Calculate the value of the following limits.

Solution

To remind us what this function such as following the graph.

hence, we can see that if we reside to the right of t = 0 (i.e. t > 0 ) then function is moving in towards a value of 1 as we get closer & closer to t = 0 , however staying to the right.  Therefore we can say that the right-handed limit is,

Similarly, if we reside to the left of t = 0 (i.e t < 0 ) the function is moving in towards a value of 0 as we get closer & closer to t = 0 , however staying to the left. Thus the left-handed limit is,

In this we do get one-sided limits although the normal limit itself doesn't exist.