How do you find $lim theta costheta$ as $theta->oo$ ?

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Answer 1 · 2017-03-07T18:53:57

DNE

$lim_(theta to oo) theta cos theta$

We know that: $-1 le cos theta le 1$

So:

$-theta le theta cos theta le theta$

And:

$lim_(theta to oo) -theta le lim_(theta to oo) theta cos theta le lim_(theta to oo) theta$

$implies -oo le lim_(theta to oo) theta cos theta le oo$

Maybe it's stating the obvious but because cosine is periodic, there is no limit.

How do you find lim theta costhetalim theta costheta as theta->ootheta->oo?