limu趋近于无穷(1+1/u∧3)∧u - 知识问答

limu趋近于无穷(1+1/u∧3)∧u

2个回答

L = lim(u->∞ ) ( 1+ 1/u^3 )^u
lnL =lim(u->∞ ) ln( 1+ 1/u^3 )/ (1/u)
=lim(y->0) ln( 1+ y^3 )/ y (0/0)
=lim(y->0) 3y^2/(1+y^3)
=0
=>L = 1

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