这个极限咋求
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x->0+
(1+x)^(1/x)
=e^[ln(1+x)/x ]
=e^[ 【x-(1/2)x^2 +o(x^2)】/x]
=e^[ 1-(1/2)x +o(x) ]
(1+x)^(1/x) /e
=e^[ -(1/2)x +o(x) ]
=1 -(1/2)x +o(x)
lim(x->0+) [(1+x)^(1/x) /e ]^(1/x)
=lim(x->0+) [ 1- (1/2)x ]^(1/x)
=e^(-1/2)
(1+x)^(1/x)
=e^[ln(1+x)/x ]
=e^[ 【x-(1/2)x^2 +o(x^2)】/x]
=e^[ 1-(1/2)x +o(x) ]
(1+x)^(1/x) /e
=e^[ -(1/2)x +o(x) ]
=1 -(1/2)x +o(x)
lim(x->0+) [(1+x)^(1/x) /e ]^(1/x)
=lim(x->0+) [ 1- (1/2)x ]^(1/x)
=e^(-1/2)
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