Multivariate Limits and Continuity

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.

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00:02 Limits and Continuity for multi-variable functions
01:07 Limits in multivariable calculus can be used to prove theoretical properties and have different techniques for evaluating limits in practice.
02:07 To find multivariate limits, we restrict our inputs to a tiny 2D neighborhood around the point of interest.
03:09 Multivariate limits must be unique
04:09 Limits at the origin may not exist due to approaching different values along different paths
05:12 To find a candidate limit, check the limit of the function along certain paths and see if it approaches the same value.
06:18 Proving the existence of a limit is tough but can be accomplished with practice.
07:18 Continuity in Calc 3 is determined by the existence of limit and match with function value.