求北大版高数第二版下册的课本习题答案！ 80
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(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
=[(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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