lim(x→+∞)(1-1/x)^√x
=lim(x→+∞)[1+(-1/x)]^[(-1/x)*(-x*√x)]
=lim(x→+∞)e^(-1/x*√x）
=e^lim(x→+∞)1/√x
=e^0
=1
或者用e^[ln(1-1/x)^√x]
=e^[√x*ln(1-1/x)]
√x*ln(1-1/x)
=ln(1-1/x)/(1/√x)(羅比達(dá)法則)
=x/(x-1)*[-(-1/x^2)]/[-1/2*x*√x]
=-1/[(x-1)x^2√x]
=0