What is the limit as x approaches infinity of #cos(1/x)#?

1 Answer
Zack M.
Dec 15, 2014

Usually, a quick look at a graph of the function is helpful. Unfortunately, the graph of #cos(1/x)# is very crowed around #x=0#, so we can't get a lot of information here.

Geogebra

However, as #x# gets larger and larger, #1/x# gets smaller and smaller. The limit as #x-> oo# is zero. So;

#lim_(x->oo) cos(1/x) => cos(0) = 1#

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