求极限lim(1-1/x)^kx,x趋于0, - 知识问答

求极限lim(1-1/x)^kx,x趋于0,

1个回答

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

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