Epsilon-delta limit definition 2 | Limits | Differential Calculus | Khan Academy

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  • Опубликовано: 8 янв 2025

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  • @6MasterYoda
    @6MasterYoda 10 лет назад +302

    I'm in the best math university in my country and nobody can explain it as good as you. Thanks!

    • @sivestvet1293
      @sivestvet1293 5 лет назад +2

      Which country and university?

    • @sahafsahaf5848
      @sahafsahaf5848 4 года назад +5

      IIT XD

    • @tonytam1185
      @tonytam1185 4 года назад +24

      this guy is graduated from MIT holding 2 bachelors and 1 master degree at the age of 22 dude

    • @justem1l
      @justem1l 4 года назад

      MSU(Moscow State University)? Or in russian МГУ?

    • @gaiseric9518
      @gaiseric9518 2 года назад +1

      That's because modern mathematicians closed the door behind them. They get to learn from G polya, Rudin, and Abbot. And we get squat, they want mathematics to be exclusive. Read the old masters. They cared more for their students.

  • @ozgokhan0
    @ozgokhan0 8 лет назад +204

    I am a project manager and work at a company.
    I spend my free time with Khan videos when I need relaxation, I sometimes watch before getting on a plane, sometimes at my breakfast table, sometimes prior to sleep.
    These videos help me remember all those calculus equations and theorems from my university life. It's like seeing old photos with my friends. I prefer Salman Khan over funny cat videos :)

    • @vishnubharadwaj8688
      @vishnubharadwaj8688 7 лет назад +1

      lol

    • @harsh.jaluka
      @harsh.jaluka 4 года назад +3

      lol learning and cat videos are not mutually exclusive.

    • @kirubel4607
      @kirubel4607 2 года назад

      ye melata lij ashkabatch

    • @slothbearanonymous
      @slothbearanonymous Год назад

      i like to learn those things i didn't have the motivation to learn while i was lazing around at university lol

  • @ad24aug
    @ad24aug 9 лет назад +43

    I wish we had teachers like you at my college. I never understood this concept and i always ran away from it. But today i totally understood everything just because of your explanation. Thanks a lot for making such a cool site and that too for free! Students like us will always appreciate you for making our studies so much more fun with your cool videos and site. :)

  • @uchihamadara6024
    @uchihamadara6024 7 лет назад +24

    Currently taking calc analysis as a com sci major, and this video has proven INVALUABLE, watching it in 2017 8 years after it was made and it's literally doubled my understanding of limits

    • @sandhanitizer7
      @sandhanitizer7 3 месяца назад +1

      2017 being 7 years ago is crazyyyyyy

  • @danthedoozy9472
    @danthedoozy9472 8 лет назад +107

    Thank you for the awesome video, Sal. Never forget how many students you are helping!

  • @stevencina6704
    @stevencina6704 6 лет назад +5

    Thank you so much for all of your videos. I read and re-read my textbook and reviewed lectures for HOURS on end and still couldn't make heads or tails of the course material. Then I watched a few ten-minute clips from your channel and completely understood what I was doing and how to complete my assignments. Thanks to your videos, I just got 100% on my first quiz.
    By the way, I haven't taken a math course in 16 years, and was just thrust into Calculus. Another testament to how good these videos are!

  • @sujatarkunde5522
    @sujatarkunde5522 7 лет назад +86

    You know something is tough even if a great teacher teaches and you still don't understand

    • @inversechaos9256
      @inversechaos9256 Год назад +2

      Had to watch it a few times before getting it

    • @pradipboro5908
      @pradipboro5908 8 месяцев назад

      ​@@inversechaos9256phew....I'm not alone.

  • @fortunatorosario2266
    @fortunatorosario2266 2 года назад +3

    I'm taking a Calculus 1 class at a local city college. My professor is discussing how to prove limits using epsilon and delta. Very confusing. But after watching your video you make it look like child's play. Keep up the good work!

  • @Musicboy801
    @Musicboy801 9 лет назад +37

    Thanks for the video =) it would be really awesome if you uploaded more videos of epsilon delta proofs of limits of more complicated functions (of one and two variables). I'm sure I'm not the only one who would appreciate that very much!

  • @hsmith8187
    @hsmith8187 8 лет назад +10

    You made this much easier to understand than my college professor.. great job!

