Question

求极限lim(x→0){x^[(1/2)*lncosx]}

基础较弱，求较详细解题步骤说明

Answer 1

应该是 x→0+ 才可能有极限。

Answer 2

lim(x→0){x^[(1/2)*lncosx]}
= lim(x→0)e^[(1/2)lncosxlnx] (利用了f(x) = e^lnf(x))
= lim(x→0)e^[(1/2)(cosx-1)(x-1)] (Taylor expansion: lnx ~ (x-1))
= e^0
= 1