Question : Verify the limit: $$\lim_{h\to0} (1+hx)^{1/h} = e^x$$
Background : I don't even know where to start with this. I am in Calculus-I (at the point in the course where we are on L'Hopitals rule), and I believe that my professor means for me to use the Delta/Sigma definition learned earlier in the semester, although I have no clue. I really stuck here. Any help would be appreciated.
$$\begin{align}\lim_{h\to0} (1+hx)^{1/h} &= \exp\left(\lim_{h\to0}\frac1h\log(1+hx)\right)\\&=\exp\left(\lim_{h\to0}\frac{x}{1+hx}\right)\\&=\exp(x)\end{align}$$ From the first line to the second, we used L'hopital's rule.