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

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Answer 1 · 2015-11-14T12:47:32

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

$-1 <= cosx <=1$ 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),

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

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