When given questions like that, having been told there are infinitely many directions to approach from, and that of any two give different answers, the limit does not exist, I was left with a question about handling the case that the limit does exist.
If it doesn't exist, and you find two different answers, then ok, your good, you found it DNE. But in the case that the limit does exist, when do you stop trying things and say, ok, the limit exists and this is it? When do stop trying to find a case that will prove it doesn't? On homework out of the book if I think I've tried enough things I can look at the answers and see, ok, that is the limit, I'm right. But when it comes time for the test... I'm worried I'll try a bunch of things, but just happen to miss a case that gives something different and shows the limit DNE, and incorrectly say it does, which i have done a few times at home.
Between schedule issues, a big class size, a bit of a language barrier and my professor being bad at responding to emails I've yet to get an answer doesn't still leave me confused about how to deal with these problems. So, hoping someone here can give me some guidance on this...