Question

What is `lim_(xrarroo) sin(1/x)/x`?

Answer 1

I found `0`

Explanation:

I would apply the property that says that the limit of a quotient is equal to the quotient of the limits:
`lim_(x->oo)((sin(1/x))/x)=(lim_(x->oo)(sin(1/x)))/(lim_(x->oo)(x))=`
as `x->oo` then `1/x->0` and `sin(1/x)->0` so you get:
`=(lim_(x->oo)(sin(1/x)))/(lim_(x->oo)(x))=0/oo=0`