Epsilon Delta Limit Definition 2

[j0licious]

CAN YOU DO the |X^2-9| orr |X^2-4|

thanks :D

[amWinRAR]

So much overexplanation...yes you taught me how to do it, but still just go ahead and do it. No need to say the same thing 10 times over.

[CJWproductions]

THANK YOU.

[niemakawy]

Haha, someone during minute seven of this video I went "OHHHHHHHHHHHHHHHHHHHHH", haha, wow. I get it now. Before I didn't understand what we were even trying to accomplish with this epsilon delta stuff, haha

[aepassion]

after 12 minutes, here comes my "i know kung fu" moment (matrix) "now .. I know limits"

[lovex3li]

omg thank you so much for explaining this in a concise and understandable way!!

my professor tries to make everything way more complicated than he needs to...

I think he always tries to get the lowest test average because he brags about that -_-

[Candiecane908]

Sosos what the hell was my professor talking about? Thanks man.

[dharnisha1234]

you rock brother!hey man can you do a video on regions in the complex plane!(complex variables)? this was awesome!

[ThePieces2]

great explanation.

[OswaldtheFourth]

I demand that you come teach at the university of chicago.

[MrCallofdutyfan123]

/watch?v=sy0ylD3pYt4

[diana102393]

OH MY GOD!Thank You!!

I finally understand this! I have a final tomorrow and now I'm a lot more confident!!

thank youu!!! :D

[R4zyel]

IFFFFFFFFFFFFFFFFFFFFFFFFF



[Loooomis]

thx, greetings from germany!

[MementoMario]

@Elzelgator Aww dude, as long as Okan Tekman doesn't look like Voldemort, he's still a human being. :(

[desbravador1]

What happened with the "-3" in 05:26? Oo

Why does it desapear??

I thought it was: |3x-3|<E |3(x-1)|<E+3 [You know..]

Help me please :}

[newkgms]

@desbravador1 Didn't disappear, if you open the brackets, it is still there.. 3x-3 = 3(x-1) He just put them into brackets. If that was your question.

[desbravador1]

@newkgms Ohh. I though he replaced x by (x-1)

;D

Thanks

[Elzelgator]

can you teach that to my calculus teacher too?

his name is Okan Tekman,

it is my first year at university EEE but my fucking teacher made me hate math

he is fucking idiot and he always wears black.. oh man believe same t shirt everday

and also he stings.

i hate you Okan Tekman i hate youu....

i wish transvestites rape you at the middle of the night. you asshole...

oh man that was good..ohh. i relaxed..

[sokaliptus1]

Dude , you are good. No , i mean it. You are good.

[magenta1000]

This is seriously better than Caltech Ma1a lectures.

[fabiouspbrsp]

I study in the best university of my country. Still, i think you are the best teacher i ever had

[lilsleepybear]

This is really helpful! Is it possible to upload some more conceptual limit proofs like the squeeze theorem and such?

[evilfindish]

I'm sure you get this 1,000 times a day, but you definitely just saved my Calculus test grade.

[selvmordspilot]

yea, the internet is the university of the world. And it's fucking free (or almost)!!! Only problem is, the universities still have monopoly on diplomas - but the knowledge is the same :)

Thanks for the lessons

[djsmilieface]

i demand that you come teach at simon fraser university

[iloveasdf]

@djsmilieface

Yeah, I have Brenda Davison for math 151 and she's horrible.

[djsmilieface]

@iloveasdf @iloveasdf hey, did you happen to go to the study session on Friday cause i have no idea what to study for the midterm XD

[iloveasdf]

@djsmilieface

Yeah, I did. It's mostly low-mid level questions from what I could tell but I think you really need to be able to state specific definitions. That won't be fun.

[lilsleepybear]

@iloveasdf

do you guys go to uchicago by any chance?

[yalij]

even though it was a one variable function, this lecture helped me understand the two variable epsilon delta limits too... awesome explaination. thanks @khanacademy

[KyleKairu]

Thanks, helpful vid.

