Evaluate the limit.

From the definition of the exponential we have

So, first we use the expansion of as (page 287 of Apostol) to write

Therefore, as we have

Now, since as we can use the expansion (again, page 287) of as to write

Therefore, as we have

So, getting back to the expression we started with,

But, as in the previous exercise (Section 7.11, Exercise #23) we know . Hence,