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
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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
(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](/uploads/image/z/3411924-60-4.jpg?t=E%E7%9A%84%E6%9E%81%E9%99%90%E6%B1%82%E6%B3%95%E7%9A%84%E8%BF%87%E7%A8%8B%EF%BC%881%2B1%2FX%EF%BC%89%5Ex%E5%BD%93X%E8%B6%8B%E8%BF%9B%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7%E6%97%B6%E7%9A%84%E6%9E%81%E9%99%90)
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.
=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.