@seanbm0nt

Yes you sure can.

[seanbm0nt]

can you have epsilon be a numerator over a denominator with x in it? for example,

|x-2| < E/|x-1|

[DNYAP]

What about when the function is not a line but something like a parabola, or a polynomial with power 3 or 5? Thank you. :) My book talks about a constant K and a point P and it is very confusing.

[DNYAP]

I come here after reading 10 times section 1.7 from Calculus 7E by Stewart. I even read the Study guide version of the section. Let me tell you, I am good at math, but I was as lost as Adam on Mother's Day! Thank you for this video! It makes sense now. Why make things complicated when everything can be made simple. :) Simplicity doesn't imply stupidity, it implies efficiency and good pedagogic methods .

[canreader]

6:11 "kind of an IFFFFF" xD

[canreader]

6:11 "kind of an IFFFFF" xD

[janan626]

why do we need the smallest delta?

[xxmack123xx]

@janan626 I think it's because the definition of a limit is that you can get infinitely close to a and still retain the property that the value of f(x) is approaching L, so any small value of delta should still prove the fact true

[RicorianGuardian]

It's so simple to apply once you actually know wtf it means. It's just a restating of something you already have somewhere in your head if you know what a limit is. That point is made here way better than in a textbook, the continuity and logic is really shown where before you would have to figure that out yourself.

[DNYAP]

@RicorianGuardian Yeah, I think it is kinda saying, f(x) = y. I f I am THIS far from y in both directions, then, how far am I from x?

[007MrYang]

This is better than a textbook!

[tylerwhitehouse1]

hahaha. if this is your notion of top notch, 24NerF, you have serious problems. also, if you are reading feynman and you can't follow calculus lecture, then you probably aren't following feynman either...

[supersmashbros011]

Thank you very much. I learned more in this 10 minute video than I did in my 2.5 hour calc class! Shit professors suck!

[Tapryne]

once again thank you Khan academy !!!!!!

[MISTERB215]

Nice job! Will be using this video in my class discussion.

[ForeverWiked]

a video involving non-lineral epslion delta proofs would be nice

[ichinarukurumaki]

@ForeverWiked why? the only difference would be the algebra.

[ForeverWiked]

@ichinarukurumaki Because theres an extra step where you have to guess what delta will be less than and every video showing that skips over how they got their guess

[ichinarukurumaki]

@ForeverWiked A guess is a guess. if it wasn't guessed then it's not a guess. <-- i was trying to cut that down as simply as possible (probably failed). No there isn't an 'extra' step. I actually just looked over a non-linear example, and the only issue is the length of the alegbra. There is quite a bit of it, but it's still the same concept as in the video. I commend sal on a very simple example that covers all of what you need for the idea. If you can show me an example of this step, ill help

[drgshnbs]

If a function is not one-to-one how can distinguish betwen 2 values of x wich have the same L+ε or L-ε values?

[zen03lea]

Sweet, read this over and over but still was never very clear on this definition. Your plain 'n simple, visual/audio method is awesome man.

[shuksnet]

Thanks! You saved my life!

[19ownage]

Thank You!!

[samagee24601]

I owe you my life. I took one glance at this particular lesson in my textbook, saw the jumble of confusion sprawled across the page, and immediately searched for this video. Enough said.

[1216superkiller]

INCREDIBLE



[TheEmperorhorde666]

I don't understand a thing my textbook is trying to tell me but after watching your video, I kinda understand it somehow, so thank you

[Klaus08]

Thank you so much, I hope I can shake your hand one day, look you in the eyes and thank you.

[Zander101084]

SAL, YOU ARE THE MAN!

[Zander101084]

SAL YOU ARE THE MAN!

[809guta809]

English is not my native language and I don't speak or even understand so well and It's incredible that I have understand more with this explanation than with spanish explanations, besides in part could be 'cause there are only two or three videos that explain that maked by students.

