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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...

Git Gud
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windy401
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    If you can't tell whether it exists or not, try to prove it exists. You'll either end up proving it or hit a wall. How you hit the wall might give a clue as to why the limit doesn't exist. Edit: See also this question. – Git Gud Oct 22 '16 at 20:43
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    Common questions asked in an undergrad calculus class for when the limit DOES exist often require some algebraic manipulation (factoring numerator or denominator of a fraction so that stuff cancels), so that after manipulating and cancelling, the resulting function is continuous at the point in question, and you can just plug the numbers in. – Nick Oct 27 '16 at 03:07
  • Yea, I know. My problem is just, without knowing if it exists or not before hand, I never know when I'm just failing at the manipulation and not finding that point, of if I'm not finding that point because it doesn't exist and I haven't figured out the ways that show it doesn't. Feels like it too much of it is just luck which is frustrating on heavily weighted graded tests. – windy401 Oct 27 '16 at 14:52

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