求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
问题描述：
求lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)
答
令t=1/x,t趋于0lim[1+(sin1/x+cos1/x-1)]^x (x趋于无穷大)=lim(sint+cost)^(1/t)=lim[1+(sint+cost-1)]^{[1/(sint+cost-1)]*(sint+cost-1)/t}=e(因t趋于0时,lim(sint+cost-1)/t=lim(cost-sint)=1)