Question

求下列极限 lim[(2x-1)e^(1/x)-2x](x趋近于无穷)

Answer 1

=lim[2x*e^(1/x)-2x-e^(1/弊镇x)]
=lim{2x[e^(1/x)-1]-e^(1/x)}
=lim{2x*(1/x)-e^(1/销卜简x)}
=lim{2-e^(1/亏裤x)}
=2-lim[e^(1/x)]
=1