How to do lim x-> 0- xe^(1/x) using l'Hopital's rule

I can't get it into the form of inf/inf or 0/0.

Thanks

This limit is actually *not* indeterminate to start with, so L'Hopital's rule does not apply.

Note that as x --> 0-, 1/x --> -infinity, and so e^(1/x) --> e^(-infinity) = 0.
So lim x --> 0- xe^(1/x) = 0*0 = 0.

Lord bless you today!