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

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.

[lolipopscandy]

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.

[learningleopard]

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

[jclarkent]

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

[grantedwards]

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.

[jeremiahswartz]

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.

[hugojulia]

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

[sujitsuram]

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

[christianbalderrama]

Hello Professor Leonard, I just want to personally thank you here at Youtube 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]

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

[akshay.s]

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

[PolSanchezJr]

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!

[AlexandreGMusic]

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!

[tashina]

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!

[thickthickitythickface]

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

[Gabi____]

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!

[lindaleckrone]

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!

[coletadlock]

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

[Emmitries]

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!

[sammyofer]

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

[ninjamonk]

My professor for Calc 3 is named Hongwei and speaks with a hard accept from china so when he goes over anything its always a bigger challenge to not only understand the concept but him as well. So when he went over this section he sped through it only talking about the epsilon-delta definition of it and then using polar to solve some problems, never fully explaining the actual concept. This video has not only saved my grade but also my understanding of limits for all future calculations I'll be doing in my career as an engineer. Thank you so much Professor Leonard!