limx->无穷大 (1+x)^(1/x)

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limx->无穷大(1+x)^(1/x)limx->无穷大(1+x)^(1/x)limx->无穷大(1+x)^(1/x)L=lim(x->∞)(1+x)^(1/x)lnL=lim(x->∞)ln(1+

limx->无穷大 (1+x)^(1/x)
limx->无穷大 (1+x)^(1/x)

limx->无穷大 (1+x)^(1/x)
L = lim(x->∞)(1+x)^(1/x)
lnL =lim(x->∞) ln(1+x) / x (∞/∞)
=lim(x->∞) 1/(1+x)
=0
L = e^0 =1