# What is the limit of (sqrt x) / (x + 4) as x approaches infinity?

$\lim \to$ infinity of the ratio of ${x}^{m} / {x}^{n}$ is 0 or infinity, according as, when m < or < n. .
Divide by $\sqrt{x}$ both numerator and denominator. The function becomes
$\frac{1}{\sqrt{x} + \frac{4}{\sqrt{x}}}$
As $x \to$ infinity, the limit is 1$/$(infimity + 0) = 0.