Calculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions (with Squeeze Th.)

แชร์
ฝัง
  • เผยแพร่เมื่อ 9 มี.ค. 2016
  • Calculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions: How to show a limit exits or Does Not Exist for Multivariable Functions (including Squeeze Theorem). Also, how to determine regions of continuity.

ความคิดเห็น • 447

  • @lolipopscandy62
    @lolipopscandy62 7 ปีที่แล้ว +976

    Doing your job right. A simple thing. But oh my God, if everyone did their job the way this man does his, our world would be a far better place.

  • @jclarkent3757
    @jclarkent3757 7 ปีที่แล้ว +559

    The only way to teach effectively is like a broken record. He never leaves anyone in the dust. Its nearly impossible to walk away from this class feeling lost or behind. So awesome

    • @JawadAli-tj3ec
      @JawadAli-tj3ec 6 ปีที่แล้ว +2

      broken record tells how to understand others ,,,,,

    • @emanuellandeholm5657
      @emanuellandeholm5657 ปีที่แล้ว +1

      Your username is so funny because Clark Kent is exactly who this professor reminds me of. :D

    • @emanuellandeholm5657
      @emanuellandeholm5657 ปีที่แล้ว

      I see he's leaning into it too :D

  • @learningleopard996
    @learningleopard996 3 ปีที่แล้ว +282

    Intro to multivariable limits: 0:00
    Showing a limit (with two variables) does not exist: 26:54
    Showing a limit (with three variables) does not exist: 1:12:19
    Showing a limit does exist: 1:32:07
    changing to polar coordinates: 1:32:28
    Continuity (domain and compositions): 1:41:47
    Summary of computing limits: 2:06:56 - 2:07:24
    Squeeze theorem (converting to inequalities): 2:07:26

    • @ahmadaloufi4067
      @ahmadaloufi4067 8 หลายเดือนก่อน

      ♈🔧

    • @herobrine1847
      @herobrine1847 6 หลายเดือนก่อน +1

      Where’s the balloon

    • @Truth_Seeker1202
      @Truth_Seeker1202 3 หลายเดือนก่อน +2

      Thanks a lot for the timestamps!

  • @grantedwards8546
    @grantedwards8546 8 ปีที่แล้ว +286

    Every professor should take note the beginning portion of your lectures. Every math professor I've had jumps straight to the computational stuff and expects students to learn what they're actually doing on their own.

    • @yasminasabra8875
      @yasminasabra8875 4 ปีที่แล้ว +1

      100%

    • @juanorellana8945
      @juanorellana8945 4 ปีที่แล้ว +8

      That single introduction makes the difference!!! >:(

    • @scottwitoff8932
      @scottwitoff8932 3 ปีที่แล้ว +7

      One thing that bothers me is how in order to be a professor you do not need a degree in education. In other words you can be an expert but not know how to teach.

  • @hugojulia7145
    @hugojulia7145 4 ปีที่แล้ว +116

    ok so he is ACTUALLY explaining ive never had a teacher that did that im shook

  • @jeremiahswartz2314
    @jeremiahswartz2314 6 ปีที่แล้ว +144

    If I had this professor I would never miss a lecture. I firmly believe in a full understanding of the subject at hand. This guy knows how to deliver.

  • @akshay.s
    @akshay.s 4 ปีที่แล้ว +73

    I wish I had found this channel earlier- would have made a lot of things easier.

  • @sujitsuram5075
    @sujitsuram5075 4 ปีที่แล้ว +131

    conceptual talk until 00:00
    Examples of 2 dependent variables: 24:00
    Examples of 3 dependent variables: 1:12:15
    Squeeze theorem : 2:07:25

  • @christianbalderrama3179
    @christianbalderrama3179 8 ปีที่แล้ว +66

    Hello Professor Leonard, I just want to personally thank you here at TH-cam for providing quality tutorials from starters to advanced topics at Mathematics. I'm currently at your Pre-Algebra courses, its just amazing! I've never been taught Mathematics this way which is very fun and intuitive way. Thank you so much!

