lim∞>[√(4x^2+x-1)+x+1]/[√(x^2+sinx)]
=lim+∞>[√(4+1/x-1/x^2)+1+1/x]/√（1+sinx/x^2)
=3,
或=lim-∞>[√(4+1/x-1/x^2)-1+1/x]/√（1+sinx/x^2)
=1,
由极限唯一性知,所求极限不存在.