Question

How do you use the Squeeze Theorem to find `lim (1/x)cosx` as x approaches infinity?

Answer 1

`lim_(xrarroo)(1/x)cosx = 0`

Explanation:

`-1 <= cosx <=1` for all `x`.

For `x > 0`, we have `1/x > 0`, so we can multiply the inequality by `1.x` without reversing its direction.

`-1/x <= (1/x)cosx <= 1/x` for `x > 0`.

`lim_(xrarroo)(-1/x) = 0` and `lim_(xrarroo)(1/x) = 0`.

Therefore, by the squeeze theorem (at infinity),

`lim_(xrarroo)(1/x)cosx = 0`