You can say that these limits do not exist in similar ways to single variable limits.
The first one yields an indeterminant form... So it may or may not exist.
To tackle this one is a bit of work but I'll work on it a little bit and edit this later.
For the second one, look below.
The third one is a classic example of multiple paths to prove nonexistence.
If you plug everything in you immediately see a 0 in the denominator, so it is indeterminate. So, we try a random path... Say, y = x... Then we get:
Now, let's try (Just to mix it up)
We plug and chug to get:
Which is NOT zero, so it does not exist.
Hope that helps.