Chapter 1.15, Problem 25P

In general, we do not expect Maclaurin series to be useful in evaluating indeterminate forms except when x tends to zero (see Problem 24). Show, however, that Problem 24(f) can be done by writing $x^n{e}^{-x}=x^n/e^x$ and using the series (13.3) for $e^x$.

Hint: Divide numerator and denominator by $x^n$ before you take the limit. What is special about the $e^x$ series which makes it possible to know what the limit of the infinite series is?