  • @thetedmang
    @thetedmang 7 ปีที่แล้ว +39

    Prof Leonard,
    You got me through Calc 1 and Calc 2, both with an A+.
    Thanks for your dedication to teaching!

  • @coletadlock4323
    @coletadlock4323 6 ปีที่แล้ว +10

    I love the way he teaches and his sometimes cringe dad jokes. Keep up the great work, I appreciate your help!

  • @thickthickitythickface
    @thickthickitythickface 7 หลายเดือนก่อน +2

    Professor Leonard is simply amazing. So glad for having someone like him on this platform.

  • @Gabi____
    @Gabi____ 6 ปีที่แล้ว +11

    I can't believe how helpful are those videos. I'll watch them in class instead of listening to my professor b/c it's such a waste of time... thank you so much!

  • @sammyofer9874
    @sammyofer9874 3 ปีที่แล้ว +12

    I'm watching this an hour before my midterm and I'm already learning more than my teacher ever taught me

    • @clayg9214
      @clayg9214 ปีที่แล้ว +1

      howd it go

  • @AlexandreGMusic
    @AlexandreGMusic 3 ปีที่แล้ว +5

    these video might just save my semester. His explanations are so simple to follow and very clear and when my professor explains the same material I don't understand a single thing. Wish we had more professor like him. Thank you for the videos!

  • @tashina7556
    @tashina7556 2 ปีที่แล้ว +5

    Thank You Professor Leonard! Your videos have helped me to Ace calculus I, II and III. I tell everyone who struggles with Calculus about your videos. They have been so helpful!

  • @PolSanchezJr
    @PolSanchezJr 5 ปีที่แล้ว +3

    Bless your soul Prof. Leonard,
    My professor explains things very strangely, using abstract notation, and she still uses blackboards without erasing the pre-existing chalk properly. You are literally going to save my life in this class and I feel like I am a part of the environment. You do a great job of explaining everything and it's worth watching you lecture for a little longer to make sure that I understand the concepts completely. Thanks for the humor!

  • @davidlunacruz1150
    @davidlunacruz1150 4 ปีที่แล้ว +5

    There is no other way to describe this man other than a living legend

  • @Emmitries
    @Emmitries 10 หลายเดือนก่อน +1

    I am so grateful I came across this lecture. If every math professor taught concepts like this, the world would be a better place! Thank you so much!

  • @alexprocel91
    @alexprocel91 7 ปีที่แล้ว +74

    Professor Leonard, will you ever make videos for linear algebra and differential equations? I really hope you do one day!!

    • @lukevandervorst5853
      @lukevandervorst5853 5 ปีที่แล้ว +7

      Procel91 he just started a differential equations series, if you still need it

  • @user-tm1ix7xi1n
    @user-tm1ix7xi1n 7 ปีที่แล้ว +6

    Your videos gets better and better every time. Thank You so much.

  • @xbriitbx
    @xbriitbx 6 ปีที่แล้ว +1

    Thank you for showing how to apply Squeeze Theorem to these problems!!! My teacher tried to explain it to us in half of a lecture and you did it under 10 minutes in a way that I can understand!

  • @ingridvenegas1211
    @ingridvenegas1211 4 ปีที่แล้ว +1

    Your classes are helping me get through this multivariable stuff during these trying times. Thank you!

  • @1agentchase108
    @1agentchase108 5 ปีที่แล้ว +2

    I have been struggling with limit continuities for weeks, this video's first ten minutes cleared up everything I had wrong!

