当x趋于正无穷时(1-1/x)^x的极限是1/e怎么算的
问题描述：
当x趋于正无穷时(1-1/x)^x的极限是1/e怎么算的
答
当x趋于正无穷时,
1/[1+1/(x-1)]^(x-1)*[1+1/(x-1)]
=1/[1+1/(x-1)]^(x-1)
=1/e
答
(1-1/x)^x=[(x-1)/x]^x=[x/(x-1)]^(-x)=[1+1/(x-1)]^(-x)=1/[1+1/(x-1)]^(x)=1/[1+1/(x-1)]^(x-1)*[1+1/(x-1)]当x趋于正无穷时,1/[1+1/(x-1)]^(x-1)*[1+1/(x-1)]=1/[1+1/(x-1)]^(x-1)=1/e