Evaluate the limit.
First, we write
From this exercise (Section 7.11, Exercise #4) we know that as we have
Therefore, as ,
So, we then have
(Here we could say that since the exponential is a continuous function we can bring the limit inside and so this becomes . I’m not sure we know we can pass limits through continuous functions like that, so we continue on with expanding the exponential as in previous exercises.)
Since as we take the expansion of as ,