题目内容：

设lim［(x-k)/x)］^（-2x）=limxsin2/x,(x→∞）.求k.

优质解答

lim［(x-k)/x)］^（-2x）=lim[1+k/(x-k)］^(2x)=lim[1+1/(x/k-1)］^(2x)=lim[1+1/(x/k-1)］^[2k(x/k-1)+2k]=lim[[1+1/(x/k-1)]^(x/k-1)]^2k*[1+1/(x/k-1)]^2k=e^2klimxsin2/x=lim2sin(2/x)/(2/x)=2即e^2k=2 => k=(ln...