# What is the limit of (sin^4x)/(x^(1/2)) as x approaches infinity?

${\lim}_{x \rightarrow \infty} \frac{{\sin}^{4} x}{{x}^{\frac{1}{2}}} = 0$
$\sin x$ is limited to the range $\left[- 1 , + 1\right]$
$\rightarrow {\sin}^{4} x$ is limited to the range $\left[0 , 1\right]$
$\rightarrow {\sin}^{4} x$ has an upper limit of $1$ while $x \rightarrow \infty$
${x}^{\frac{1}{2}} \rightarrow \infty$ as $x \rightarrow \infty$