lim(cosx)^(1/(1-cosx)).x趋向于0

网友回答

原式=lim(x->0){[1+(cosx-1)]^[(1/(cosx-1))(-1)]}
=1/lim(x->0){[1+(cosx-1)]^(1/(cosx-1))}
=1/lim(t->0)[(1+t)^(1/t)] (令t=cosx-1)
=1/e (应用重要极限).