🟡05 - Limit and Continuity of Functions of Two Variables

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  • เผยแพร่เมื่อ 25 ม.ค. 2025

ความคิดเห็น • 103

  • @Divine-Education-1980
    @Divine-Education-1980 6 วันที่ผ่านมา +1

    Sir I am watching from India, you are my favorite teacher.

  • @SkanCityAcademy_SirJohn
    @SkanCityAcademy_SirJohn  ปีที่แล้ว +6

    Right answer for Q4,
    step 1: g(1,2) = 0,
    step 2: lim of (x^2 + 4y) as x,y approaches 1,2 = 9,
    step 3, since value for step 1 is not equal to that of step 2, the function is not continues at (1,2).

  • @amarjithazra8861
    @amarjithazra8861 2 หลายเดือนก่อน +3

    This topic kept troubling me...finally from your amazing video, I learnt the process..
    You have explained beautifully..
    Thank you sir 🙏🏻🙏🏻🙏🏻

  • @BabluPandey-z4p
    @BabluPandey-z4p 9 ชั่วโมงที่ผ่านมา +1

    Thanks so much sir and I like your teaching style.

  • @makyzainelabdin
    @makyzainelabdin ปีที่แล้ว +4

    Thank you for your beautiful explanation. It helped me a lot in understanding mathematical problems. I did not understand anything from the book after your explanation. I understood, thank you very much 👏🏻👏🏻

  • @TymomaishNgari
    @TymomaishNgari 3 หลายเดือนก่อน +7

    Everywhere i go in my field,i find your videos😂😂 i guess??

  • @chriscadag3374
    @chriscadag3374 ปีที่แล้ว +2

    This video is very helpful. Thanks to this, i was able to understand our lesson

  • @IsmailaBah-d1v
    @IsmailaBah-d1v ปีที่แล้ว +11

    Can’t thank you enough. My maths professor make these seems so difficult and i was really struggling to catch up.

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว +3

      Awww sorry about that. But finally, you understand now. Thanks for watching and commenting to show your appreciation.
      Tell me where you come from?

    • @HussainShah-tr8yz
      @HussainShah-tr8yz 7 หลายเดือนก่อน +1

      ❤❤❤

  • @blurzzbee
    @blurzzbee 11 หลายเดือนก่อน +2

    thank you so much sir, i can finally understand how to do it now

  • @TheForgottenOne1
    @TheForgottenOne1 ปีที่แล้ว +2

    Your a genius! Life saver!!

  • @Elnino12336
    @Elnino12336 10 หลายเดือนก่อน +2

    sir I am from India love you so much sir you are gem

  • @manavsood6020
    @manavsood6020 ปีที่แล้ว +3

    concept crystal clear
    i don't know why in every other vidio i watched in yt every one is doing 0/0=0 which is creating big confusion

  • @agirl8369
    @agirl8369 10 หลายเดือนก่อน +2

    thank u for this clear explanation

  • @yassjobe6764
    @yassjobe6764 ปีที่แล้ว +2

    Your video is really helpful can't thank you enough, the explaination s very clear too u ar a great teacher trust me keep it up❤

  • @NeolAlemu11
    @NeolAlemu11 ปีที่แล้ว +2

    Your video is really helpful can't thank you enough, the explanation s very clear too u are a great teacher trust me keep it up❤ live long mister but if you have worked examples on level curves and graphs of several variables please
    Baay'een sitti gammade ulfaadhu!!!!!!!!! replay me soon

  • @PRAKHARSINGH-x5j
    @PRAKHARSINGH-x5j หลายเดือนก่อน +1

    When to take y= mx either anyone of y=x½,x¼,etc... while finding limit ? you just only took y=x

  • @shitpostnut6293
    @shitpostnut6293 หลายเดือนก่อน +1

    Thanks man. Very helpful

  • @SAJJAD_HISSAIN
    @SAJJAD_HISSAIN 9 หลายเดือนก่อน +1

    Billions and trillions of thanks ♥️

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  9 หลายเดือนก่อน +2

      Aww thanks so much 🥰
      Where do you watch me from?

    • @SAJJAD_HISSAIN
      @SAJJAD_HISSAIN 9 หลายเดือนก่อน +1

      @@SkanCityAcademy_SirJohn I'm watching you form Pakistan

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  9 หลายเดือนก่อน

      @mughal___hu-------yara aww that's great. Thanks so much

  • @oneboneyt
    @oneboneyt 2 หลายเดือนก่อน +1

    Brother, how do I know which line/curve to use to approach the equation to check if limit exists like you chose y=x in Q5? Is there any method for it or is a guess through practice?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  2 หลายเดือนก่อน

      It's a guess. You just choose any simple line to solve with

    • @oneboneyt
      @oneboneyt 2 หลายเดือนก่อน

      @SkanCityAcademy_SirJohn thank you

  • @Myles_.webster
    @Myles_.webster ปีที่แล้ว +2

    Your videos are very helpful, but l am a bit stuck as to where l should actually use the polar coordinate approach, how do l necessarily know that it applies here.

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว

      It comes by experience, you can't really tell, but then as you solve more and more examples, you get to know where exactly to use it.
      Thanks so much for your words of appreciation.
      Where do you watch me from?

