Multivariable Calculus | Showing a limit does not exist

We introduce the notion of the limit of a function with more than one variable and provide a strategy for showing that the limit does not exist.
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[@steveying1305]

Amazing video

[@cycklist]

Very interesting.

[@JossoJJossoJ]

How can we know if we've checked all directions?

[@Boringpenguin]

In order to say that the limit exists for a function at a certain point, the answers coming from all directions must be the same.
So, to prove that the limit does not exist, you only need to find two "directions" such that their answers don't agree with each other.

[@xahiru]

isn't the limit of (-y)^2/y^2 = 1? @4:55

[@SuperDreamliner787]

Yes, but we had to consider -y^2/y^2 instead of (-y)^2/y^2

[@georgettebeulah4427]

I can see it but they all look the same I can not understand a lot from it and can not make so much sense of it.