[syedhaniraza]

Oh man..what kind of calculus is this..i havent seen this in my whole life..how intelligent was the inventor of this was that..!!!

[MultiFreaka]

i feel silly

[z06tiKo]

lol'd at IFFFFF

[Dixtosa]

i dont get the most important part:why is that epsilon delta tricks the proof?

[UchiihaSasuke]

@Dixtosa Because thats the only way mathematicians could prove it. It took them over 2000 years to come up with this proof. --> Bolzano and Weierstrass.

[corkery12]

This guy can beat up Chuck Norris.

[moonmilk15]

thank you! I love how you can explain it in less than 30 minutes and my professor gets paid to stand there pointing at the definition for about 2 hours mocking students and making excuses.

[bourbs1]

I just wish this fuckn guy wouldn't stutter so much! it's like you're following so well but then you lose him cuz he starts falling all over his own words.... it's like "just spit it out!!!"

[corkery12]

@bourbs1 why dont you try teaching this shit. It isnt easy to understand let alone teach it in an comprehensive fashion. He is a life saver to say the least.

[RobSchneeberger]

very good example quite helpful, isn't it sad that university professors that get paid money to teach can't explain it as well

[BunnyHanyou]

I need to date a smart guy >_<.

[MaTuraTemMetum]

His voice is motivating.

[vgadepa]

Hi

I would like to know how to show this video to my students as youtube is blocked by organization where I teach.So please let me know how can I get DVD of these videos on calculus from your site.

[ruthpol]

@vgadepa For example, you can download this video as a *.flv and then convert it with a free programm like SUPER to a mp4-file or whatever you need, and then put it on a dvd or a USB stick.

[radashevskiy]

10:18 there wad a sound like a baby ;)

[LAnonHubbard]

Finished watching this now - brilliant video.

[LAnonHubbard]

I got confused at 1:51 when | x - 1 | was written up. I couldn't understand why the denominator was put there. Then I replayed a couple of times and heard Sal say the 1 is referring to the limit point. DUH! Of course :)

[brtlrt]

I've spent the entire year trying to understand this concept and only now once I've watched this video do I finally get it. University professors can be awful at explaining confusing concepts like the epsilon delta proof

[connie15125]

i got 35% in my calculus class test... wish i watched this earlier! thanks so much though, hopefully will do better in my exam in jan :) x

[warvad]

Oh man fantastic video. This helps a bloody ton.

[ErinKayErin]

Thank you so very much for this video. It is a great resource and the clarity of epsilon delta is perfect! Thank You Thank You Thank You!

[apanapane]

Thank you so much for this video. It helped clear things up for me. However, I think that it would be useful to see an example of when you can't proove it. (In other words when the statement is false.)

For instance, if the supposed limit in this example had been claimed to be 4 instead of 3, it should not be possible to proove that statement. Is that due to the fact that you can't simplify it down to an equation with |x-1| as a component in it?

[rananaires]

Dear Khanacademy: Thank you for the video.

Do you have explanations about linear algebra as well??? If so, I'll love you.

Thank you!

[rananaires]

טו-אוב!!!!!!!!!!



[ruthpol]

good video, I still did not completely understand it but almost.

[jiguzzetti]

Si apruebo calculo en una variable, le hago un templo al dios Khan

[georgyplay]

really.. THANK YOU!! for explain it as clear as you did and make me finally understand the epsilon-delta definition.. i've been just running in circles with this definition untill i found this, it seems you are one of the few people in this world who are able to make it easy to see xD

[PCGamerPortal]

thanks a million, this will help me out in my next test!

[lilkev098]

Well the ridiculously fast pace of first year math means profs don't fully explain the fundamentals of ideas in class. Slower pace is definitely needed to absorb and reflect on new ideas learned. Horray for khanacademy!!!

