Introduction to Limits (HD)

[xthexcolorxredx]

Hahaha I was not expecting the calculator to show up on the screen

[deniskatashkentskiy]

that truly WAS the most beautiful parabolla in the history of drawing parabollas xD

[bengalifob2]

you have a nice voice!

[Bakugantsuvai1]

I wish you can do English Lit AP videos.

[darknlovli]

@Bakugantsuvai1 oh em gee thats so true!!!!!!

[Intuition4tw]

My teacher said 0 / 0 is not undefined but it is called 'indeterminable' or something in math. :] I guess ti doesn't matter.

[13jobinbs13]

all i could notice was that the thing he drew at 1:25 looks a bit like something :D

[mesqueunclub101]

SAL! Seriously i dont know how i would have made the exams without you! I am sure to pass Chemistry and calculus becouse of u. I am sure to pass biology, if i watch all of ur videos about biology! I owe u big time! Tnx man!

[helmesjo]

08:50 NEIN! NEIN! NEIN! NEIN! NEIN! NEIN! NEIN! NEIN! NEIN!

[AlexHeemann]

@helmesjo that's what she said

[Superfresh602]

how did you get the calculator on your computer?

[dlghwns]

instant subscribe,

[mxsunayv]

What the limit concept really means?

[sxehitman007]

I just can't tell you how thankful I am, for people like you Sal.

[Viperstrike28]

@kaweeku now on to grammer school!

[sketzartist]

whoa, that calculator surprised me

[ErnieBEWB]

In Example one, why does y=f(x)?

[Metallicedearth]

@ErnieBEWB y and f(x) are interchangeable. They mean the same thing for the most part. Each of them can be easier to work with than the other depending on the sort of problem you need to do.

[R4zyel]

you have a cool voice



[eleven999yogurt]

amazing

[ihavemonkeysinmybutt]

Wow I'm so angry right now. I've been trying to wrap my head around this concept for weeks and then I find out it's the most simplest shit I've ever seen.

[sebzim4500]

Why aren't all videos available in HD?

[aniketkedare8]

@kaweeku not safe........its called "Save"

[CodPK2]

Teacher shows us your vids

[fatimalaraib1]

You teach really very nicely sir ... the best part is that u understand the mentality of modern students & try to teach accordingly ... by the way, I like the finger. makes me think of a hand on the black chalkboard!!

[Johnnymarzo]

10:35....owned

[orfnsz]

well , the vid is really cool. it's like watchin my tutor .well done.

[jay2k510]

thank you, thank you,thank you, thank you, thank you, thank you,thank you, thank you

[32guitar]

10:40 really really really really.. LOL !

[TheGreatBrendon]

Sal, you are the greatest teacher there is, thank you for all your time.

[rhymenorreasonable]

I love you... This is amazing. And what program do you use as a calculator?

[bmxrival1]

so fucking confusing my brain hurts

[ifrostythe]

0/0 is not undefined, its undetermined.

[Kor88Di]

What program is he using?

[nabeek999]

@Kor88Di paint



[LalallaSN]

you sir is a god

[Ne062]

YOU DA MAN SAL

[vinishdo]

I'm so glad that everybody is interested in different things. As a painter, this stuff is horribly boring and confusing, but I'm so glad that SOMEbody understands it. Viva la Difference!

I wish you had been my math teacher.

[ikbenharm]

use paint!!

[CompoundK]

hes like 1.nononononono if ur german

NEIN NEIN NEIN!

[suliemanhs]

watch?v=EhrYQrLBiTQ

[feraligatr8]

I'm really loving maths right now thanks to you! :D

[Trouter92]

i dont get how 0/0 is undefined when 5/5-5/5=0/0 right? isnt 1-1/1-1 0 as in 0/0?

[themagynus]

@Trouter92

Using a calculator, divide somethig, for example 1, by a small number, say 0.1. Then divide 1 by 0.01, then by 0.001, and so forth. Do you see that the number is getting bigger when the denominator is getting smaller? In fact, it looks like the number approaches infinity as the denominator approaches 0. The problem is that infinity is not defined as a single number. (infinity + 9487 is still infinity!) Hence, you can not divide by zero!

[frogger832]

WHY CAN'T ALL TEACHERS BE LIKE YOU. WHY WHY WHY WHY WHY !!!!!!!

[32deej]

sweet. a digital texas instruments calculator

[karanaussie]

guys, does all this come in SAT MATH 2? whats the syllabus of sat math 2 and what all does it cover??

[christoflers]

Ha ha he Sounds like hitler at 8:52 ^^.... "Nein! Nein! Nein! Nein!"

[stubbornVN]

@stubbornVN why do you claim that times a number by zero it would disappear? Or that in the opposite case if you times zero by any number that it would cease being anything but zero times whatever? But in this case (obviously) zero getting divided by zero will definitely occur in equal amount to any other number - resultant once. Where did this early assumption come from?

[idiotrun1997]

I don't get this function though, I mean why wouldn't the function actually equal to 4 when x is exactly 2 though? At around 11:08

[MastodonAD]

@kaweeku Haha, all you need now is an English teacher, :P

[tiff4annie]

how come it's not equal to 1?

