I'm teaching a recitation for a calculus 1 class this quarter and through some miscommunication I was under the impression that I needed to present a method to finding the limit of
$\lim_{x\rightarrow 0} \frac{9^x-5^x}{x}$
without using L'Hospital's rule. I found rather quickly, much to my annoyance, that I was unable to find the limit without applying L'Hospital's rule. I asked several of my friends who were also unable to solve it. I was wondering if there was an elementary solution to such a limit, that is something understandable by a beginning calculus 1 student.
Edit: To be more clear the students in my recitation have only just learned limits and haven't even reached derivatives yet.