  • @MarcDragon
    @MarcDragon 15 лет назад +3

    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!! :)

  • @rickshawty
    @rickshawty Год назад +1

    This man is 100% responsible for my education!!! We appreciate you Sal Khan

  • @spacejunky4380
    @spacejunky4380 2 года назад +1

    I'm rewatching to rehash what I already picked up. In the last video, he explained epsilon in a way it made the absolute values of the definition understandable and it clicked. So nice having this guy

  • @juliusceasarhortelano7020
    @juliusceasarhortelano7020 5 лет назад +2

    The video is almost 11 years and still very helpful. That's the beauty of math, the rules never change.

  • @mikechaves2868
    @mikechaves2868 7 лет назад +23

    haha I love it!
    "IFFFFFFFFFF..."

  • @SRCmandan
    @SRCmandan 11 лет назад +1

    I study maths at a fairly prestigious university, but still, I understand this so much more now than I do reading my stupid textbook and being at unimaginably complicated lectures. So much better to just do education (at least first or for review) through khan academy so maths isn't so hieroglyphic all the time... :)

  • @moonmilk15
    @moonmilk15 14 лет назад +3

    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.

  • @zen03lea
    @zen03lea 13 лет назад +1

    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.

  • @zp_suki2836
    @zp_suki2836 4 месяца назад +1

    My math professor tried to teach this to us the second day in a beginner calculus class… I really am praying for those that haven’t done calculus before 😭

  • @syedhaniraza
    @syedhaniraza 13 лет назад

    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..!!!

  • @arxuna26
    @arxuna26 14 лет назад

    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!!!!!

  • @vishaldalavayi8258
    @vishaldalavayi8258 3 года назад

    You made this video when I was in 1st grade, 12 years later I'm watching this and its helping me so much more than my professor or TA.

  • @georgyplay
    @georgyplay 14 лет назад +1

    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

    • @ebadyo2906
      @ebadyo2906 3 года назад

      Hello are you there?

  • @gforhan1
    @gforhan1 12 лет назад

    I just spent two days trying to figure this out.... and you had me an expert at it in under an hour. Thank you so much!

  • @hfserran
    @hfserran 12 лет назад +2

    Very intuitive. Surprisingly clear. Thanks for taking the time to explain topics like these Sal!

  • @pepemundial
    @pepemundial 10 лет назад +68

    You are the "Lionel Messi" of Education

    • @6subswith0vids80
      @6subswith0vids80 6 лет назад +5

      José Saavedra Cristiano Ronaldo*

    • @snake9965
      @snake9965 6 лет назад +8

      Khan is the best, so Messi is the one you want to compare him to.

  • @arthurthegreat216
    @arthurthegreat216 11 лет назад

    Glad to hear I'm not the only one. I'm a joint honours physics and math and my physics prof used this limit definition in the definition of phase spaces, so I've decided I'd finally go back and make sure I understand this well.

  • @justinchanjinle
    @justinchanjinle 13 лет назад

    I just started my actuarial science course and we were learning bout the epsilon-delta definition for nearly 2 hours. I couldn't really register what the lecturer was trying to convey. But damn Sal conveys it in 10:56. He sure has magic. \m/

  • @joseluis8291
    @joseluis8291 11 лет назад +3

    Oh, God! Finally I understood the definition of limits! Thank you Khan :)

  • @myqueensindel
    @myqueensindel 14 лет назад +1

    Oh my God, I seriously just.... love you.
    You are my favorite person right now, you're just.... incredible.
    Stay God-like

  • @konchu5221
    @konchu5221 Год назад

    I FINALLY UNDERSTAND!!!! this is like the 5th video I've watched

  • @camf1991
    @camf1991 15 лет назад +1

    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.

    • @ebadyo2906
      @ebadyo2906 3 года назад

      Hello are you there?

  • @zephyr1871
    @zephyr1871 5 лет назад

    I don't comment on videos like these but I have to, you took a topic I've been struggling with for days and made me understand it so well. I love you homie.

  • @denizcelebicom
    @denizcelebicom 12 лет назад

    omg i love you. after watching everything and anything i understood what i actually have to do. thank you so much !

  • @prog2ma
    @prog2ma 12 лет назад

    Sal remains the best video instructor i have seen so far. Correct me if I am right.

  • @LuisReyes-zs4uk
    @LuisReyes-zs4uk 6 лет назад

    Had been trying to understand this for a week and I was stressing out!! And boom it just clicked! I’m so happy, thanks!