  • @tm67245
    @tm67245 7 ปีที่แล้ว +18

    oh my god! he makes math sounds soo much fun n easy!! thank you

  • @akshay.s
    @akshay.s 4 ปีที่แล้ว +2

    In my view, Professor Leonard is the Best Math Teacher online

  • @kristelshull8568
    @kristelshull8568 4 ปีที่แล้ว +1

    Thank you for taking the time to explain this! Amazing job! I hope that all math professors could explain the way that you do!

  • @nontobekodlamini6709
    @nontobekodlamini6709 8 ปีที่แล้ว +2

    Thank you much Professor Leonard for the calculus 3 videos , you such a wonderful teacher you made me like calculus , you my best teacher ever.

  • @BB-bq4oo
    @BB-bq4oo 7 ปีที่แล้ว +1

    Honestly your videos help me out so much! I'd be lost without them! I can't thank you enough!!

  • @jisungyu2
    @jisungyu2 7 ปีที่แล้ว +4

    I really like your lectures. I appreciate it very much for making them available!! very learner friendly!!!

  • @georgesadler7830
    @georgesadler7830 2 ปีที่แล้ว

    Professor Leonard, thank you for another well organized video/lecture on Limits and Continuity on Multivariable Functions with the classic Squeeze Theorem in Calculus Three. These concepts are introduced in Calculus One, which improve my understanding of the subject in Multivariable Calculus.

  • @ishitapandey6349
    @ishitapandey6349 3 ปีที่แล้ว +5

    It's really a blessing to be taught by u. Your dedication level soars the sky.
    Thank you sir for making mathematics easy for everyone one of us!
    With love
    From India!!

  • @shadiam.6694
    @shadiam.6694 8 ปีที่แล้ว +2

    It's funny how on calc 1, I watched your videos in regular speed. In calc 2 it was in 2x it's speed, and now I'm able to manually watch calc 3 in 3x it's speed. Just goes to show how clear it is, thanks so much for creating smooth transitions to new topics and info (:

  • @makeclub
    @makeclub 5 ปีที่แล้ว +2

    Went all around the internet looking for engaging and relevant content like this. This is so much better than my stanford math prof. I really appreciate your delivery of concepts (and this is the first youtube comment i have been compelled to make in years)

    • @ProfessorLeonard
      @ProfessorLeonard  5 ปีที่แล้ว

      Thanks so much!! I'm very glad you are enjoying the videos :)

  • @hamnahteli990
    @hamnahteli990 3 ปีที่แล้ว +1

    This man is truly inspirational! loving the lectures! so helpful!

  • @sarveshkamat7784
    @sarveshkamat7784 5 ปีที่แล้ว +3

    Professor Leonard,
    May god bless you with a continuous eternal function of health and wealth with no holes and asymptotes ☺😘💝

  • @natanbenchimol8159
    @natanbenchimol8159 6 ปีที่แล้ว +9

    A year and a half later this is still the best math lesson I've ever had

    • @Salamanca-joro
      @Salamanca-joro 2 หลายเดือนก่อน

      Eight years later and this is still the best math lesson I've ever had , first time watching his videos and it looks like that it won't be the last!

  • @SamuelLee-gw6wr
    @SamuelLee-gw6wr 2 ปีที่แล้ว

    Following in the footsteps of SQ Flyer who got an A+ in math2011 intro to mul cal in 2019 fall, I have watched so many of your vids and I am going to be the next beneficiary of you!
    I managed to get a past exam question correct on 1/12/2022 but my semester starts on 2/4/2022. Thanks a lot!

  • @kartikaysingh8132
    @kartikaysingh8132 6 ปีที่แล้ว +1

    All the concepts you explained sir, you made it all look so simple. Thank you so much.

  • @johndoe-sh6bi
    @johndoe-sh6bi 2 หลายเดือนก่อน

    Dude this guy is amazing. He needs to zoom these lectures live so we are actually there. A lot of people would pay for that.

