Precise Definition of a Limit and Proving - Linear Function Example

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  • Опубліковано 15 гру 2024

КОМЕНТАРІ • 135

  • @jiayiluo9260
    @jiayiluo9260 5 років тому +171

    Want to say goodbye to the ad"what! still searching math help from youtube?"
    yes, i am still doing that and it is really helpful and free

    • @adeelali8417
      @adeelali8417 5 років тому +11

      lmao that ad pissed me off so bad.
      Oh and Use adblocker.

    • @jayceinfinitealgharhythmns9814
      @jayceinfinitealgharhythmns9814 5 років тому +12

      Don't use adblocker... it demonetizes his videos. If at possible watch the ads and let them play through and show him some support. Beside I don't mind them spending money on a product I'll never buy to support ones I would pay for.

    • @pedroafonso8384
      @pedroafonso8384 5 років тому

      Exactly

    • @lynettealexandragonzalez7173
      @lynettealexandragonzalez7173 5 років тому +3

      7 months later and I get the same ad

    • @ilanzatonski8826
      @ilanzatonski8826 4 роки тому +1

      Just got it now..

  • @zepherinkevinfrancis7539
    @zepherinkevinfrancis7539 4 роки тому +109

    Thank you so much, you are a godsent, my Calculus 1 Professor is making me learn this on my own and you just saved my life

  • @henrycolvin3473
    @henrycolvin3473 2 роки тому +4

    I don't know what the difference between my textbook and my professor and you is, but something just clicked watching this. Thank you so much, you are saving my grades.

  • @maniksethi551
    @maniksethi551 4 роки тому +28

    DUDE THANK YOU SO MUCH THIS IS ABSOLUTELY CRAZY THIS MAKES SO MUCH SENSE NOW.

  • @Nomul16
    @Nomul16 5 років тому +26

    Thankyou so much, my professor didn't do a great job of showing this and now it all makes sense!

  • @Harjindersingh-xv9xu
    @Harjindersingh-xv9xu 4 роки тому +19

    Hey. I now understand how this relates to the overall picture of limits definition that is for every epsilon we have a delta, but things would be even better if we approached this problem from a geometric perspective: getting delta from a graph. And thanks for your videos!

    • @blacktape52black72
      @blacktape52black72 3 роки тому +2

      lol it took me a month to figure out derivates means rate of change at point.

    • @EfeAikpokhio
      @EfeAikpokhio 3 роки тому

      @@blacktape52black72 lol XD

  • @sgtcojonez
    @sgtcojonez 9 років тому +19

    I feel so bad because I finished all three CALs and now I am in differential equations, but I was never able to master this proof. I just hate the stupid epsilons man.HAHAHAHA. Thank you for the video Patrick.

  • @blessinggorengecho3973
    @blessinggorengecho3973 8 років тому +5

    I really don't know what I would do without you sir. Thank you ver much...

  • @protestant_mezmur1
    @protestant_mezmur1 2 роки тому

    I regrettably feel that after finishing and currently studying differential equations, I was never able to fully understand this proof. Thank you to my advisor for pointing me in the right direction.

  • @naghmeharmanieh
    @naghmeharmanieh 7 років тому +6

    so clear! never understand the concept of precise limit but u just cleared that out

  • @FredHandle1
    @FredHandle1 6 місяців тому +1

    It seems [to me] that this epsilon-delta strategy can only affirm a limit, if the function behaviour is well behaved around the point of discontinuity.
    Which presupposes prior knowledge of the behaviour of the function. That would make the proof, self serving, in that it aims at proving a property thats already evident.
    By well behaved, I mean that the function is either sequentially increasing/decreasing on either side of the proposed limit.
    What about irregular functions that make jumps in F(x) as we get closer to the proposed limits?
    I really don't know, so I need some coaching.
    May be it would be helpful if we began with a definition of the types of functions where this approach can work or not. TYSM for the vid

  • @GagandeepKaur-km2rj
    @GagandeepKaur-km2rj 3 роки тому

    thank you so much. I was thinking I'm never gonna get this concept ..but after watching this video, I feel like I got it.