  • @tanishqsharma8765
    @tanishqsharma8765 8 лет назад +2

    sal i have a question:
    At 3:30 why haven't you stated that [3x(x-1)/x-1] -3 also NEEDS to be bigger than zero because if it does equal to zero that means that in the given function at 3 on the y-axis there is a point that exists. HOWEVER
    at 3 on the y-axis there shouldn't be any point in existence because if x cannot be equal to 1 y cannot be equal to 3, unless you've defined that there is a point on the y-axis at 3 but not when x=1 (which you haven't done)

    • @jewbacha1137
      @jewbacha1137 8 лет назад +2

      In the very beginning, he stated that epsilon has to be greater than zero. Thus, since epsilon is already defined to be greater than zero, there is no reason to restate it. You may then ask, however, why did Sal then include that for the delta inequality when it was also already defined to be greater than zero, but not for epsilon (which in fact is the case in my textbook as well as Wikipedia and many other sources, which leads me to think it is intentional)? This is because we want to force the absolute value statemen in the delta inequaly to be greater than zero as well. This is because the absolute value could result to zero, and still hold with delta being greater than zero, but we also want the absolute value statement of x-1 to be greater than zero, so that the value x never actually equals what its approaching. Hope this helps! :)

  • @harshilshah8983
    @harshilshah8983 2 года назад

    Oh my god!! I have been struggling to understand this definition of limit. And your video cleared it in seconds. Thank you so much man.

  • @RicorianGuardian
    @RicorianGuardian 13 лет назад

    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.

  • @Chippeh
    @Chippeh 11 лет назад +1

    Praise our lord and saviour Khan!

  • @Cdoddsy
    @Cdoddsy 14 лет назад

    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.

  • @diana102393
    @diana102393 13 лет назад +1

    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

  • @vyx6005
    @vyx6005 7 лет назад +1

    I don't know what my education would've been like without Kahn.

  • @lilkev098
    @lilkev098 14 лет назад

    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!!!

  • @KirbehsBizzatch
    @KirbehsBizzatch 14 лет назад +1

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

  • @ryanshota7382
    @ryanshota7382 12 лет назад

    this guy is a BEASTTTTTT
    thank you so much you are my new calculus teacher

  • @PlasmaPrestige
    @PlasmaPrestige 12 лет назад

    Thanks Sal. I generally don't have trouble with Calc, but the notation for these proofs confused me utterly. This makes much more sense.

  • @magenta1000
    @magenta1000 13 лет назад

    This is seriously better than Caltech Ma1a lectures.

  • @GamingSolutions
    @GamingSolutions Год назад

    it took me a whole day to understand my teacher lecture but still could not understand. Then i headed to University of RUclips and i got Sal. Thanks for saving us!

  • @found2273
    @found2273 2 года назад

    It took me watching this video three times with solving and pausing and thinking, to hopefully fully understand the concept, and its really okay if you can't get the full picture in the first go.

  • @da_knug
    @da_knug 2 года назад

    I have never really understood epsilon delta proofs until now. Great video!

  • @TheDutch1291
    @TheDutch1291 10 лет назад +2

    You are a math hero. Thanks for the help!

  • @buzzboy7
    @buzzboy7 13 лет назад

    I'm a very visual learner. This was brilliant.

  • @MoaazQaddah
    @MoaazQaddah 10 лет назад +2

    YOU ARE A LIFE SAVER!! THANKSSSSS

  • @adityaprabhakar7368
    @adityaprabhakar7368 2 года назад

    These lectures are gold mine for us. Heartiest Thanks to Khan Academy team.

  • @cutefamily1472
    @cutefamily1472 3 года назад

    You deserve all my college money cause you care to teach more than my professors do

  • @znap89
    @znap89 15 лет назад

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

  • @hazarilalmeena3455
    @hazarilalmeena3455 6 лет назад

    Thanku very much sir....it clears my concept upto 90 percent..

  • @thebrainfeed402
    @thebrainfeed402 4 года назад +2

    I am in a IIT and still watching a 11 year old Khan academy video...

  • @aphoskins95
    @aphoskins95 11 лет назад

    Thank you so much, youre the reason i'll pass calc

  • @kanadagirlswims
    @kanadagirlswims 11 лет назад

    OMG exam tomorrow and you saved my life! thank you :)

  • @SandeepTiwari-hq2cd
    @SandeepTiwari-hq2cd 4 года назад

    Watched many videoes on the same topic but understood the concept by this.

  • @charlsielem
    @charlsielem 15 лет назад

    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!