  • @EG-ne7yp
    @EG-ne7yp 4 ปีที่แล้ว +3

    Преп просто охеренный! Зачет. Cool teacher! I really enjoy his attitude. He is genuinely interested in what he is doing. On the other hand majority of university teachers barely tolerate students and see them as a nonsense and a distraction from scientific research.

  • @omarmagdi2732
    @omarmagdi2732 9 หลายเดือนก่อน

    you are such an Artist....It's very satisfying when you find one of those gems on youtube!!!

  • @tumarisyalqun7327
    @tumarisyalqun7327 6 ปีที่แล้ว +2

    Thank you so much for sharing your lecture, you are truly an amazing professor!

  • @TomLawsonANIMATIONS
    @TomLawsonANIMATIONS 8 ปีที่แล้ว

    Excellent explanation! It's people like you who make the world go 'round

  • @anbreenmuqaddas
    @anbreenmuqaddas 10 หลายเดือนก่อน

    Your students are so lucky!
    Thank you so much professor this means a lot for a lot of us
    Your lectures are well delivered and clears out every confusion in my mind

  • @kidistyetimgeta1006
    @kidistyetimgeta1006 3 ปีที่แล้ว

    i am really thankful for Professor Leonard and I even recommended your lecture for my friends and the are thankful too

  • @muazothman7416
    @muazothman7416 8 ปีที่แล้ว +1

    YOU ARE AMAZING!!!!!! I HAVE CALC 2 EXAMS COMING UP IN FIVE DAYS AND YOU ARE MY SAVIOUR TO ENDING THIS COURSE WITH AN A..:)))) thanks keep this up, much better than patrick jmt

  • @lindaleckrone6153
    @lindaleckrone6153 4 ปีที่แล้ว +1

    I refer many of my students to these videos, they are fantastic. With this one, I have one comment - around minute 43, part a says to be certain your point (a,b) is on your path. But then goes into testing along the x and y axis. If your point of interest is NOT the origin, do not try x=0 or y=0 as your path. Try x=a and y=b instead!

  • @NirmalyaGanguli
    @NirmalyaGanguli 5 ปีที่แล้ว

    I don't know if it's really good enough to say just a "Thank You"...but still "Thank you very much"....ur detailed conceptual explanations are a treat to watch and understand.

  • @BL-om2hn
    @BL-om2hn 7 ปีที่แล้ว +3

    Such a wonderful professor !!!

  • @jinks908
    @jinks908 3 ปีที่แล้ว +1

    Please, please, please, PLEASE stop saying "heighTH." You are a MATHEMATICS professor; this is cringe-worthy.
    However, this channel is honestly a godsend. It is an absolute shame that I have to get my instruction from somewhere beyond my class (where the instruction SHOULD be the best). I am forever indebted to this man for supplying the necessary intuitions behind these extremely subtle and precise concepts.

  • @sl-nj5ry
    @sl-nj5ry 5 ปีที่แล้ว

    This is the best lecture on youtube! Thank you so much!

  • @chemist7908
    @chemist7908 5 ปีที่แล้ว

    Thanks a mil, its amazing that you teach for two hours off of one piece of paper

  • @gabbyeebzie4103
    @gabbyeebzie4103 7 ปีที่แล้ว +3

    This was so helpful! Thank you!

  • @SweRaider1993
    @SweRaider1993 8 ปีที่แล้ว +1

    Thank you so much! I'm surprised my book never mentions the squeeze theorem and instead goes through a bunch of other non-sensical stuff... You made it all perfectly clear, and the theorem kind of makes sense intuitively as well.

  • @kezianathaniel2901
    @kezianathaniel2901 4 ปีที่แล้ว +1

    Thank you for being extremely elaborate and clear!

  • @ibrahimislam1608
    @ibrahimislam1608 4 ปีที่แล้ว

    You are amazing, Professor Leonard. Thank you.

