求lim(sin1/x+cos1/x)^x,其中X趋向于无穷

令t=1/x,t趋于0lim(sint+cost)^(1/t)=lim[1+(sint+cost-1)]^{[1/(sint+cost-1)]*(sint+cost-1)/t}再因为t趋于0时,lim(sint+cost-1)/t=lim(cost-sint)=1所以lim(sint+cost)^(1/t)=lim[1+(sint+cost-1)]^{[1/(sint+cost-1)]*(sint+cost-1)/t}=e