  • @connie15125
    @connie15125 14 лет назад

    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

  • @mahavirbhakta6910
    @mahavirbhakta6910 6 лет назад

    This is is better than the updated video you guys have

  • @LAnonHubbard
    @LAnonHubbard 14 лет назад

    Finished watching this now - brilliant video.

  • @ishanihira4305
    @ishanihira4305 4 года назад

    Oh my god it makes perfect sense now and I can even visualise this stuff... Awesome video.

  • @xavierbaltazar2453
    @xavierbaltazar2453 5 лет назад

    That moment when it FINALLY made sense. So good. Ty

  • @CageMatchRunnerUp
    @CageMatchRunnerUp 11 лет назад

    I never understand anything until Khan academy explains it to me.

  • @maxpolaris99
    @maxpolaris99 15 лет назад

    hip hip hurray! For he's a jolly good fellow, which nobody can deny!
    I wish I had the internet when I was in college!

  • @yalij
    @yalij 13 лет назад

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

  • @ajitj2562
    @ajitj2562 9 лет назад +2

    Beautiful explaination ! ....Thank you .

  • @007MrYang
    @007MrYang 13 лет назад

    This is better than a textbook!

  • @mcridiculose
    @mcridiculose 12 лет назад

    that's usually the case. the epsilon side can usually be simplified to be the delta value so that the final value will be the delta

  • @elzorro35
    @elzorro35 11 лет назад

    wonderful work. you manage to be precise without being overwhelming and the moderated length (measured in t dimension) of the videos is highly pedagogical.

  • @aleksey6151
    @aleksey6151 6 лет назад

    Can't believe this is in Calc 1 for me but that's okay. I feel like I can learn everything from you!

  • @matthewwroblewski8752
    @matthewwroblewski8752 10 лет назад +1

    Awesome. Love the notation. Thanks Sal!

  • @ayliarajani
    @ayliarajani 5 лет назад

    Thank you Mr. Khan for teaching the entire concept of limits

  • @phillipho5190
    @phillipho5190 3 года назад

    Thank you! save me from elementary real analysis!

  • @Imaginaari1984
    @Imaginaari1984 11 лет назад

    Back in the days this was the only thing I could not understand in my math course. Now that I watched this I think it was because then I had bad teacher

  • @thewariomanofdoom
    @thewariomanofdoom 12 лет назад

    All of a sudden everything makes sense. THANK YOU.

  • @mongoosezxc
    @mongoosezxc 11 лет назад

    Man I am glad I looked this up in my 3rd week of freshman year

  • @evilfindish
    @evilfindish 13 лет назад

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

  • @RobSchneeberger
    @RobSchneeberger 14 лет назад

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

  • @xToTaLBoReDoMx
    @xToTaLBoReDoMx 12 лет назад

    Not everyone's a genius like you.

  • @robbbieraphaelday999
    @robbbieraphaelday999 5 лет назад

    Finally this actually makes sense

  • @marieshwarankaliappan1559
    @marieshwarankaliappan1559 7 лет назад +1

    Really good explanation...
    I thank u for such video u uploaded.

  • @Tapryne
    @Tapryne 13 лет назад

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

  • @abidmalak2724
    @abidmalak2724 10 месяцев назад

    Really thankful for this video specially I really couldn't get this concept till on even though i tried

  • @Skygerobrian
    @Skygerobrian 15 лет назад

    You really make great instructional vids. thankyou.
    And quick ...or at my own pace..

  • @arwinlashawn
    @arwinlashawn 8 лет назад +1

    Love from Malaysia.

  • @Ogrmedia
    @Ogrmedia 12 лет назад

    I finally understand!!! U hve been my biggest help ever!!

  • @809guta809
    @809guta809 13 лет назад

    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.

  • @prabhavagrawal1712
    @prabhavagrawal1712 5 лет назад

    The best University of the world.
    I will donate you when I will earn money.
    But you need to wait for at least 5 years

  • @naircat
    @naircat 14 лет назад

    Oh man fantastic video. This helps a bloody ton.

  • @seekluv
    @seekluv 15 лет назад

    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!

  • @fashionvella730
    @fashionvella730 Год назад +4

    Any one like who is here after 14 years

  • @lovex3li
    @lovex3li 13 лет назад

    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 -_-

  • @apestogetherstrong341
    @apestogetherstrong341 2 года назад

    man, i miss the times when they taught logic in school... if, then, if and only if, all this is explained in logic, and students could tie the two objects so well with each other...

  • @MrMoneymeister
    @MrMoneymeister 12 лет назад

    9:00 WHOA... I got it! I understand the circular proof as not circular!!!