  • @jshringo77
    @jshringo77 4 роки тому +1

    Thank you so much! Wayyyy better explanation than my professor.

  • @craigt8432
    @craigt8432 2 роки тому

    This video saved me from poor instruction. Thank you sm

  • @diablohorer
    @diablohorer 3 роки тому +2

    But HOW did you decide that delta=epsilon/2?

  • @shancunma6001
    @shancunma6001 3 роки тому

    This video explains the precise definition better than the other one you showed. thx ✌️

  • @edwardkarak2517
    @edwardkarak2517 4 роки тому +2

    Shouldn't it be 0 < |x-a| < δ, not just |x-a| < δ, to ensure x≠a?

    • @denisvalentin4258
      @denisvalentin4258 4 роки тому

      Yes, that's true. He probably didn't write it to simplify things.

  • @parsat5567
    @parsat5567 6 років тому

    Thanks dude, got exam tomorrow and it really helped

  • @MtlFT
    @MtlFT 9 років тому +4

    If only I had this last week or my calc1 test!

  • @kwirkLA
    @kwirkLA 9 років тому +4

    Wow, perfect timing to post this...my first calc1 test in a few hours and this proof is the hardest concept of the first section.

    • @uyujnnqaal
      @uyujnnqaal 3 роки тому +1

      Yo how did the test go?

    • @kwirkLA
      @kwirkLA 3 роки тому

      @@uyujnnqaal lol I ended up dropping the class, didn't need this level of calc for my major it turned out

  • @anzatzi
    @anzatzi 6 років тому +7

    Saying ' just reverse the steps' is very confusing--you should focus on the implication issue. great video!

    • @betterfly7398
      @betterfly7398 3 роки тому

      Indeed! This is why I couldn't get it. I was like, why in the hell are we doing the same thing, but in reverse order?! of course we're going to get the same thing!

  • @marcushines4172
    @marcushines4172 9 років тому +2

    Thanks for all the videos bro. Listen, can you do an example where the inequality cannot be solved algebraically, so you have to "enlarge" the function in order to get something that CAN be solved, then from there prove that the enlarged function is less than epsilon, which proves that the original function we started with is ALSO less than epsilon since its smaller than the function we enlarged. I hope I was able to explain what I'm asking.

  • @HK-ni6cn
    @HK-ni6cn Рік тому

    oh my god i love u😭i was struggling so hard

  • @ChefFarisMom3
    @ChefFarisMom3 2 роки тому

    I can't express my gratitude 💕💕💕💕

  • @beegalgo1757
    @beegalgo1757 7 років тому +1

    Thank you very much sir!! Your channel helps and motivates mi in school 😊

  • @_ohamachi
    @_ohamachi Рік тому

    Hello can you reverse
    |x-a|

  • @quiet6740
    @quiet6740 7 років тому +12

    i don't understand why E/2 = DELTA.
    for example:
    6

    • @dangerousangel777
      @dangerousangel777 4 роки тому +1

      @@bilaltariq7819 you neglect to mention that epsilon is totally arbitrary and delta DEPENDS on epsilon....and how crucially important that is....but still FACTS.
      Lol for example if you have a function f(x) = 2x
      2x = 10 < 11
      and 2x = 4 < 11
      SURELY, you ain't gonna say 10 = 4 lol....
      It's more like f(epsilon) = delta so to speak.
      So since f(epsilon) = delta
      we have f(epsilon) = (1/2)E = E/2 = delta.
      If he didn't work the other way, it would be a prank. lol A complete s c a m.

  • @noahmnyenyembe1559
    @noahmnyenyembe1559 6 років тому

    Thank you very much Mr Patrick. Now am confident enough that i will muster calculus!!!

  • @BangMaster96
    @BangMaster96 5 років тому

    Don't get confused by all the technical terms guys. The simple intuition behind limit is the value approached by a function as the input approaches a certain value.
    That's all, the epsilon and delta definition is stating the same thing.
    As long as you understand the meaning of what a limit is, you don't need to know the technical confusing terminology.

