xsin(√x)是x的几阶无穷小量,x趋向于0

题目

xsin(√x)是x的几阶无穷小量,x趋向于0

答案

因为lim(x->0)xsin(√x)/x√x
=lim(x->0)(x√x)/[x√x]
=1
所以
xsin(√x)是x的2分之3阶无穷小量.