Calculate the value of the following limits, Mathematics

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Calculate the value of the following limits.

1744_limit17.png

Solution

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

1957_limit18.png

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,

716_limit19.png

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,

989_limit20.png

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


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