  • @imposter2210
    @imposter2210 29 днів тому

    How can we let delta equals to epsilon by 2 ??
    I mean in what sense is it supposed to work??
    Please reply...

  • @t.r.icraftsworld8389
    @t.r.icraftsworld8389 3 роки тому

    Super explanation sir I could really understand your lecture

  • @dantecastillodelasfuentes1026
    @dantecastillodelasfuentes1026 5 років тому

    In what part of the limit definition it´s said that the point can´t be L? or a ?

  • @ttviper9t
    @ttviper9t 9 років тому +1

    i subbed and it was worth it. Thanks Mate!

  • @Mr.X-qu1lw
    @Mr.X-qu1lw 8 місяців тому

    Why epsilon over 3 over 4 and all will work....???please help

  • @yesboss2800
    @yesboss2800 3 роки тому

    1st : absolute of function is less than e and prove absolute of points less than a manipulation ( related to e which is dell )
    2nd : now take that absolute of points less than dell (but put manipulated value) will always implies absolute of function is less than e

  • @dskchari9469
    @dskchari9469 4 роки тому

    Here what is meant by Delta and epsilon exactly .can we take any other letter instead of them as which means small +ve number

  • @rushel4608
    @rushel4608 3 роки тому

    My professor did it by getting a inequality for f(x) - L from the delta and then he chosed a ephsilent for that delta is it correct? Sorry for my english

  • @seadric6372
    @seadric6372 5 років тому +3

    When I look through my textbook, they randomly get values for delta and then I get confused because idk how they did it

  • @ledah8165
    @ledah8165 6 років тому

    Did you use Differential and Integral Calculus by Love & Rainville as a reference for this video?

  • @yesboss2800
    @yesboss2800 3 роки тому

    Watch from 3:40

  • @vedinmuratovic2274
    @vedinmuratovic2274 4 роки тому

    I am confused about the part where we let delta = epsilon/2. Why does this work because wouldn't substituting ABS x-4 make it so that delta is less than epsilon/2

  • @danielzambrano7487
    @danielzambrano7487 10 місяців тому

    Great video thanks man!

  • @josuedelatorre35
    @josuedelatorre35 6 років тому

    What if you get a problem where a is a negative number?

  • @argoneus21
    @argoneus21 3 роки тому

    THIS IS GEM! THANKSSSS!

  • @juan3141
    @juan3141 4 роки тому

    the only part im confused on is why youre allowed to say L = E / 2 ?

  • @SkyMine911
    @SkyMine911 6 років тому

    what about the pre-proof?

  • @berylni7806
    @berylni7806 8 років тому

    Thanks! I love your video!

  • @lyricc9
    @lyricc9 3 роки тому

    NOW I UNDERSTAND THANK YOU!

  • @navidmafi
    @navidmafi 3 роки тому

    YEAHH NOOWWW I UNDERESTAND IT THANK YOU LETS GOOOOOOOOOOO

  • @fluffycharizard8835
    @fluffycharizard8835 6 років тому

    plz can you show how to prove lim 1/(1-x)^2 = infinity x tends to 1

  • @XFOYS
    @XFOYS 5 років тому

    Sangat Membantu, Terima Kasih ( Indonesia) = So helpfull, Thank You
    this video helps me to pull an all-nighter cause my (smart) lecturer :D

  • @InnocentErasto-v5b
    @InnocentErasto-v5b 11 місяців тому

    Thank you buddy❤

  • @fuatutku
    @fuatutku 7 років тому

    Patric u are amazing i've learnt things from u in two nights watching u is also enjoyfull.u deserve fucking oscar prize

  • @prestonjensen6172
    @prestonjensen6172 9 років тому

    Hey Patrick! Just curious, is this your main job, or do you have a day job?

  • @2Berm1
    @2Berm1 9 років тому

    Nice explanation.

