Evaluate the limit.

First, we rewrite the expression using the definition of the exponential:

Next, we need to get a series expansion for as . The most straightforward way is to take the first few derivatives (we’ll only need the term).

Therefore, we have as

Hence, as

Since this is going to 1 as we may apply this exercise (Section 7.11, Exercise #4) to conclude

Now, we have the expansion as

Therefore,