来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/21 04:18:00
当x趋于正无穷时(1-1/x)^x的极限是1/e怎么算的
(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
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