Reason for why limits not existing : In the previous section we saw two limits that did not. 

We saw that

did not exist since the function did not settle down to a single value as t approached t = 0 . The closer to t = 0 we moved the more passionately the function oscillated & in order for a limit to exist the function have to settle down to a single value.

However we saw that did not present not since the function didn't settle down to a single number as we moved in towards t = 0 , but rather then because it settled into two distinct numbers based on which side of t = 0 we were on.

The problem was that, as we approached t =0 , the function was moving in towards different numbers on each of the side.