How do you find $lim cos(1/t)$ as $t->oo$ ?

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Answer 1 · 2017-12-07T09:26:16

It is one.

Logically speaking, as $t rarr oo$ , it follows that $1/t rarr 0$ .

Since $cos0 = 1$ , it follows that $lim_(t rarr 0) cos(1/t) = 1$ .

Answer 2 · 2017-12-07T12:56:49

$lim_(t rarr oo) cos(1/t) = 1$

We have:

$lim_(t rarr oo) cos(1/t) = cos(lim_(t rarr oo) 1/t)$
$" " = cos 0$
$" " = 1$

We can see that the graph of $y=cos(1/x)$ rapidly approaches $y=1$ even for relatively small $x$ :
graph{cos(1/x) [-6, 6, -2, 2]}

How do you find lim cos(1/t)lim cos(1/t) as t->oot->oo?