求极限 limx→o (e∧x +x)∧(1/x)

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求极限 limx→o (e∧x +x)∧(1/x)

求极限 limx→o (e∧x +x)∧(1/x)
求极限 limx→o (e∧x +x)∧(1/x)

求极限 limx→o (e∧x +x)∧(1/x)
lim(x→o) (e∧x +x)∧(1/x)=lim(x→o)e^[(1/x)ln(e∧x +x)]
=e^[lim(x→o)(1/x)ln(e∧x +x)]

lim(x→o)(1/x)ln(e∧x +x)=lim(x→o)(1/x)ln(1+e∧x +x-1)
=lim(x→o)(e∧x +x-1)/x (无穷小等价替换)
=lim(x→o)(e∧x +1)/1 (罗比达法则)
=2.
于是lim(x→o) (e∧x +x)∧(1/x)=e^2.