Is the lim exists when #lim_(x->0) f(x)= +- oo?#
2 Answers
No, the limit does not exist.
Explanation:
Consider the example
and
Hence, one could conclude that
However, since the limit tends to different results from above and from below the limit does not exist.
Many of us teach that so-called "infinite limits" are not limits that exist.
Explanation:
There are various ways that a limit can fail to exist.
One way is exemplified by
In this case, the limit fails to exist because as
We indicate this be writing
The definition is:
We write
Refusing to say that this limit exists allows us to simplify statements like:
If both
This theorem fails if we include