When simply evaluating an equation 0/0 is undefined. However, in taking the limit, if we get 0/0 we can get a variety of answers and the only way to know which on is correct is to actually compute the limit.

Does 0 0 mean the limit DNE?

Just because you get a "0/0"-situation doesn't mean the limit does not exist. It does mean that you need to do some more work to find out what the limit is and whether it actually does exist.

What is a 0 0 limit called?

According to some Calculus textbooks, 0^0 is an ``indeterminate form''. When evaluating a limit of the form 0^0, then you need to know that limits of that form are called ``indeterminate forms'', and that you need to use a special technique such as L'Hopital's rule to evaluate them.