Question

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

Answer 1

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.

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`