How do you find the limit of #cos(1/x)# as x approaches #oo#?

Question

4907 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-26T13:44:58

#1#

We have

#lim_(xrarroo)cos(1/x)#

If we were to "plug in" #oo#, we would see that the argument of

#cos(1/oo)#

is approaching

#cos(0)=1#

The trick here is knowing that the limit as #xrarroo# where you have the form

#"constant"/xrarr"constant"/oo#

is going to result in #0#.

We can graph #cos(1/x)# as well -- it should have a horizontal asymptote at #y=1#.

graph{cos(1/x) [-9.71, 10.29, -3, 3]}