My prof said there was three ways, so far I've found two:
When the limit goes up to infinity, and when the left and right limits don't match. What are the other ways a limit cannot exist?
There are indeed three ways in which the cannot exist.
1. is not well defined inthe neighbourhood of .
For example does not exist
since is not defined in the neighbourhood
of though it is defined at .The same
is true for .
2. does not display tendency to approach a fixed numerical value.
For e.g. it is not known as to what value
will assume though we are
sure that it is a finite quantity on the interval
Similarly,
Here, .But if you try to evaluate we will not be able to decide to what value should f(x)
assume on the interval .
3.Of course ,the last condition being Left hand limit Right hand limit