Limits and Limit Laws in Calculus

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  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 150

  • @jashansehgal7347
    @jashansehgal7347 5 років тому +189

    You are the best teacher.
    Please do not leave this channel ever
    I really consider you as my mentor because u are unfolding the fundamentals

    • @vasanthisuperkaruna3407
      @vasanthisuperkaruna3407 3 роки тому +6

      exactly. none in the world teaches like him. beautiful explanation indeed!!!

    • @NewWesternFront
      @NewWesternFront 2 роки тому +13

      i'm putting a giant portrait of Dave in my living room. I will stare at it everyday

  • @crofregernish4695
    @crofregernish4695 4 роки тому +90

    Trying to do calculus online for a college course where the professor only teaches what's literally in the book (no further explanations)
    This was so helpful!!!

  • @mrmoth26
    @mrmoth26 2 роки тому +48

    Dave, you truly have no limits.

  • @melontusk7358
    @melontusk7358 4 роки тому +14

    I've been wondering about why the formal definition of a continuous involves a limit for such a long time, and the epsilon-delta definition didn't help either, but this video lecture really made it crystal clear to me. Thanks so much.

  • @matthewlepage1253
    @matthewlepage1253 Рік тому +1

    Thanks!

  • @billcook4768
    @billcook4768 2 роки тому +10

    Random trivia: One of the examples in this video is that limit x-> 0 of sin(x)/x = 1. Seems simple here using a graph or calculator, but this is one of the most important “facts” in all of math. Not necessarily in this form, but in equivalent forms such as the idea that if x is “small”, sin(x) is approximately equal to x.

  • @tomsdailystudy
    @tomsdailystudy 2 роки тому +6

    Thank god. I thought I lost Professor Dave since last semester. Just subscribed so the search is way easier. Good stuff on this channel. And for whatever reason it’s also a fun channel which makes learning easier.

  • @typalfi7139
    @typalfi7139 6 років тому +13

    You are good at explaining Professor Dave. Thankyou!

  • @salonisharma2807
    @salonisharma2807 6 років тому +45

    Thank you sir your all videos have cleared my concepts! 😊

  • @jonathanjohnny225
    @jonathanjohnny225 6 років тому +328

    he knows a lot about science stufffff, science jesus explains

    • @lits0_042
      @lits0_042 5 років тому +12

      this is mostly math

    • @satrickptar6265
      @satrickptar6265 5 років тому +12

      @@lits0_042 but math is science

    • @lits0_042
      @lits0_042 5 років тому +6

      @@satrickptar6265 no, one helps the other

    • @satrickptar6265
      @satrickptar6265 5 років тому +16

      @@lits0_042 Science is the main seed, math is just a branch

    • @lits0_042
      @lits0_042 5 років тому +14

      @@satrickptar6265science is the human interpretation of math

  • @GavinLon
    @GavinLon 5 років тому +7

    This is a very clear explanation. Thanks Professor Dave.

  • @jayadevpandey10
    @jayadevpandey10 5 років тому +10

    you are very good at explaining all science stuff thank you professor Dave

  • @kavyahegade6477
    @kavyahegade6477 4 роки тому +7

    None other than you can teach like this😊.. you're amazing and unique 👌don't know how many times i passed the exam by watching your videos🤝🤝

  • @robertwood2424
    @robertwood2424 Рік тому +1

    8:45 Lim f(x)=6
    Lim g(x)=2
    Then it goes to lim[f(x)-3g(x)] =6-3(2)=0
    Why is g(x) now being multiplied by 3, instead of 6-2=4?

  • @shubhamjoshi9624
    @shubhamjoshi9624 9 місяців тому

    Professor dave is just so good and all rounder in field of science.

  • @DarinBrownSJDCMath
    @DarinBrownSJDCMath 4 роки тому +4

    11:51 cancelling factors, not terms

  • @Kiky_MedPhysicist
    @Kiky_MedPhysicist 4 місяці тому

    Thank you sir for your dedication and for making this free!

  • @dimitriosmenounos1009
    @dimitriosmenounos1009 5 років тому +4

    Congrats! You explained it very well.

  • @MathCuriousity
    @MathCuriousity Рік тому

    I have to say Dave used the word parameter incorrectly; this word means either a constant such as a particles mass, or it can mean a function of two other functions such as if we parametrized the unit circle for t and said y=sin(t) and x=cos(t)

  • @khalolyyan7971
    @khalolyyan7971 3 роки тому +2

    Could you please make a video about the precise definition of limits ( epsilon and delta) thank you in advance!