  • @brendanfinnie8233
    @brendanfinnie8233 6 років тому +6

    makes sense that a left handed person is tutoring calculus XD

  • @zigooo_5611
    @zigooo_5611 5 років тому

    this is beautiful

  • @miso-ge1gz
    @miso-ge1gz Рік тому

    what do you mean prove it just does

  • @rohandandi5999
    @rohandandi5999 5 років тому

    bro can you tell me express this definition of limit using quantifiers

  • @janerouge5541
    @janerouge5541 6 років тому

    helps a lot!!
    thanks!

  • @davidhou4256
    @davidhou4256 6 років тому

    thx bro, IM FROM TUCKER.

  • @taysstudyblog3971
    @taysstudyblog3971 2 роки тому

    Im awestruck

  • @BrickTavernFilms
    @BrickTavernFilms 6 років тому +4

    The philosophizing is necessary

  • @mrinalchoudhary7525
    @mrinalchoudhary7525 6 років тому +1

    Tqsm sir 😍

  • @Tiktok-hk8vg
    @Tiktok-hk8vg 9 років тому

    nice but can you please make a video to help me do better in algebra one thank you

  • @aasthasharma7161
    @aasthasharma7161 4 роки тому

    thank uh so much sir🥰

    • @patrickjmt
      @patrickjmt  4 роки тому +1

      Most welcome

    • @aasthasharma7161
      @aasthasharma7161 4 роки тому

      @@patrickjmt can you plz make more vedios on this topic🤗. Love from india

  • @azyle2104
    @azyle2104 4 роки тому

    Thank you

  • @r.sorker2590
    @r.sorker2590 3 роки тому

    i want to get solution of the end

  • @gauthampracharya9592
    @gauthampracharya9592 4 роки тому

    Give a smart guy a sharpie and a camera, and he will do wonders!

  • @kleodavelajarca7479
    @kleodavelajarca7479 6 років тому

    Thank You! :)

  • @myeshafarzanatahi9154
    @myeshafarzanatahi9154 3 роки тому

    Thank you a lot lot lot lot lot lotttttt

  • @nicktokar2459
    @nicktokar2459 6 років тому

    I sure love that i'm taking calculus as a biology student.
    But, this was actually very helpful.

    • @patrickjmt
      @patrickjmt  6 років тому +1

      You should be taking Calculus if you are a Biology student though...

  • @faighashimli1452
    @faighashimli1452 9 років тому +1

    Thx Man :)

  • @zacharyddrzipac
    @zacharyddrzipac 7 років тому +3

    What I learned:
    if 1+1=2, then subtract 1 from both sides:
    1=2-1
    1=1, then let 1 equal to 1,
    1=1
    add one to both sides:
    1+1=1+1
    which is also equal to 1+1=2
    BOOM here you go, enjoy your accomplishments, you've proved absolutely nothing.

    • @abdoxd2911
      @abdoxd2911 4 роки тому +1

      Are you still there?
      Well just wanted to say that you are the only comment that made me laugh in this horror movie
      Thx for it

  • @cbranalli
    @cbranalli 7 років тому +1

    it would help if you could show a case where the limit DOES NOT exist - eg at a step discontinuity.

  • @r.sorker2590
    @r.sorker2590 3 роки тому

    very nice

  • @nurizyannabilah5580
    @nurizyannabilah5580 4 роки тому

    Thank sir

  • @erickfranciscogudinoperez7327
    @erickfranciscogudinoperez7327 5 років тому

    Cool thank you

  • @paulpassiglia9997
    @paulpassiglia9997 7 років тому

    Praise

  • @vatitopatitopotitopolitopo4918
    @vatitopatitopotitopolitopo4918 3 роки тому

    thx

  • @batteryjuicy4231
    @batteryjuicy4231 Рік тому +6

    I don't get why this isn't a tautology. You basically did some math, then you did the opposite steps to get back to where you started and somehow that is a proof?

  • @milastevanoska536
    @milastevanoska536 3 роки тому

    a?

  • @sophita_
    @sophita_ 9 років тому

    Thank yooouuu!

