Voorbeeld 1
$
\eqalign{
& \mathop {\lim }\limits_{x \to - \infty } \frac{{x + \sqrt {2x^2 + 1} }}
{{x - \sqrt {2x^2 + 1} }} = \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{x - x\sqrt {2 + \frac{1}
{{x^2 }}} }}
{{x + x\sqrt {2 + \frac{1}
{{x^2 }}} }} = \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{1 - \sqrt 2 }}
{{1 + \sqrt 2 }} = 2\sqrt 2 - 3 \cr}
$
Voorbeeld 2
$
\eqalign{
& \mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {9x^2 - 2} }}
{{\sqrt {x^2 + x} - \sqrt {4x^2 + 1} }} = \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{ - x\sqrt {9 - \frac{2}
{{x^2 }}} }}
{{ - x\sqrt {1 + \frac{1}
{x}} + x\sqrt {4 + \frac{1}
{{x^2 }}} }} = \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{ - \sqrt 9 }}
{{ - \sqrt 1 + \sqrt 4 }} = \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{ - 3}}
{{ - 1 + 2}} = - 3 \cr}
$