[beachbunny85]

you are the jack of all trades. amazing.

[statixc]

I haven't done advanced math since I left college. This is incredibly clear. My professors never made it this clear. Keep it up.

[Cypherdude1]

On the khanacademy org site, if you add a coach, how do you communicate the math terminology to him? For example, how do you transmit differential & integral symbols to your coach? Does the site have some kind of editor you use?

[Neomniblad]

he wants his perabilla to be correct lol

[sansewai]

@Neomniblad Parabola.

[leoqaz003]

1.99999999999999999999999 

[ViniciusFiocco]

Man, I know a lot of people that can't do that, not because they're stupid but because they never learned it with Sal.

[CabalaCicero]

I like your calculator :)

[paulceltics]

100 likes :))

[tjobtjobtjob]

because these are educational videos, u dont have idiots coming all over it and thumbing it down...

[mdwael]

@tjobtjobtjob good point, but in a rare case someone may not be in a good mood and has not quite understood the lesson so retalitates by disliking the vid. I think that explains the one dislike on the video.

[mrfrankincense]

0/0 certainly is undefined and so is 0 * n, infinity/infinity and infinity * n.

[supercalifragilismic]

i wish theres a vid explaining why calculus is that important to study before diving into how its solved for me to get interested in the subject. but i love khanacademy!!! one of my fave channels on yt

[ecuasion100]

@supercalifragilismic calculus is used in engineering and economics

[Yyansquared]

but when x gets to 2, isn't it getting closer to 1 since g(x)=1 when x=2?

or was he just talking about the g(x)=x^2 when he set the limit. HELP!!

[inthekeysofz]

I love your channel!

[alkalait]

I like to think of discontinuities as portals.

[Jigiligy]

@alkalait haha lol

[Mode2]

I think the hand is too distracting, sal. Whatever happened to the arrow? X3

[TheImpressionable]

Khan, if f(1) = 0/0 is undefined, does that mean f(0.9 recurring) is also undefined because 0.9 recurring is equivalent to 1?

[Phatency]

I love how Khan got back into making calculus videos <3

[TheGstar1985]

too complicated for me

[masar1992]

@TheGstar1985 How old are you?

[TheGstar1985]

@masar1992 old enough to be screwing your mum

[masar1992]

@TheGstar1985 Where is your manners? Its not polite to reply with such a bad comment to someone you dont know. You need to sit with yourself for a while.

[IronChefWannabe]

@TheGstar1985

quiet child, grownups are talking 

[hedonism13]

So much clearer than your old one - is he re-doing the vids, or only the ones that need redoing?

[Swetlana0]

Maybe you should consider redoing your electricity videos too.

[mackblayz24]

Iew

[AcademiaVasquez]

Khan, can you please let me know what software you are using? I'm pretty sure it's not SmoothDraw anymore (since I use that myself). I am redoing your vids in Spanish. Thanks!

[JettyXYZ]

@AcademiaVasquez It looks like something you could do in Photoshop with the appropriate brushes, too.

[SMMsideproject]

Oh cool, you uploaded this today and I was looking for something to do with calculus

[Vorbis5]

This is legitimately legit. Cool.

[1Mperios]

Great video, the colours are much more vibrant in HD. Loving the calculator!

[dishonesttAbe]

Can you re-do some of the vector calculus videos? Particularly the curl, gradient, double integral, etc? They're all grainy-looking and you never went into much detail beyond 1-2 videos.

[Maniclysane]

Literally just watched the original an hour ago at the library.

Thanks.

[MatrixOfDynamism]

where is the integration and differentiation theorem proved?

[Jigiligy]

@MatrixOfDynamism exactly what i wanted to learn

[MatrixOfDynamism]

@Jigiligy so where is it than?

[Jigiligy]

@MatrixOfDynamism no idea

[TheOnlyCoolestGuy111]

can i borrow ur brain ? i got the test next week T_T

[Swedishpersondude]

Its fun to learn from you!

[anjula2010]

Please tell me with what program are u writing.Thanks

[dannyboy12357]

in HD lol nice

[rinwhr]

Sal, please DO NOT REMOVE YOUR OLD VIDEOS!!!!! PLEASE! Also since you are looking back at your Calculus videos will you do a video on Stroke's Theorem? It will almost just complete the Calculus playlist....

[Humanity0destroyer]

thanks a lot !

[gmv0570]

there actually is a common place where you see those crazy, discontinuous functions:

the computer's floating-point representation of real numbers---regardless of how many bytes your computer architecture has, you can simply set an arbitrarily-high level of precision for your problem---and your nice, continuous, real number line breaks into millions, billions, ... of separate points---and they are not even the same distance apart...

[jackdestisbest]

@gmv0570 Can you give more real life examples of those "gap - discontinious" functions. I was just wondering when i watched this movie.

[gmv0570]

@jackdestisbest sorry, i encounter the floating-point representation problem all the time because i do computer programming---i just thought i recognized the scenario

besides computer engineering, the other field i know of that deals with this floating-point representation problem is "Numerical Analysis"---i would suggest looking there for other examples

[invictorium]

ok



[MarkQP]

ok

[mance1234]

ok