What is lim x → ∞ cos(1/x)/(1+1/x) ?

lim x → ∞ cos(1/x)/(1+1/x)

1 Answer
Apr 22, 2018

The limit of the required function would be 1.

Explanation:

First look at the limit of cos(1/x) as x-> oo :
as x -> oo : 1/x -> 0
Thus cos(0)=1

Then look at the limit of the bottom line:
1+1/x -> 1+0 as x->oo

Putting the numerator and denominator together we get:
lim x-> oo 1/1=1