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

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Answer 1 · 2016-04-19T12:18:55

$lim_(xrarroo)(sin^4 x)/(x^(1/2)) = 0$

$sin x$ is limited to the range $[-1,+1]$
$rarr sin^4 x$ is limited to the range $[0,1]$
$rarr sin^4 x$ has an upper limit of $1$ while $xrarroo$

$x^(1/2) rarr oo$ as $xrarroo$

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