求极限lim<sub>x→0</sub>(1-sinx)<sup>x→0</sub>

求极限lim_x→0(1-sinx)^x→0

求极限lim_x→0(1-sinx)^{x→0
【正确答案】：lim_x→0(1-sinx)^cotx =lim_x→0(1-sinx)^cosx/sinx =lim_x→0[(1-sinx)^1/sinx]=e^-1．}

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