calculus - Solving $lim_{xto 0}frac{ln(1+x)}x$ without De L'Hospital

Trying to solve this limit without derivatives I found this answer that is pretty straightforward and I can easily follow the flow. I can understand why ${u\to \infty}$ because:

$$\lim_{u\to\infty}(1 + \frac{1}u)^u = e$$

but how there is a relation to ${x\to 0}$ with ${u\to \infty}$ when we need to find the limit that approaches $0$.

Answer

When $u \rightarrow \infty$, $x = \frac 1u \rightarrow 0$, as needed.