lim->无穷大(1-2/x)^(x/2-1)

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lim->无穷大(1-2/x)^(x/2-1)

lim->无穷大(1-2/x)^(x/2-1)
lim->无穷大(1-2/x)^(x/2-1)

lim->无穷大(1-2/x)^(x/2-1)
=[(1-2/x)^(-x/2)]^[(x/2-1)/(-x/2)]
=e^[-(x/2-1)*(2/x)]
=e^[-(x-2)/2*(2/x]
=e^[-(x-2)/x]
=e^(-1)
=1/e

lim(x->无穷) (1-2/x)^(x/2-1)
=lim(x->无穷) 1/[1+1/(x/2-1)]^(x/2-1)
=1/e

想问什么?

其中limx->∞(1-2/x)^(-x/2)=e
limx->∞(1-2/x)^(x/2-1)
=limx->∞(1-2/x)^(x/2)·limx->∞(1-2/x)^(-1)
=limx->∞[(1-2/x)^(-x/2)]^(-1)·1
=e^(-1)
=1/e