Epsilon Delta Limit Definition 1

[Aliyare20101]

Sucks

[Domukas64]

Here's your ϵ. Now give me my DELTA!

[pink2bluee]

@Domukas64 ∂

[MisledTrick]

@pink2bluee Wrong, it's δ.

[pink2bluee]

@MisledTrick Then what did I make?

[MisledTrick]

@pink2bluee You made a ∂

[pink2bluee]

@MisledTrick But what is it called? If not a delta.

[MisledTrick]

@pink2bluee That looks quite like a vertically flipped delta symbol. I'm not sure where you got that from, is it Greek? :o

[pink2bluee]

@MisledTrick Probably. I got it by pressing alt+d on my mac. I figured it was delta since it's on the letter 'd'.

[henrysaltandson]

This was fabulous!!! I can't wait to watch the next video!!

[MrTelaviv123]

I am going to nominate you for a special noble prize for mathematics.Great stuff. Keep up the good work.

[TheStfu1000]

listening to some lecture for an hour with someone maths person who's numbers and writing is all unreadable is an ancient way to learn. really one above the age of 13 could get a well rounded education from wikipedia and the internet.

[0oJMPo0]

Best part: 2:42 =D

[IhateMissouriALot]

epsilon delta = erectile dysfunction

[TheVortexLord]

Man, you are the best.. I could not get into a high level mass class, because I'm in full IB and don't have an extra free period for math 35 next year, so I try to keep up with the HL stuff on my own, thank you for these videos, they are very helpful.

[hanthonypiano]

Writing everything down along with him helps even more... this guy is great

[starlinej]

I never learned this in Calc 1, but we just started learning about it in Real Analysis and this video was a big help.

[yiya1717]

OMFG! DUDE YOU ARE A SAINT! I WOULD HAVE FAILED MY EXAM IF IT WASNT FOR YOU! Bcuz my instructor doesn't speak english well, and I don't know what the hell she tries to say during lecture.

[TnTLeGenD]

Awesome

[Wacko375]

Excellent explanation.

[MrSamarthz]

thanks a lot

[popshuvitskater]

the Epsilon Delta definitions in all my calculus books are always ridiculously complicated

[rynull92]

how can i prove that the functionx^2 is continious with the epsilon delta definition?

[TasteMyNutss]

@rynull92 derive limit theorems from epsilon delta and use those

[Vorbis5]

And this year of Calc AB will be a breeze. TY.

[hameed]

KHAAAAAAAAAAAAAAAAAAAAAAAAAAAA­NNNNNN!!!!!!!

[DzSchuur]

Thank you very much, never got it with calculus.

Now I do!

[NoneOfTheAbove312]

is delta always the same length on both sides?

[fosheimdet]

10^-100 would not be one in a trillionth, Sal. It would be one in a googolth :D

[niggakilla911]

@fosheimdet whenever i put that into my calculator it says error. I think this doesn't exist so lets not call it anything for now

[fahim5358]

some time we say that f(x) is not define at "a" what does we mean itt. i mean that how it is possible.

[flopski]

@fahim5358 because at f(a) you may be diving by zero have a negative in a root function.

f(x) = (x+4)/(x-2)

f(x) is undefined at x = 2 because f(2) = (2 + 4)/(2 - 2) = 6/0

[gmandog6]

A champ....your the best

[iPinkheart]

I cannot thank you enough, Khanacademy! I am currently enrolled in an online calculus course, and I have seriously no idea what is going on until I remember your website! Before coming to this video, i starred at the page on the textbook that talks about this epsilon delta limit thing for almost an hour, not understanding anything.... I spent this 12 minutes and 48 seconds way more effectively than the hour I wasted!

[Zander101084]

this is pretty easy if you just sit down and pay attention to it. YOU'RE AWSOME SAL!!!

[scamander24]

Thank you so much!!! You've helped me more than my math teachers lol

[rockerstolle]

great job,thank you!!!

[slatz20]

draws look like kindergarten stuff...anyway amazing videos u made;)

[vkgoku2012]

I understand this now thanks for your proofs I hate learning math without understanding where defintions come from then its just memorization and relying on intution which becomes guess work, especially considering when you get older you forget most definition.

[pranagy]

12 minute video = what 3 hours of lecture time couldn't explain.

This guy is amazing

[MyHugestFan]

This video is most popular with:

Gender Age

Male 45-54

Male 25-34

Male 35-44

I'm 18 and i feel like the new fermat

[himing02]

@MyHugestFan i'm 17. what does that make me.?

[MyHugestFan]

@himing02 old enough to be my pupil.

[avilesnba]

oh man great stuff....kudos

i just started my first ever course on calc....and the whole limits thing was confusing. Like you said, i was confused about this stuff and we were already moving into derivatives....

thanks for the help though, i completely get it now

[InfiniteExistence]

absurd drawings

[jackstorm777]

I read this in my textbook and was COMPLETELY confused, you have totally cleared it up for me! YOU ARE AWESOME!!!

