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答案在纸上
热心网友
x->0
2^x ~ 1+ (ln2)x
3^x ~ 1+ (ln3)x
( 2^x + 3^x ) /2 ~ 1+ (1/2)(ln6) x
lim(x->0) [ ( 2^x + 3^x ) /2 ]^(1/x)
=lim(x->0) [1 + (1/2)(ln6) x ]^(1/x)
=e^[(1/2)(ln6)]
=√6