Question

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

Answer 1

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

Explanation:

`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`