L'Hôpital's Rule/Examples

Examples of Use of L'Hôpital's Rule

Example: $\frac {\sqrt {1 + x} - 1} x$

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

Example: $\frac {x^2 - 4} {2 x - 4}$

Let $f: \R \to \R$ and $g: \R \to \R$ be real functions defined as:

\(\ds \forall x \in \R: \, \)

\(\ds \map f x\)

\(=\)

\(\ds x^2 - 4\)

\(\ds \map g x\)

\(=\)

\(\ds 2 x - 4\)

Then:

$\ds \lim_{x \mathop \to 2} \dfrac {\map f x} {\map g x} = 2$