求函数极限 lim x(ln(x+1)-lnx){x->+∞}
问题描述：
求函数极限 lim x(ln(x+1)-lnx){x->+∞}
答
limx(ln(x+1)/x)=lim (ln(x+1)/x)^x=lne=1
答
=lim x(ln(x+1)/x) {x->+∞}
=lim x(ln(1+1/x)) {x->+∞}
=lim x*1/x (洛必达法则）
=1
答
lim x(ln(x+1)/x)
=lim ln[(x+1)/x]^x
=ln lim(1+1/x)^x
=ln e
=1