求极限limx→α+[(lnx-lnα)/(x-α)]．

求极限lim_x→α⁺[(lnx-lnα)/(x-α)]．
【正确答案】：lim_x→α⁺[(lnx-lnα)/(x-α)]=lim_x→α⁺ln(x/α)^1/(x-α)=lim_x→α⁺ln{[1+(x-α)/x]^α/x-α}^1/α=ln e^1/α=1/α．