第1个回答 2014-02-28
为了解题看起来方便，设 y = - 3/x，则 x = -3/y。当 x →∞时，y →0
那么，
lim(1 - 3/x)^x
= lim (1 + y)^(-3/y)
= lim [(1 + y)^(1/y)]^(-3)
=[lim (1 + y)^(1/y)]^(-3)
=e^(-3)
=1/e^3本回答被网友采纳
那么，
lim(1 - 3/x)^x
= lim (1 + y)^(-3/y)
= lim [(1 + y)^(1/y)]^(-3)
=[lim (1 + y)^(1/y)]^(-3)
=e^(-3)
=1/e^3本回答被网友采纳
第2个回答 2014-02-28
lim[x-->+∞](1-3/x)^x
=lim[x-->+∞]{[1+(-3/x)]^(-x/3)}^(-3)
=e^(-3)
=1/e^3
=lim[x-->+∞]{[1+(-3/x)]^(-x/3)}^(-3)
=e^(-3)
=1/e^3
第3个回答 2014-02-28
e的负3次方
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