作业帮lim(x→0)(1-2x)^1/x 极限?
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lim(x→0)(1-2x)^1/x 极限?
lim(x→0)(1-2x)^1/x 极限?
lim(x→0)(1-2x)^1/x 极限?
lim(x→0)(1-2x)^1/x
=lim(x→0)(1-2x)^(1/2x*2)
=[lim(x→0)(1-2x)^(1/2x)]2 lim(x→0)(1-1/x)^x=1/e
=(1/e)^2
=1/e^2
设t=1/x
lim(x→0)(1-2x)^1/x = lim(t→∞)(1-2/t)^t
=(1+(-2/t))^((-t/2)*-2) = e^(-2)
谢谢采纳
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