  • @slickyy21
    @slickyy21 Рік тому +8

    Where is the comprehension check?

  • @pfever
    @pfever 4 місяці тому

    9:57 this could have been explained much easier. Wherever you have f(x) you can replace by lim f(x), and wherever you have x you can replace it by a.

  • @suchadathaiy01
    @suchadathaiy01 2 місяці тому

    You’re the best thing I ever known, Thank you 🙏🏼

  • @RazorM97
    @RazorM97 5 років тому +30

    People who disliked this video have no limits

  • @TheseOfWe0112
    @TheseOfWe0112 3 місяці тому

    Such an easier way to understand, thank you

  • @aminnima6145
    @aminnima6145 3 роки тому

    Math is not taught tha way in our school.... They just give the rule and u memorise.... Thank you sir

  • @sagar-uj1nb
    @sagar-uj1nb 4 роки тому +2

    your videos are awesome sir. I think you are referring to stewart calculus book for example problems....

  • @MOizSUAVE14
    @MOizSUAVE14 6 років тому +13

    dang i wish i watched this video before my 1st exam.

  • @fernandoportal5422
    @fernandoportal5422 Рік тому

    Min 10:25 I was thinking why not just graphic the function but now, i get why not

  • @supercheese8663
    @supercheese8663 4 місяці тому

    this might be weird to comment on a calculus video but I only passed Further Linear Algebra because of your videos.
    Just wish I watched this playlist before my calculus exam.

  • @lightning77125
    @lightning77125 Місяць тому

    Function y=f(x)
    x represents Dave's teaching
    y represents my understanding
    lim(x➡♾)(f(x))=♾

  • @srinidhiav
    @srinidhiav 5 років тому +2

    Very nicely explained!! 👍

  • @barcinnicrab9562
    @barcinnicrab9562 4 місяці тому

    Amazing explanation really nice to hear :) Everything makes sens

  • @carinamcallister4409
    @carinamcallister4409 Рік тому

    its time for summer courses again. that means all prof dave all the time

  • @EfeAikpokhio
    @EfeAikpokhio 2 роки тому +1

    Wow, this was amazing! Thanks Professor

  • @dakshbadal7522
    @dakshbadal7522 4 роки тому +4

    If you want him to make money but can't afford patreon, just watch half of the unskippable ad. If you skip the ad asap, no money goes to the creator.

  • @williamadams137
    @williamadams137 5 років тому +2

    6:00, is that the unit step function

  • @apothe6
    @apothe6 7 місяців тому +1

    The first question of why don't we just plug the value in is exactly what I was wondering.

  • @SÀN-D-MAN
    @SÀN-D-MAN 9 місяців тому

    Professor Dave here, let's take about limits 🔥🔥🔥🔥🔥

  • @Jesuisunknown
    @Jesuisunknown 10 місяців тому +3

    My tiny brain is going to expload 😆

  • @meltdown6856
    @meltdown6856 6 років тому +3

    So a limit just tells us what a function would normally do as x approaches a value on the x axis rit? ( Pls correct me if I am wrong)

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  6 років тому +3

      yep!

    • @adeboyebamgboye2486
      @adeboyebamgboye2486 2 роки тому

      This is perhaps the most important thing I learned from the video...Like the idea wasn't exactly conceptualized before I started taking in the laws. Thanks!

  • @farhanahmed2508
    @farhanahmed2508 6 років тому +3

    Love this!

  • @drakulaki1380
    @drakulaki1380 5 років тому +1

    Thank you professor!

  • @kamalaambika9520
    @kamalaambika9520 6 років тому +4

    He knows a lot about different stuff, science Jesus here explains !^_^

  • @santoshgujar5237
    @santoshgujar5237 10 місяців тому

    ✨Thank you, Sir, 🙏🌺✨

  • @matokurin
    @matokurin 3 роки тому

    Very very kind. Thank you

  • @manismanai2276
    @manismanai2276 6 років тому +1

    Your helped me to pass in my exam.

  • @thestoryofmylifesearchingf9631

    YESS FINALLY I GOT IT THANK U SO MUCH

  • @ankitaaarya
    @ankitaaarya 5 років тому +2

    3:00 no one ever told me that, thanks

  • @joschaberg6940
    @joschaberg6940 3 роки тому

    I don't see why laws 6 and 8 require a positive integer for n.
    For example I could plug in 0 for n and don't see where an error happens.
    Clarification would be much appreciated!

