In this video I go over the concept of a limit for a multivariable function and show how to prove that a limit does not exist by checking different paths. I then go over the definition of continuity and show how to evaluate limits of continuous functions and vector valued functions.
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You can check out my multivariable calculus textbook here:
http://www.amazon.com/gp/product/1518... (paper)
https://leanpub.com/multivariablecalc... (free pdf)