limx²(1-cos1/x)是等于1/2还是1/4啊

问题描述:

limx²(1-cos1/x)是等于1/2还是1/4啊

x→∞?
得1/2

当x→∞时,
limx²(1-cos1/x)
=lim(1-cos1/x)/(1/x²)
=lim(y→0)(1-c0sy)/y^2 (y=1/x)
=limsiny/2y (罗比达法则)
=1/2