考研求高级数极限举隅

原公式= lim(x-->；∞)a^(1/x+1){a^[1/x-1/(x+1)-1]}/(1/x^2)

= lim(x->；∞){a^[1/x(x+1)-1]}/(1/x^2)

= lim(x->；∞){[1/x(x+1)×lna}/(1/x^2)

= lim(x->；∞) {x/(x+1)×lna}

= lim(x->；∞){ 1/(1+1/x)×lna }

=lna