Question

What is the limit of `sin^4(x)/x^0.5` as x goes to infinity?

Answer 1

It is `0`

Explanation:

`0 <= sin^4x <= 1` for all `x`

`x^0.5 > 0` for `x > 0`, so we can divide in the inequality without changing the directions of the inequalities.

`0 <= sin^4x/x^0.5 <= 1/x^0.5` for all `x`

We note that `lim_(xrarroo) 0 = lim_(xrarroo) 1/x^0.5 = 0`,

so, by the squeeze theorem, `lim_(xrarroo) sin^4x/x^0.5 = 0`