precise definition of the limit for multivariable functions (KristaKingMath)

In this video we'll learn about the precise definition of the limit for multivariable functions, also known as the epsilon-delta definition of the limit.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[ahanshetty]

8 years on and still capable of clearing the doubts of any confused math student. Great video Krista!

[hecz]

When I turned the page and saw that dreaded epsilon symbol, I felt like throwing my chair out the window and shrieking like an ostrich in labor. But thanks to you, all is well. I really appreciate how you summarized the 3-part procedure and gave reasoning to your steps. Thank you *so much* for this detailed and digestible explanation of limits.

[KartikayKaul]

Thank you so much! Honestly, college professors never help and do not give much time to explaining stuffs. Your video was able to explain this concept so well within about 30 minutes! The geometric interpretation also helped a lot in understanding! I love you! Thanks again!!!!

[AndreaLovelieee]

BEYOND AMAZING VIDEO!!! My professor NEVER shows step by step as you did. I am so thankful for professors / tutors like you that show STEP BY STEP for people like myself. Thank you for such a helpful and AMAZING video!!!

[caducoelho]

Colorful boards videos rule. First KhanAcademy, and now I've found your channel. I'm so glad people like this really exist. <3

[kgetsepemkhabela]

My sister, you're the best. You simplify things much better. Thank you.

[akshatgururani]

This is probably the best lecture I ever listened to, for multivariable Calculus. Thank you so much.

[luigivincenzo]

That awkward moment when the example used in this video is exactly the question in my maths assignment...

[silversky]

I can't believe this video was posted 7+ years ago. Absolute quality!!!

[RealationGames]

Brilliant video! I had to look 5 different clips on Youtube and this was the only one that explained this fully to me.
Thanks!

[thetruereality]

Thank you very much. Very much grateful for devoting 35 mins of your time for this.

[jamesd]

Really great video! I really appreciate how your explanation is so detailed and how you started with explaining the concept in 2D before going to 3D!

[eddierosell]

Wow! I'm studying engineering physics in Sweden and I've been reading about the epsilon, delta definition but never quite grasped it completely.. You just made me understand it so much better than my books ever did. Thank you!

[bassamaboona]

Thank you very much for this thorough explanation! I am taking calculus III online, and this video really helps understanding the concept. 

[estebanm]

I have to say. The world needs more teachers like you. Because human kind is very capable but we are misguided.

[mongoqueen]

Wow! I tried to understand the epsilon-delta definition like for half a year and i really didnt get it. Your awesome explanation finally made me understand it and with the example i also know how to use it now ! Thank you so much !
You are a awesome teacher!

Saludos

[lakshya]

awessome, surely saved my times to go around several books .

[oguzhandogan]

so glad i found you. thank you for explaining these complicated things articulately. and i must say you have a beautiful voice :D

[MrJon]

Quite a long video but very worthwhile to watch. If I can like this video a million times I would.

[LariosGiveNoFucks]

Holy crap, my mind was blown within the first 17 minutes. You explained it far better than both my Calc 1 and 3 professors ever did.