求极限lim(1-1/x)^kx,x趋于0,

题目

求极限lim(1-1/x)^kx,x趋于0,

答案

lim (1-1/x)^kx
=e^k*lim xln(1-1/x),代换x=1/y,x->0时y->∞
=e^k*lim ln(1-y)/y
=e^k*lim -1/(1-y),洛必达法则
=e^-k*0
=e^0
=1