当x趋于无穷大时
lim xln(1+1/x^2)
=lim [ln(1+1/x^2)]/(1/x)
运用洛必达法则
=lim (1/[1+(1/x²)])*(-2/x³)/(-1/x²)
=lim (2/x)/[1+(1/x²)]
=lim 2x/(x²+1)
再次运用洛必达法则
=lim 2/(2x)
=lim 1/x
=0