[aaronhoodrich]

omg. my professor and TA failed at explaining this. THANK YOU SO MUCH

[gaboonviper6969]

I challenge all math genius' to slay #9A..... because I have no damn clue. Please help.

cs.sjsu.edu/~beeson/courses/Ma­30/Exams/Midterm1 dot pdf

yes I wrote dot instead of "."

[MyHugestFan]

@gaboonviper6969 link is broken

[qstong]

some professors are just not meant to be teaching. you should go to unis and be a lecturer.

[24NerF]

Every time I'm stumped in math or physics class, I turn to one of two things. I open up a book by Feynman, or listen to one of his lectures. Or I hit up Khanacademy. I feel ripped off that I'm paying 9 thousand dollars a year for confusing lectures from mediocre profs, when I can get a top notch education with the purchase of DSL.

[qstong]

@24NerF guess you are in u of t

[flopski]

@24NerF Feynman is a great inspiration for me too.

[wsgalinaitis]

@24NerF

You are correct about getting ripped off. Self learners are getting screwed by the monopoly of the ivory towers.

[myqueensindel]

Oh my God, I seriously just.... love you.

You are my favorite person right now, you're just.... incredible.

Stay God-like

[jckb4]

is delta always within 1 of the x value of the limit, or can it be +/- 0.1, or even +/- 2?

[masteralo2234]

@jckb4 in this particular example, he is given the range, which is 1. but if the problem had the lim as x approached 0.1, THEN you have that particular delta.

[frostbitezch]

the colors ands the explainations are just.... mindblowing.

[katarena09]

I Love Yu!! lol thanks so much!!

[Cdoddsy]

You almost had me with the first video, but by half way through the second...you had blown my mind. I am going to have to watch this again.

[jt11347]

I loveeeeeeeeeeeeeeeeeeeeeee youuuuuuuuuuuuuuuuuuuuuuuuuu!!­!!!

[cyruses89]

omg u saved my life thank you

[elementoxygen]

really funny if you put on transcribe audio, real hilarious words. Anyway, great vid Sal!

[AnkleSnapperz]

i love you

[ucsbfiji]

@chaos control - Non profit doesnt mean non revenue

[chaoscontrol2400]

99¢ to download? i thought this is a non-profit organization?

[diane947]

@chaoscontrol2400 it is a non-profit organization. That's youtube charging you the money, not khanacademy. You'll see that its like that for several other popular youtube videos.

[Yvesiscool]

Which video deals with limit derivative notation?

[KirbehsBizzatch]

Alright! Once I find a couple of practice problems to test drive this concept on, I think I'll be set. Thanks!

[ErickSvensson]

Thank you for your time, very well explained

[ThePrincenuada]

awesome man! beautifully explained.

[akondude]

i don't understand this at all.....

[evgageforce]

ty dude help me a lot i from chile i say thanx from the distance =)

[RealXXXTurkey]

This is so awesome! So interesting and well explained! You´re awesome Sal!

[Grobannela]

Please,. please can you explain the definition of limits with two or more variables..I'm going crazy!

[arxuna26]

I've been trying to understand this for a long time, I've searched a lot in the web and I must say this is the clearest explanation I've found. It's awesomely clear!!!!!!!!

Thank you very very much!!!!!

[rinwhr]

Why can't you use L'Hospital's Rule to solve this?

[arxuna26]

@rinwhr you can, but the whole point is to have a formal definition of limit. L'Hopital's rule uses derivatives and to define derivatives you need limits

[qwertytraper]

You're a live saver I got a test tomorrow.

[huanpoo]

thx Sal! I luv ur videos!!

[KaanMusic]

this is great. you are a great teacher. keep up the good work!

[brittany51791]

i second that! i would continue getting "D"s on all my tests without this.

[ki85]

Can you prove with the same definition that some value is NOT the limit, for example that the lim x->1 of 3x(x-1)/(x-1) is NOT equal to 9? Maybe this is the wrong question but to me a proof that can only prove right and not wrong seems to be odd...

[LoneRiver1]

@ki85 if you prove that the limit is 3, it can't possibly be 9, or any other number.

