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]}