  • @aaronguerrero592
    @aaronguerrero592 9 หลายเดือนก่อน

    1:08:45 AND THAT WHY HE IS THE G.O.A.T!!! THE SMALL DETAILS, I love it! Thanks again Professor Leonard. Just killed my Ch.12 exam with a 99. Plan on going for a killing spree in calc 3.

  • @RichardAxon
    @RichardAxon 6 ปีที่แล้ว

    Give this man a medal please! Thanks for your help!

  • @TheTaniaVanesa
    @TheTaniaVanesa 6 ปีที่แล้ว +3

    Thank you so much for clearing this up for me! greetings from México profesor Leonard! :)

  • @Realfeziwe
    @Realfeziwe 4 ปีที่แล้ว

    this guy is the best ....The way he explain Everything you can even see some logic

  • @maxusldragold5641
    @maxusldragold5641 4 ปีที่แล้ว +1

    Best Calculus Professor i ever seen

  • @reynantejr.marangga35
    @reynantejr.marangga35 7 ปีที่แล้ว +2

    this is the best professor that i've ever known :-D

  • @conservativedeveloper7289
    @conservativedeveloper7289 6 ปีที่แล้ว +47

    1:01:36 Proof Professor Leonard is just a hologram.

  • @michelletheatom
    @michelletheatom 5 ปีที่แล้ว +2

    Watching from Mexico. I love your videos!

  • @waltercarrillo6065
    @waltercarrillo6065 5 ปีที่แล้ว

    Great professor, those students must be proud of him. D for done.

  • @dmkarlien
    @dmkarlien 7 ปีที่แล้ว

    Thank you professor Leonard for these videos ,it saves lives and also does anyone get that satisfactory feeling when he wipes the board ?

  • @davekaushik4863
    @davekaushik4863 2 ปีที่แล้ว

    Goated prof, nothing made sense before this video, but even in the first 10 minutes, so many misconceptions I had were cleared up :)

  • @Since-vd5cn
    @Since-vd5cn 7 ปีที่แล้ว +1

    i seriously love your sir, thank you so much.

  • @austinpolk7213
    @austinpolk7213 2 ปีที่แล้ว

    I am just letting you know that I wished i found this series sooner but I found it in time for my finals. So thank you

  • @matthewel-sirafy7266
    @matthewel-sirafy7266 ปีที่แล้ว

    man i wish i found this channel sooner, you are like a calc legend. I might just have to move to the USA so that i could have you as my prof.

  • @dezhouung6227
    @dezhouung6227 4 ปีที่แล้ว

    Wow, first time watch your vid and learnt a lot. So clear....

  • @andrea1955
    @andrea1955 4 ปีที่แล้ว

    I finally understand this! Thank you very much.

  • @revivemuzunzandare479
    @revivemuzunzandare479 6 ปีที่แล้ว +1

    Thanks very much Professor Leonard

  • @estefaniakiara-elizabeth8538
    @estefaniakiara-elizabeth8538 6 ปีที่แล้ว

    Thank you so much, awesome class! Your students are very lucky

  • @aequanimus63247
    @aequanimus63247 7 ปีที่แล้ว +1

    thank you for clearing this up for me!

  • @joaquinbrandan8664
    @joaquinbrandan8664 3 ปีที่แล้ว

    you have half a million subscribers for a reason, great job!.

  • @gcdebate3226
    @gcdebate3226 4 ปีที่แล้ว

    Thank you for your video. Bloody good explanations!

  • @chipicaua
    @chipicaua 5 ปีที่แล้ว

    You're a gift to humanity i just wish I could watch your lectures IRL but sadly I'm just a NTUA student here in Greece-ville. :( Cheers!

  • @Sofialovesmath
    @Sofialovesmath 2 หลายเดือนก่อน

    Incredible stuff, you are a gem.

  • @monikajangir4107
    @monikajangir4107 6 ปีที่แล้ว +1

    Hey I am from india!! Your video helped me alot!!!The way u teach is very excellent!!

