# What is the limit of  (x-x^(1/2)) as x goes to infinity?

$x - \sqrt{x} = \sqrt{x} \left(\sqrt{x} - 1\right)$
Since both factor increase without bond as $x$ increases without bound, we get
${\lim}_{x \rightarrow \infty} \left(x - \sqrt{x}\right) = {\lim}_{x \rightarrow \infty} \left(\sqrt{x} \left(\sqrt{x} - 1\right)\right) = \infty$