[radashevskiy]

omg finally someone explained this so that it actually makes sense. the key phrase for me was the " Ican guarantee you that..." Thanks so much! now i dont like my calc teacher even more

[ijoly]

Great video!

thx

[MelTurpin]

Excellent video! I think the thing that makes this so difficult for students is the number of variables involved in the formal statement. Look at those last 2 equations you wrote:

0 < I x -a I <d and I f(x) - L I < E

That's 6 different variables! And on top of that we're throwing in abs value signs which also often confuses students (it's just a distance though)

Nice work!

[SaphiraPorter]

hey i should watch all of these vids and then i'll be smarter than my math teacher XD

[Saypayaa]

This is so awesome! You should get a Nobel Peace Price for preventing so many students from ripping their own hair off. Good job and thanks a lot!

[trybalnet06]

why cant i have you as my professor?

[xjaat]

Sal I wanted to know why E and S have to greater than zero? they dont do they.

[warvad]

@xjaat You want the distance between the points to be negative? Nice.

[pithikoulis]

@xjaat you mean epsilon and delta? because if they are 0 then it means that they are the same as L and a. That's something that we don't want. We want values that are close to but don't touch a and L

[playitverysmart]

meh.... ap calc bc didnt make and our teacher trys to only go over whats on the ap exam so we arent going over delta-epsilon :\

[myqueensindel]

I just shed a tear.

[delinquentnerd]

you > my professor

[xAsianZombie]

Thanks Sal, im in AP calc and i have a quiz tomorrow.

really i was absent on friday due to EID, so this video really helped

[evilcitrus]

you sir, are awesome. we learned this on the first day of my high school calculus class and after that the teacher expected us to understand it. this is the first video ive found that actually makes sense to me. thanks a million.

[emubreath]

you sound like john mayer lol

[sameeoh]

thank you sooooo much. this cleared any questions i had with this definition. your my calc savior.

[siebenhens]

my college calc teacher is adamant we learn this and i was having so much trouble with this. good video, very helpful

[jt11347]

I love you!!!! plz make more videos!!!!

[TheMarco007]

Gosh!, after more than twenty years since I first was explained the definition of limit I have finally come to grasp its true meaning!. Thank you very much Sal from Madrid

[1073601]

i'm confused T_T

[MonaRocks09]

this helped me so so so much. you have no idea how loved you are sal. thanks sooooooo much. god bless you :)

[siddharth93214576]

Execellent!! You explain really well. Finally - a rigorous mathematical definition of the limiting operation which connects calculus to our more familiar mathematics

[stelity]

u talk too much

[123Kaduk]

Saaal i wanna be suuuper close :D

great help, thx!

[rinwhr]

10:35 something doesn't make sense to me, why do you need to say it is greater than 0 when whatever the absolute value is going to be positive?..

[Jag0n03]

@rinwhr

Because you need to be some distance away from a. If the distance from a was 0, then you would be directly on top of a. With a limit, you're approaching a from the left and right sides of it but you're never coming onto it.

[bbnl1990]

@rinwhr coz |x-a| CAN be zero, which is not permitted

[rambo1525298]

thx a lot !!!! if all math teachers were like you all the people in the world would be mathematicians.

[emcue786]

thanks so much! huge test tommorow and my professor and TA and tutors did not help at all!

[CogitoErgoCogitoSum]

Sal, Im confused about this. Suppose I did say I wanted to be "super close", and I gave you a very small epsilon. According to your explanation, you can "guarantee" a delta that works. But what if delta necessarily must increase in value as epsilon decreases? Wouldnt the definition still be value? And yet the notion of a limit would become pointless.

[sponsoredwalk1]

@Deuterium2H

Thanks for the mention of Non-Standard Analysis, looks interesting, but it's based on set's and how can people who haven't approached the theory of set's rigourously learn non standard analysis?

If you have a link or book mention please let us know but it seems the set theory used is even beyond intro set theory.

[clixsyt]

Thanks soooo much

[terstenfatiha]

thank you

[GYmystery]

thank you

[moltenthoughts]

wow thats so amazingly and beautifull simple yet so hard to understand. thank you i would rate this video 6 stars if i could!!!!!

[NickPlante]

Thank you Thank you Thank you! This saved me for my test tommorrow.!

[thedoc0109]

what was the drawing software used for this?

[bellatesla]

Windows Paint with Inverse colors :)

[dillon4321]

OMG TY

[shailensobhee]

Six Stars! Who is the professor talking?

[wingegia]

wow, great explanation of epsilon-delta theorem. you explain better than most teachers. cheers, im glad i watch this vid.

[jasonwies123]

very good video, clears up a lot of confusion, thank you so much

[supersmashluva123]

hm. For all you people taking AP Calc BC I'm not sure why you are doing epsilon-delta proofs. I'm in my second year of calculus -- Multivariable Calculus. (That's the level after AP Calc BC) I didn't touch upon epsilon-delta proofs in BC and it didnt show up on the AP exam. (I got a 5) I'm not saying you shouldn't try to learn it if your teacher goes over it, but it won't show up on the AP Exam. Nevertheless, I had to learn epsilon delta proofs by myself over the summer and this video helps.