    • @joschaberg6940
      @joschaberg6940 3 роки тому

      ​@Erik Awwad Hi Erik, i didn't raise any complains about law 7) so no worries concerning the 1/n powers. :)
      As for your excellent question "What times itself 0 times yields a number?" I agree, that this doesn't make sense. But that does not mean that b^0 is undefined.
      You are correct that for a positive exponent b^n is equivalent to the product of n times b.
      However, the power b^n also has a reciprocal 1/(b^n). It is also be written as: b^(-n)
      Now what is b^2 * b^3? It is b^5
      This actually generalises:
      b^n * b^m = b^(n+m)
      And now you might answer what:
      b^n * b^(-n) is equal to.
      Dave has a great video about that as well btw: ua-cam.com/video/K_TD9GuP9uQ/v-deo.html

  • @kontiimanalatit8987
    @kontiimanalatit8987 Рік тому

    Good explanation about limits, but you didn't delve into the important limits or methods about calculating limits, which aren't just f(a) (like factoring highest powers in denominator and numerator or 1/infinity 1/0 forms, which are considered as 0 and +inf)

  • @theteenengineer7589
    @theteenengineer7589 4 роки тому +1

    i think they teach that in high schools here in canada, its good to understand them before i get there :):):)

  • @gaminisiriwardana5946
    @gaminisiriwardana5946 5 років тому +1

    excellent way of explaining. I got amazed with your explanation and did lot of calculus sums. Sir I will be sending very special 4 questions through email to you. Please be kind enough to reply. Interestingly waiting for your explanation . Thanks

  • @lahiru1k
    @lahiru1k 10 місяців тому

    Thank you❤

  • @gabygarcia0123
    @gabygarcia0123 11 місяців тому

    amazing teacher

  • @asheshmandal4952
    @asheshmandal4952 6 років тому +1

    Thank you sir

  • @ummahyehmmm7403
    @ummahyehmmm7403 3 роки тому

    That was such a help 😫 thanks sm

  • @dylanrobichaud9853
    @dylanrobichaud9853 Рік тому

    Thank you!

  • @floweytheflower5261
    @floweytheflower5261 10 місяців тому +2

    5:29 AAAAGHHH IT'S ALL 0.017!!!

    • @weebo1926
      @weebo1926 5 місяців тому +2

      the sine function depends on degrees being used, if you use radians, it will give the right answer which is close to 1, do not use degrees for this operation.

  • @hansisbrucker813
    @hansisbrucker813 5 років тому +4

    Wait. Since when are limits defunct? I thought they replaced infinitesimals in calculus

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  5 років тому +5

      well they still have application, it's just that we don't need them to take derivatives.

    • @hansisbrucker813
      @hansisbrucker813 5 років тому

      @@ProfessorDaveExplains oooh ok. Thanks

  • @matamuverner
    @matamuverner 3 роки тому

    prof..... how about accumulation of point?

  • @camellemons3737
    @camellemons3737 5 років тому +2

    i need to know how many of that shirt you have. and if it is 1 what happens if it gets worn out?

  • @ephremephi2501
    @ephremephi2501 3 роки тому

    thank you

  • @MathCuriousity
    @MathCuriousity Рік тому

    Anybody know what program he used to create these videos? Also what program do I need to "record" the videos or are they automatically recorded by the same program? Thanks!

  • @reanwithkimleng
    @reanwithkimleng 4 місяці тому

    Dear sir could you help me please ❤❤
    😊Limits and Differential Calculus
    @ Introduction to limits, continuity, and importance
    @ Techniques for finding limits and understanding
    continuity
    @Differentiation rules (power, product, quotient,
    chain) and techniques
    @Applying derivatives: optimization, related rates,
    motion analysis
    @Multivariate calculus: partial derivatives, gradients,
    optimization
    😊Calculus in Machine Learning
    @Role of calculus in ML: optimizing cost Functions
    @Gradient descent: derivation and implementation
    @Backpropagation in neural networks and derivatives
    @Advanced optimization: SGD, Momentum, RMSprop,
    Adam

  • @nisaaaa35
    @nisaaaa35 2 місяці тому +1

    Teşekkürler

  • @kriswillems5661
    @kriswillems5661 Рік тому

    You should have mentioned that both limits need to exist for the limit of a sum to be the sum of the limits (if they don't exist the sum can still have a limit).

