Multivariate Limits and the Squeeze Theorem - Examples

This video is based on content from "MATH 237 - Calculus 3" at the University of Waterloo. Check out the rest of the playlist here:
MATH 237: • Calculus 3 (MATH 237)
The above playlist is far from complete, but you're welcome to check out my other (complete) playlists covering various topics in Calculus:
Approximation and Infinite Series: • Approximation and Infi...
Multivariable Differential Calculus: • Multivariable Differen...
Multivariable Integral Calculus: • Multivariable Integral...
Vector Calculus: • Vector Calculus
Videos by Zack Cramer, University of Waterloo.

[@purpleapple-el7kb]

the heavy breathing at 7:21 🤣🤣🤣

[@Youtubewatcher585]

love the enthusiasm man, you make these problems not scary at all!

[@shrexy8095]

Best approach I've seen for this kind of limits so far
Thanks Mathemation!

[@powzewu7854]

I like the way you explained this. Very clear

[@krumpy8259]

very nice content, keep it up, thank you!

[@mathemation]

Thanks very much! I’m glad you’re enjoying the videos :)

[@shanghaireminiscence8369]

Thank you very much, your approach gives me a better understanding to solve multivariate limits. During last assignment, I only pick several paths (when the outcomes are the same) and said that is the limit instead of using squeeze theorem to prove it. Wish I viewed your video sooner. It helps a lot. Is it possible you can make more videos about MAT237? Appreciate that.

[@mathemation]

Thanks very much for your comment, I'm glad that the video has been helpful to you. I have some videos specific to MATH 237 that you can access in my MATH 237 playlist: th-cam.com/play/PLL9sh_0TjPuOxWvcGm5AOpxL6g3bmqnzb.html. These videos are from the spring 2021 iteration of the course. If there are topics that are not included in this playlist, you might find it helpful to review some of my other playlists on multivariable calculus.
Remember though that your iteration of MATH 237 may present these topics differently, use different notation, or focus on other topics that are not covered in these videos. The videos on this channel are not officially affiliated with the course and should be used only as a supplemental resource.

[@shanghaireminiscence8369]

@@mathemation Thank you for the playlist, very helpful. Yes, sir. I will focus on my textbook first and then learn what I missed from your video.

[@Lexyvil]

You explained the Squeeze Theorem better than my prof did! Thank you! The Triangle Inequality was something I never learned, it explains why I was confused at my university. So an equality becomes an inequality when applying the triangle inequality if I understood correctly? I just had trouble knowing when = becomes

[@mathemation]

If you're working with the absolute value of a sum of two (or more) terms, |a+b|, you can bring the absolute value into the sum at the cost of an inequality:
|a+b|