  • @habondoemmanuel7558
    @habondoemmanuel7558 4 หลายเดือนก่อน +1

    What if I use let x²+y² = t

  • @mahindranmahi3940
    @mahindranmahi3940 4 หลายเดือนก่อน +2

    Thank ❤... From Tamilnadu (India)

  • @AkhilaChirumamilla-kc2dg
    @AkhilaChirumamilla-kc2dg ปีที่แล้ว +1

    Thank you so much.... Actually I have exam in 2 days... And I cleared one of my confusing topics...

  • @PRAKHARSINGH-x5j
    @PRAKHARSINGH-x5j หลายเดือนก่อน +1

    Why you took only y=x...
    We can also take y=mx ,y =x½,x¼,etc... And when to take these line equations

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  หลายเดือนก่อน +2

      The thing is we can take any line y = mx + c, buy we want to take a simpler line equation for easy computation.

  • @alexandra-amaliacodreanu4700
    @alexandra-amaliacodreanu4700 ปีที่แล้ว +2

    why wasn't polar coordinates used in the first and you used them in the second and third?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว +2

      polar coordinates were not used in Ex 2 and 3, but rather Ex 6 and 7. In addition i want to understand that you want to ask why eg 1 was quite simpler as compared to 2, and 3. Eg 1 is a polynomial function in x and y, hence it is continuous everywhere, however for eg 2 and 3, we have a rational function, a rational function is continuous everywhere except where the denominator is zero making the whole function undefined, at that point, the function is discontinuous.

  • @certacito1599
    @certacito1599 2 หลายเดือนก่อน +1

    Concepts are very clear. But please, when and how do I know I have to use the polar co-ordinate form? Is there any exceptions?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  2 หลายเดือนก่อน +1

      It's based on experience. When you solve over and over, at a point you will know which approach to use for various questions

    • @RynAndres
      @RynAndres 2 หลายเดือนก่อน

      Cant we use just a normal approach that we solve the question in two ways , along x-axis and along the line y=x??

  • @muzzammilyousuf2265
    @muzzammilyousuf2265 8 หลายเดือนก่อน +1

    What if the question also stated that also find whether is function has removable discontinuity?
    How will we determine this?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  8 หลายเดือนก่อน +1

      Since the limits along different paths are not the same, the limit does not exist.
      Because the limit does not exist uniformly, this discontinuity is not removable.

  • @surendrakverma555
    @surendrakverma555 8 หลายเดือนก่อน +1

    Very good. Thanks 🙏

  • @NelumboNucifera-gh1pe
    @NelumboNucifera-gh1pe 10 หลายเดือนก่อน +1

    Sir in the last question why polar coordinates were used?can we do it by approaching x axis,y axis,y=mx?????how to know when to use polar coordinates?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  10 หลายเดือนก่อน +2

      yes you can approach the limit point from different directions. In fact you can choose to use polar coordinates all the time, but it's usually dependent of the question. I feel with much experience gathered as a result of constant practice, you will know the best approach to use, because sometimes approaching from different directions will help you to get the results faster

  • @amhakabaw
    @amhakabaw ปีที่แล้ว +1

    Tnx sir🙏🙏 your video is help full me

  • @peaceofmind9775
    @peaceofmind9775 ปีที่แล้ว +1

    when do we use the polar coordinates method?

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว +1

      You can use it anytime, just that that approach does not also confirm the limit of the function...

  • @newsnestofficial
    @newsnestofficial 4 หลายเดือนก่อน +1

    Best 🎉 Love ❣️ from Pakistan

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  4 หลายเดือนก่อน +2

      Thanks so much for watching, and good luck in your studies

  • @emeldahowell8668
    @emeldahowell8668 11 หลายเดือนก่อน +1

    Is It okay to put it as (r,theta) approaches (0,0)

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  11 หลายเดือนก่อน

      Kindly reference the time in the video for easy identification of your question

    • @emeldahowell8668
      @emeldahowell8668 11 หลายเดือนก่อน +1

      24.44 -25.30
      Instead of just writing r->0 is it correct to have it as (r,theta)->(0,0)

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  11 หลายเดือนก่อน

      @emeldahowell8668 yes please, you can

    • @emeldahowell8668
      @emeldahowell8668 11 หลายเดือนก่อน

      @@SkanCityAcademy_SirJohn Thankyou

  • @muchimwanamwila5259
    @muchimwanamwila5259 ปีที่แล้ว +2

    Thank you so much

  • @rohitpurkait1969
    @rohitpurkait1969 11 หลายเดือนก่อน +1

    Thank you so much sir

  • @frankkalobwe107
    @frankkalobwe107 ปีที่แล้ว +1

    For example 4, why did you refer to (0,0) and not (1,2)

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว +1

      you are perfectly right, i was supposed to reference (1,2) and not (0,0), that was a mistake from my end. Thanks so much for notifying me.

    • @thespaceagent3991
      @thespaceagent3991 ปีที่แล้ว +1

      could you go through that part in another video?@@SkanCityAcademy_SirJohn

    • @SkanCityAcademy_SirJohn
      @SkanCityAcademy_SirJohn  ปีที่แล้ว

      Noted

  • @zeraiikhlass1184
    @zeraiikhlass1184 ปีที่แล้ว +1

    i don't understand why u didn't use the HR in the first example.

    • @williambisson8632
      @williambisson8632 11 หลายเดือนก่อน +1

      same idk why

    • @kejsigjikola2351
      @kejsigjikola2351 4 หลายเดือนก่อน

      if you're required not to use HR will you know how to solve it? Im an engineering major and we're not allowed to use HR in exams lol

  • @CHIFUNIROMACHESO
    @CHIFUNIROMACHESO หลายเดือนก่อน +1

    nice