Question

Question #330d8

Answer 1

I would say: `-oo`:

Explanation:

Have a look:

Graphically:
graph{(ln(x))/x [-10, 10, -5, 5]}

Answer 2

Because the function evaluated at 0 results in the indeterminate form `(-oo)/0`, one should use L'Hôpital's rule .

Explanation:

`lim_(xto0)ln(x)/x`

Apply L'Hôpital's rule:

`lim_(xto0)((d(ln(x)))/dx)/((d(x))/dx) =`

`lim_(xto0)(1/x)/(1) =`

`lim_(xto0)1/x`

This limit is known to be unbounded

Answer 3

`lim_(xrarr0^+) lnx/x = -oo`

Explanation:

`lim_(xrarr0^+) lnx = -oo` and

`lim_(xrarr0^+) 1/x = oo`.

So the product has a limit of `-oo`