都是1^∞型未定型极限,采用重要极限lim (x→0) (1+x)^(1/x)=e求解
(1) lim (x→0) (1+2x)^(1/x)
= lim (x→0) (1+2x)^[(1/2x)*2]
= lim (x→0) [(1+2x)^(1/2x)]²
=e²
(2) lim (x→+∞) [1+(1/x)]^(x/2)
=lim (x→+∞) [1+(1/x)]^[x*(1/2)]
=e^(1/2)
=√e