Get over it. Better yet, get over yourself.

[josecitomadera]

I agree. The problem with folks back then is that something that was obviously simple was made difficult to justify their supposed intelligence. Calculus and basically nothing is hard if explained CORRECTLY. Descartes said this many centuries.

[josecitomadera]

@floppyorange Me too, I'm tired about today's youth have it made. The problem is that these OLD ROTTING FOSSILIZED CORPSES of yesteryear believe that nonsense. They're all just right wing "pick yourself up by your bootstrap" fanatics, LOL.

[rarejd]

@Vegasred125 We'll say similar to our offspring in 20 years.

[treeandplant]

@Vegasred125 good i like the the spirit.I'am 27 and would like to learn math from the scratch!!.Are you on twitter by the way?

[smileyj]

@Vegasred125 Seems like its not just young people who have it made.....old snobs who cant remember what they were taught are getting alot out of it too

[roodawgy]

i watch 3 lectures of his every week. This is amazing.

[gavilanch]

@HyperBorealOperator (First of all, I don´t speak english as a native language, so, sorry for my mistakes) I think that is kinda stupid to criticize these videos that are free, I mean, if Somebody were paying it would be ok to give "not flattering" comments...

There is a expression in my country "A caballo regalado, no le mires el diente" (Never look a gift horse in the mouth)

This is free men/woman...don´t worry, I know you are just making a observation and not criticizing

[LV07TSK]

Damn, this prof. is great!

[liusinger]

i hope i get accepted by mit =)

[blakescello]

evaluating lim (1+(1/n))^n for n = 1,000,000,000,000 just crashed my iPhone

[LogicalFlawDetector]

@blakescello

Bahahaha Made in China!!!

[666modac1]

@blakescello Works on a TI-89 Titanium.

[panda20091]

This teacher is really the best! Many thanks to him.

[woodmaster413]

would single variable calculus be calc AB

and multivariable calculus be calc BC in high school level?

[scigamerfan07]

Single variable calculus (aka Calculus I and II) is equivalent to AP Calc AB and BC.

In AB, there is material from Calc I and a bit from Calc II. In BC, the material revisits Calc I to some extent (that's why there's a B in the course names AB and BC) and then covers the Calc II material.

Calculus III (multivariable) is not covered in high school because most students don't reach that far (the ones that do might take a special class or they enroll in a college class while in high school).

[maodvdiiect]

Does anybody know which lecture actually contains hyperbolic functions? The class notes and these videos are a year off so they don't really correspond as well as they should. But I don't think MIT would skip a section in a foundations math course... Any MIT students know? Thanks.

[blakescello]

You won't find this in the video lectures, I'm afraid. I thought I saw a brief review in the notes from the MIT site, but I'm probably mistaken since you said you checked them out already. I purchased the textbook and it definitely has a good review. The textbook is not cheap, though. . .

[bgreeson]

@maodvdiiect hyperbolic functions aren't so important

[3xor3]

that the most convoluted explanation for what "e" is. I now feel like i don't understand it.

[yyeppesz]

Haha i agree. Instead of convoluted he called it circular...no wait "circuitous"...lmao!!

[nohyaya]

thank you!

wish i have money to donate ;)

[Owleyes888]

One of my fav!!!

[PianoWallaby]

Thank you, MIT, for posting these.

[danrah7]

Awesome