lim(n趋向无穷)[（5x^2+1）/（3x-1）]sin1/x
=lim(n趋向无穷)[（5x^2+1）/（3x-1）*1/x
=lim(n趋向无穷)（5x^2+1）/（3x^2-x）
=lim(n趋向无穷)（5+1/x^2）/（3-1/x）
=(5+0)/(3-0)
=5/3