  • @oguztizlak2699
    @oguztizlak2699 5 років тому

    Güzel anlatım 👍

  • @chrislliatsos
    @chrislliatsos 5 років тому +1

    im confused, how is it mathematically proven that "delta" is equal to "epsilon dived by 2?" thanks guys

    • @garrettnicolay6310
      @garrettnicolay6310 4 роки тому

      I know its been awhile since you posted this but the reason delta = epsilon divided by 2 is simply that we are letting delta = epsilon divided by 2. We wanted to find out what we needed to set our delta value equal to so that we could get | 2x + 3 - 11|. If you ever take Calc 3 this will still be useful to know when taking limits in multiple variables.

    • @garrettnicolay6310
      @garrettnicolay6310 4 роки тому

      It just makes it easier to solve

  • @SinaHeidari522
    @SinaHeidari522 4 роки тому

    god bless

  • @dantaemartin7326
    @dantaemartin7326 9 років тому

    AMAZING

  • @arumteguh2762
    @arumteguh2762 5 років тому

    quentin tarantino?

  • @rima7286
    @rima7286 4 роки тому

    DUUUUUUUUUDEEEEEEEEEEEEEE

  • @Jyotikumari-hq1ut
    @Jyotikumari-hq1ut 7 років тому

    You are reading from thomas calculas

  • @the-dan-signal3595
    @the-dan-signal3595 6 років тому +1

    I understood everything except for the part where you said we could use epsilon/3 or epsilon/4 and it would still work. At that one moment you completely lost me

    • @SupaThePink
      @SupaThePink 6 років тому +3

      To prove that this limit exists and satisfy the definition, we need to establish a relationship between δ and ε such that, if x is within δ of a, f(x) is within ε of L. For example, say we find that δ is ε/2 for a particular limit, and say we arbitrarily pick 4 for ε. This means that, in order for f(x) to be no more than 4 away from L, x must be no more than 2 from a. If we change δ to ε/4, this definition is still satisfied because for an ε of 4, we have a δ of 1, and an x no more than 1 away from a still produces an f(x) no more than 4 from L. We can make δ whatever we want as long as it is not more than ε/2. Basically, we can make the tolerances for δ as strict as we like, but we cannot make them more lenient. If δ is greater than ε/2 in this example, f(x) will no longer be within the desired distance of L, and the definition cannot be satisfied.

    • @win4cambo
      @win4cambo 5 років тому

      delta = 0.00000000000000001 and epsilon = 0.000000000000000002 make a tiny difference.

  • @Aa_1220_
    @Aa_1220_ 2 роки тому

    thank you for the explanation. Please use a normal pen or pencil while writing on a paper

  • @xXxilovecatsxXx
    @xXxilovecatsxXx 5 років тому +1

    can't even watch this with his hand in the way of everything written had to pause like 125 times ... leftys

  • @Abdullah-nc2vd
    @Abdullah-nc2vd 6 років тому

    This epic

  • @DanT-iu6oc
    @DanT-iu6oc 5 років тому

    god this is never going to make any sense to me. i give up on precise definition of a limit. this is just totally beyond my INTELLIGENCE.

    • @cadu7698
      @cadu7698 4 роки тому

      Well, I kind of started getting it just now, and I've attended around four Calculus courses... so keep trying and someday it will make sense (that's not supposed to sound pessimistic).

  • @comfycozyarewe388
    @comfycozyarewe388 5 років тому

    😸

  • @StephaniePennings
    @StephaniePennings Рік тому

    So hard to see anything with your hand in the way. I had to keep rewinding to see what was under your hand. What should have been around a 7 minute video took me nearly 30 minutes to watch. Also, there's only one example and more are needed to fully understand this topic.

  • @mowu662
    @mowu662 4 роки тому

    wtf

  • @Cricketfunda9
    @Cricketfunda9 7 років тому

    Hindi me bolo hard eng heijauchi

  • @elchefe7421
    @elchefe7421 6 років тому

    Markers on paper is making my ears bleed