E的极限求法的过程（1+1/X）^x当X趋进于无穷大时的极限

E的极限求法的过程
（1+1/X）^x当X趋进于无穷大时的极限

lm(x-∞)[(1+1/x)^x]=e^{lm(x-∞)[xln(1+1/x)]}
=e^{lm(x-∞)[ln(1+1/x)/(1/x)]}
=e^{lm(x-∞)[1/(1+1/x)]} (0/0型,应用罗比达法则)
=e^[1/(1+0)]
=e.