  • @DanielaSantos-tv8tt
    @DanielaSantos-tv8tt 8 ปีที่แล้ว

    Thank you so much! This was exactly what I needed :)

  • @susanlove9620
    @susanlove9620 2 ปีที่แล้ว

    reviewing again, cuz i want it to be like...hate adding... like geometry when i was young. honestly, this is where it gets exciting. also, each time i study a lesson, as i understand it even more clearly, i realize even more what a good teacher you are.

  • @satyajeetkumar6497
    @satyajeetkumar6497 5 ปีที่แล้ว

    Thank you for this great video sir , it really help me a lot

  • @juanmartincorrea9698
    @juanmartincorrea9698 2 ปีที่แล้ว

    Great video, you are really good explaining, thanks!!

  • @Shivamkh9
    @Shivamkh9 6 ปีที่แล้ว

    This was so helpful! Thank you! sir

  • @Yo-pn9qp
    @Yo-pn9qp 3 ปีที่แล้ว +4

    THE 35 DISLIKES: EXPLAIN YOURSELF!

  • @humraabdullah6521
    @humraabdullah6521 3 ปีที่แล้ว

    I'm from Pakistan . Sir I really loved your lectures and way of teaching.that's amazing 😍

  • @Ali-qc3ym
    @Ali-qc3ym 6 ปีที่แล้ว +1

    thank you best professor ever

  • @amrhamdy2976
    @amrhamdy2976 6 ปีที่แล้ว

    I am in computer engineering and this help me so much THANKS

  • @David-nk7pv
    @David-nk7pv 7 ปีที่แล้ว

    You are great. Thank you for this.

  • @shashankshekhar2091
    @shashankshekhar2091 6 ปีที่แล้ว +2

    great explanation

  • @zsolttildy5742
    @zsolttildy5742 7 ปีที่แล้ว +1

    wish i was in his class. truly an inspiration

  • @howardwolowitz762
    @howardwolowitz762 5 ปีที่แล้ว

    You are the best, my good sir. You are the best.

  • @clementcu4827
    @clementcu4827 7 ปีที่แล้ว

    Doing a good job there sir !

  • @patrickpoirier4521
    @patrickpoirier4521 8 ปีที่แล้ว

    best prof ever!!! thanks a lot!

  • @BigTimeBrad
    @BigTimeBrad 8 ปีที่แล้ว +29

    Professor Leonard, I'm always excited to see new material. I'm currently in Calc 3, and you've been a major help along the way! I have finals next week and I can understand your probably very busy yourself... Do you plan to release more videos in the next week or so? Thanks!

    • @ProfessorLeonard
      @ProfessorLeonard  8 ปีที่แล้ว +41

      +Brad Nissen I'm releasing them as fast as I can make them, I hope they will help. Good luck!

    • @sandilemabika8656
      @sandilemabika8656 8 ปีที่แล้ว +1

      +Professor Leonard when are you gonna release double and triple integral videos?

    • @ZnNlove
      @ZnNlove 8 ปีที่แล้ว +12

      +sandile mabika
      He actually already has released it, but the video was shot with a 4-D device in 4-D setting so unfortunately 3-D people are unable to see it. Maybe you should get 4-D glasses, I am selling if you are interested.

    • @Nicoder6884
      @Nicoder6884 8 ปีที่แล้ว +1

      +ZnNlove Efil I'm interested.

    • @presidentevil9951
      @presidentevil9951 7 ปีที่แล้ว

      Could you also give more examples of proving the limit DOES exist in different ways and what methods to use when?

  • @samkelo_m_
    @samkelo_m_ ปีที่แล้ว

    Thank you so much. You made it clear

  • @gabrialpetersen914
    @gabrialpetersen914 3 ปีที่แล้ว

    Simply a godsend. My hero.

  • @mohammedeldakak4592
    @mohammedeldakak4592 4 ปีที่แล้ว +1

    Best professor ever❤️❤️❤️