Limits of functions of two variables

We discuss limits of functions of two variables and how to evaluate them. We present some simple examples and some more involved epsilon-delta techniques. We apply the ideas to continuity of functions.

[dmayder]

I just watched your video, and I was so confused with how to approach problems with the definition of a limit for two variable functions. However, now I understand the approach completely! Your students are so lucky to have a rational professor. Cheers from the University of Calgary!

[SayinPrincess]

Gotta go to class now, but I'll definitely watch this lecture later. I'm studying Actuarial Science in South Africa and I've come to realise that if you hear the same explanation in different ways from different lecturers you'll understand better. Hence, I've resorted to youtube. Thanks a lot Dr. T!

[shishiscott]

Morning Dr Chris tesdell my name is Shishi student at cape town university really Dr tesdell you really change my life in science special in mathematics God bless you and your family and keep doing what you doing Dr chris . I'm telling u I'm proud my self in math in general coming complex number, triple integral, line integral, Flux integral, Divergence vector field etc.  I did quite a lot really Thanks ..I'm proud of you Dr Chris knowing all of these . you did effected me with a virus in maths now . I do have a virus in Maths  like you .

Kind regards
Shishi Scott .south Africa .cape t  UCT 

[mosesmccabe]

wow you're great at what you do...this is the best explanation of two variable limits on youtube. please keep up the great work.

[danib]

Dear Professor Tisdell, thank you so much for your amazing ability to actually explain maths. This subject is so incredibly confusing and you have been a lifesaver! However, it would be amazing if you could please go over some of the proofs (or even how to prove aspects) of the subject? They are super confusing and part of the Higher Multivariable Course (and giving everyone panic attacks).

[thandononofo]

Thanks a lot Dr Chris this was helpful to me. I am wring an exam this coming week I hope I will crush it. Thanks for the other videos. South Africa

[sparkldust]

My new favorite math teacher! Are the snazzy notes you include in the video available online?

[boscojay]

its 2019 i'm still watching these videos again!!!!

[meganwilson]

epsilon delta proofs are truly challenging. Thank you, video helped a lot, great explaining. Wish my math professor was as great as you are.

[BespontovyiPirozhok]

that's so awesome, i can not believe.
The best epsilon-delta proofs!
so cool. Thanks!

[MetallurgyGATE]

Awesome Technique of teaching. Thanks for the video.

[reinaldomjunior]

thank you very much Dr Chris Tisdell, this was absolutely helpful! Thanks from São Carlos, Brazil

[DrChrisTisdell]

Yes, it can be done. Consider what it means for the limit to exist (in epsilon - delta terms) and then form the negation of that.

[JimBob]

Thanks, quite useful. Though i find you made too large of a jump at the end which may lose some people. When he is simplifying the limit he converted to polar coordinates he factored out an R^2 from the denominator which simplified down to an r*cos^(theta) in the numerator and cos^2 + sin^2 on the denominator. Then, using an identity that cos^2+sin^2 is equal to 1, the top then becomes what he had, which is r*cost^3(theta).

[DrChrisTisdell]

Thanks and best of luck with your studies.

[DrChrisTisdell]

No problem at all. I am glad you liked it. Hope the ebook is also of interest, the link is in the description.

[DrChrisTisdell]

Great! Interesting to hear that you're in South Africa. At one point in my life, Univ of Wits offered me a position, so I've always wondered what that path in life would have lead to.

[hongnian]

you're much clearer than my prof...
thank you

[semirumutkurt]

so clear... ı understood the concept that is underlying limits of functions of several variables. thanks sir

[yannid]

thank you very much for your effort it really helped me to prepare for my examination, May Lord Jesus bless you in His Name.