求极限lim(x->0)(x+e^x)^2/x

∵lim(x->0)[ln(x+e^x)/x]=lim(x->0)[(1+e^x)/(x+e^x)] (0/0型极限,应用罗比达法则)=(1+1)/(0+1)=2∴lim(x->0)[(x+e^x)^(2/x)]=lim(x->0){e^[(2/x)ln(x+e^x)]}=e^{2*lim(x->0)[ln(x+e^x)/x]}=e^(2*2)=e^4。