Let $f, g : \mathbb{R} \to \mathbb{R}$ each be a D4364: Real function such that
| (i) | $x_0, \lambda \in \mathbb{R}$ are each a D993: Real number |
| (ii) | \begin{equation} \lim_{x \to x_0} f(x) = 0 \end{equation} |
| (iii) | \begin{equation} \lim_{x \to x_0} g(x) = \infty \end{equation} |
| (iv) | \begin{equation} \lim_{x \to x_0} f(x) g(x) = \lambda \end{equation} |
Then
\begin{equation}
\lim_{x \to x_0} (1 + f(x))^{g(x)} = e^{\lambda}
\end{equation}