lim x-->∞ (x^1/3 - 5x + 3) / (2x + x^2/3 - 4)?

請參考以下答案：

lim x-->∞ (x^1/3 - 5x + 3) / (2x + x^2/3 - 4)
=lim x-->∞ [(x^1/3 - 5x + 3)/x] / [(2x + x^2/3 - 4)/x]
=lim x-->∞(x^-2/3 -5 +3x^-1)/(2+x^-1/3 -4x^-1)
=-5/2

Sol
A=lim(x->∞)_[x^(1/3)－5x+3]/(2x+x^(2/3)－4)
Set x=y^3
x^(1/3)=6
x^(2/3)=y^2
A=lim(y->∞)_(y－5y^3+3)/(2y^3+y^2－4)
lim(y->∞)_(1/y^2－5+3/y^3)/(2+1/y－4/y^3)
=(0－5+0)/(2+0－0)
=－5/2