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数学
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极限公式
求其极限 lim(1-1/x)的根号x次方,x趋于正无穷.
苦想半天实在无从下手,恳请那位大虾帮忙解答下.
人气:308 ℃ 时间:2020-03-31 08:35:09
解答
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)(罗比达法则)
=x/(x-1)*[-(-1/x^2)]/[-1/2*x*√x]
=-1/[(x-1)x^2√x]
=0
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