Question

What is `lim x → ∞ cos(1/x)/(1+1/x)` ?

`lim x → ∞ cos(1/x)/(1+1/x)`

Answer 1

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`