[jaxuber]

@ki85 negate the symbolic definition and you have your counter example.

[Xerxal]

You're an excellent teacher and much appreciated.

[MarcDragon]

Whenever this came up in lectures and worksheets, I always found myself only getting a vague idea of what was actually going on, even after reading through many times and getting help from my tutor. But these two videos have succeeded in connecting all the dots and now everything makes perfect sense! Thanks for providing such a useful resource!! :)

[myez]

I wish I had this video when I was taking calculus. Epsilon and delta seemed like super advanced topics when I first took calculus and it took me hours of re-reading my text book until I finally got the gist of it. Epsilon and delta, at this level, are extremely simple concepts.

Your two videos explains it so well that most people can get the gist of it after a few views.

[CogitoErgoCogitoSum]

Sal, what if your delta was found to be a function of epsilon such that as epsilon approached 0, delta approached infinite?

[CogitoErgoCogitoSum]

I mean, by proving a relationship, you have proven that a range in one infers a range in the other... and thus proving the limit exists through delta-epsilon proof. But in my mind it doesnt work because your delta is growing larger at a faster rate than epsilon grows smaller. I dont know if that makes sense.

[DiceEsque]

@CogitoErgoCogitoSum Its the whole point of proving the limit. It's saying if you want to come within a certain distance of f(x), your x value must be within delta units away from the point x is approaching, and since this is a linear function, it's changing at a constant rate. Wait until you get to quadratics, where since it has a variable rate of change (derivative), you have to pick an interval for allowable x's just to prove the limit.

[charlsielem]

wow. thank you. i really hate these proofs.. but i think i understand it a bit better. i'm sure a second time watching this and i'll be good to go!

[Ehmke25]

Nice Job!! I will be recommending this video to my students when I teach them this concept.

[pamBBB]

u r awesome! Thank u SO much

[andymacmac11]

I get it now! Thanks a lot!

[evry190]

do a hard example

[gombligan69]

thanks alot sal

[thedoc0109]

what drawing software is used for this?

[Guest12929]

WITCHCRAFT!!!!!!

[sedberg1]

Genius!! Better than any book I've read!!

[deathbystarship]

you deserve a medal. i love how you repeat things over and over to drill them into my head. thanks!

[dsprack]

Khan Academy is better than any teacher I've ever had.

[treecko4000]

Thanks dude, now I have understanded what's behind the caculus of limits.

[camf1991]

THANK YOU! I have an exam that involves this on frdiay, and I was absolutely lost until I watched this video. I will be coming back to you for future calc problems I have.

[znap89]

Thank you SO much!! You made me understand this way better than my teacher did during three lectures IN MY OWN LANGUAGE!!

[seekluv]

Yes!! Thank u sooo much! for some reason noone else explained the logic of these problems they only told how to do it. So thanks soo much for explaining! Plus i love the tech u are using. This video was EXACTLY what i was looking for! Im gonna get A's beatch!

[vince12345]

good shit

[bbbruke17]

thank you so much.

[FoxyJD22]

this helps so much, thank you for sharing your wisdom :)

[roflcoptergoswoosh]

thanks alot

[June28July]

Sal the Stockbroker? Thank you so much!!! :D

[leebeanhai]

means E=MC2

[bloodydonny2009]

fuck yer bro, ur the shit!!! out of ppl who tried to explain this to me, ur the 1 who made me understand it!!!!! thanx vewy mwuch sir!

[greatmoose]

ty sir

[life4blood]

I LOVE YOU.

[spamhead29a]

This is the only video that made the penny drop on this subject. Thank you and well done.

[KyGoHo]

great video...one suggestion though, if you were to do another video on the formal definition of a limit, writing out the proof would surely help. but great video, keep it up!

[Skygerobrian]

You really make great instructional vids. thankyou.

And quick ...or at my own pace..

[Lambda3e]

Very nice Sal. You always help me get an intuition for these things. Thanks a lot :)