=lime^x(xln( 1+ 1/x)- 1)
=lim(xln( 1+ 1/x)- 1)/e^(-x)
= lim(ln( 1+ 1/x)+x(- 1/x？ )/( 1+ 1/x))/-e^(-x)
=lim( 1/(x+ 1)-ln( 1+ 1/x))/e^(-x)
=lim(- 1/(x+ 1)？ -(- 1/x？ )/( 1+ 1/x))/-e^(-x)
=lim-e^x/(x+ 1)
=-∞