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求极限,这题这么做为什么不对,还有求极限的时候要注意哪些问题

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飞舞V云端 幼苗

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1的无穷大次方是未定式.
(1+t/n+t^2/2n^2)^n
=(1+t/n+t^2/2n^2)^[1/(t/n+t^2/2n^2)][t/n+t^2/2n^2]n
=(1+t/n+t^2/2n^2)^[1/(t/n+t^2/2n^2)][t+t^2/2n]
(1+t/n+t^2/2n^2)^[1/(t/n+t^2/2n^2)]趋于e,
t+t^2/2n趋于t
极限=e^(-t)

1年前

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