L'Hôpital's Rule/Examples/(Root of (1 plus x) minus 1) over x

Example of Use of L'Hôpital's Rule

 * $\ds \lim_{x \mathop \to 0} \dfrac {\sqrt {1 + x} - 1} x = \dfrac 1 2$

Proof
Let $f: \R \to \R$ be defined as:
 * $\forall x \in \R: \map f x = \sqrt {1 + x} - 1$

Let $g: \R \to \R$ be defined as:
 * $\forall x \in \R: \map g x = x$

We have that:

Then: