Răspuns:
Explicație pas cu pas:
Aplicam regula Hospital
lim (x×e^1/x)=lim(x×e^1/x)'=lim[e^1/x+xe^1/x×(-1/x²)]=lim (e^1/x-e^1/x/x)
=lim e^1/x(1-1/x) cand x⇒∞ e^1/x⇒1 1-1/x⇒1
lim e^1/x(1-1/x)=1×1=1
