求lim(sin1/x+cos1/x)^x,其中X趋向于无穷

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/18 01:57:15

令t=1/x,t趋于0
lim(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

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