[rinwhr]

This video isn't for just the AP exams......

[powerfury]

I can guarantee you that you do not have the level of intelligence allowing you to be as smug as you are.

[CPLains]

Norsk? Quake? :P

[supersmashluva123]

whats with the haters? If you guys read the comments I'm just replying to all the people who said something like "Oh! this makes so much sense. my AP CALC (AB)(BC) teacher didnt make sense at all. I'm just saying it's not on the ap calc test and I didnt have to do it. I understand this isnt just for the AP test and this video is very helpful.

[ykhanian]

you're a math genius and def. a lifesaver! ;)

[mayco90]

thanks for your help, u sound like a wise guy lol. i felt like i was in church listening to the jesus quotes, lol. (the tone)

[HerrSchenkel]

Very nice. After watching both of these videos, I think I have a much better grasp on this. But to really wrap my head around it, I'll have to do some practice (which these videos did a good job of preparing me for).

And I wish they waited three weeks to dump this on us, but we went over it on the third day.

[sergito1111]

haha we went over it on the very first day, gotta love AP BC calculus!

[annoymage]

thank you very much

[craigadambennett]

Good explanation of the topics, very helpful, best ive found yet. You need a better tool for doing your presentations though cause its hard to read sometimes.

[anotherNemesy666]

Thank you! This made calculus a lot clearer.

[manolomanca]

khanacademy for  president

[Jtking3000]

wow delta is a russian b

[justin984]

I've never cared enough to post on youtube so this is my first post ever. I just wanted to say thank you so much. I'm taking calculus now and these videos are awesome!

[joshuayap2005]

Now, i understand those delta-epsilon things. Thanks very much!

[sbrian28]

taking calculus now and believe me, I am very thankful for your videos.

[nietzsco]

O sweet merciful intuition, smite down those who take formulas at their face value.

[brilliantfranz]

excelent, i never really got to actually understand this thing even though, I did a lot of exercises findind limits

Cheers from Venezuela

[PedanticPirate]

I'm not sure if my e-mail caused you to put this up, or if you already had it planned, but either way thanks so much!

[khanacademy]

I've been meaning to do a video on this for a while and forgot about it. Your email was indeed the catalyst.

[punkvijay224]

thanks sal.......

[vickiormindyb]

I have no idea what you're teaching, b/c I'm still studying Geometry. I do, however, know that epsilon and delta are two Greek letters.

My best friend's husband is Greek; he moved to the U.S. when he was three.

He gave me a list of the entire 24 letters of the Greek alphabet and what they look like.

Does the Epsilon Delta Limit derive from the Greek letters or is that a coincidence?

[CogitoErgoCogitoSum]

It is the Greek letters. We often steal variable names and shapes from other alphabets... 26 English letters arent enough.

[billyimpcvau]

it is derived from Greek letters. However in this case Epsilon just mean a small change in Y while Delta is a small change in X.

Mathematicians often use greek letters as

variables or to substitute for a known value. In this case epsilon and delta are only substituting for very miniscule values.

[ad2181]

Sal,

Since you must know the "limit" before you apply the epsilon-delta technique to prove the assumed "limit" is true. Epsilon-delta is only a test not a limit finder. Please show some counter-examples, For example (x->3) of (X^2)=10 or some clever function that would be on a standard test for the purpose of proving some people's understanding of the concept a less than others. Thanks, P.S. I've enjoyed your financial-economic series, your anaylsis is excellent.

[CogitoErgoCogitoSum]

I second that. How exactly does delta epsilon fall apart if the limit is false? What are the give-aways that you have the incorrect L? How do you know you simply havent worked the algebra into the proper form hard enough

[Nandine2]

thank you !!!!!

[CogitoErgoCogitoSum]

Every single delta-epsilon proof that I see online examples for use a standard line. They are easy to prove. I have never seen anyone successfully demonstrate the method on a more obscure limit form.

[CogitoErgoCogitoSum]

Does delta-epsilon count as a proof? An evaluation? A demonstration? It seems to me that you need to already know the limit before you can apply delta-epsilon, so the method doesnt really help

[khanacademy]

You are correct. The definition does not help you to find the limit. You need it when you want to prove that a value really is the limit (a value that you would determine using other means).

[clerlic]

I've always had problems with epsilon-delta, so glad you're making videos on them!

[lvecsey]

Perhaps simpler to refer to it as a constraint. It also reminds me of a limit order in the financial markets because you can specify a "Discretionary amount" which is similar in concept to say Epsilon, for a price point around your limit price for the stock to trigger.

Although I sometimes wonder about how the broker and/or exchange actually implements this. I often get the trade to go through at .199999, etc, right next to the end of the "Epsilon"

[Cagebreaker21]

never did this prior college.. needed to watch twice. thanks good video