Question

How do you find the limit of `(x)(sin(1/x))` as x approaches infinity?

Answer 1

`lim_(x->+oo) xsin(1/x) = 1`

Explanation:

Substitute `t=1/x`.

Evidently we have:

`lim_(x->+oo) t(x) = 0`

Thus:

`lim_(x->+oo) xsin(1/x) = lim_(t->0) (sin t)/t =1`

graph{xsin(1/x) [-10, 10, -5, 5]}