若limx→∞[(x-α)/(x+α)]x=2，则α=_____．

若lim_x→∞[(x-α)/(x+α)]^x=2，则α=_____．
【正确答案】：-(1/2)ln2 分析：2=lim_x→∞[(x+α-2α)/(x+α)]^x=lim_x→∞[1+-2α/(x+α)]^x+α-α =lim_x→∞{[1+-2α/(x+α)]^-(x+α)/2α}^-2α•[1+-2α/(x+α)]^-α=e^-2α， 所以-2α=ln2，即α=-(1/2)1n2．