lim(x →∞) (x√x sin1/x)/(√x -1)
=lim(x →∞)[x√x sin1/x]/[√(x -1)]
=lim(x →∞) xsin1/x
=lim(x →∞) (sin1/x)/(1/x)
令1/x=t
则：=lim(t →o) sint/t
=1