  • @ronaldjorgensen6839
    @ronaldjorgensen6839 4 роки тому +1

    I WILL PAY YOU ASAP DAVE THE MATH DEMANDS MY LUCK MUST CHANGE

  • @hosinsinaga4694
    @hosinsinaga4694 10 місяців тому

    can you tell me what aplication you use draw all graph?

  • @46-firozc73
    @46-firozc73 6 років тому +1

    Sir what happens if we get 0/0 instead of - 1/11??pls reply

    • @meltdown6856
      @meltdown6856 6 років тому +2

      0/0 is not a fixed value and is undefined as 0/0 can be 1,2,3 all the way up to infinity as anything multiplied by 0 is 0

    • @meltdown6856
      @meltdown6856 6 років тому +2

      So it's like a void

    • @angelisvegan5826
      @angelisvegan5826 3 роки тому

      In plain English.. it's undefined

  • @Vietothief
    @Vietothief 17 днів тому

    amazing...

  • @engnrrmuhammadali7453
    @engnrrmuhammadali7453 4 роки тому

    Sir upload video over contuinity please help me sir.....

  • @dariustbt6840
    @dariustbt6840 5 років тому +14

    There are no limits for science jesus!

  • @thefact6225
    @thefact6225 3 роки тому +1

    Proffecer:"0/0 could be doing anything" 🤣

  • @KristineOjide
    @KristineOjide 5 місяців тому

    7:09

  • @clemsante9048
    @clemsante9048 2 роки тому

    I like your videos

  • @tGoldenPhoenix
    @tGoldenPhoenix 3 роки тому

    Done.

  • @harishgehlot2020
    @harishgehlot2020 2 роки тому

    I am from India 👍🔥☺️

  • @ingvark1968
    @ingvark1968 5 років тому +1

    I just agree to all the roses below

  • @gardenmenuuu
    @gardenmenuuu 4 роки тому +1

    Great explanations but too short and vague,difficult to catch up due to overloading new words in a short time .please be slow and go thoroughly

  • @hareecionelson5875
    @hareecionelson5875 4 роки тому

    Ahh, so even though f(0) = 1 when x>= 0, the limit of f(0) depends on the direction, since the limit of f(x) is not always = f(x)

  • @Chriss123HD
    @Chriss123HD 5 років тому +2

    you had me at x

  • @thisismyname7599
    @thisismyname7599 Рік тому

    i know this may sound dumb but couldent you find out what 1/0 is based on this
    lim x=>0 f(x)=1/x would that not = infinity?

  • @benquinney2
    @benquinney2 4 роки тому +1

    Infinitesimal

  • @slowfern
    @slowfern Рік тому

    lol i just realized singularity in a black hole is the same thing as discontinuity here

  • @teekay9498
    @teekay9498 Рік тому

    These are great information but the videos are not organized making things hard

  • @aselim20.
    @aselim20. Рік тому +1

    I wrote it.

  • @peterheath7960
    @peterheath7960 3 роки тому

    So, Acillies,DOES beat the tortoise. Nice

  • @ericpham4011
    @ericpham4011 4 роки тому

    The real dificulty is that we are using physical law and logic to measure a sensitive being of truth and super natural reality. In graph we can draw and the graph would touch but in uncertainty priciple Prime chemistry and quantum probabilty it is imposible to touch the face Prime God

  • @shubhamnath8888
    @shubhamnath8888 5 років тому

    Wtf is wrong with the 10 ppl who disliked????

  • @jamesmccreery250
    @jamesmccreery250 4 роки тому +1

    Why did this take 3 weeks in Calculus class? No offense Garry, but I think Dave is smarter than you.

  • @eigentlichtoll02
    @eigentlichtoll02 5 років тому +1

    only watch this for the intro

  • @bushbuddyplatypus
    @bushbuddyplatypus 5 років тому

    It really doesn't get more boring than this.

  • @qualquan
    @qualquan 6 років тому +1

    Yada yada yada.
    Unless you learn what is and how to eliminate the "averaging error" during differentiation you have learned calculus as a religion, and not as a science. BTW never mention 0/0. Its about as respectable as invoking God in science.

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  6 років тому +14

      I'm not sure that you know what a religion is. Math can never be religion, because math does not contain dogma. Math also is not a science, so I'm not sure you know what science is either. Never mention zero over zero? I have no idea what you're talking about.

    • @sunithavs8901
      @sunithavs8901 5 років тому +3

      You just reveled to people that you are dumb

  • @rishik-w1j
    @rishik-w1j 9 місяців тому

    Thank you