定义域x-1≠0,x≠1垂直渐近线为x=1 ∵lim(x-->∞)[y-(x+2)]=lim(x-->∞)[x³-(x-1)²(x+2)]/(x-1)=lim(x-->∞)(3x-2)/(x²-2x+1)=lim(x-->∞)(3/x-2/x²)/(1-2/x+1/x²)=(0-0)/(1-0+0)=0又y-(x+2)≠0恒成立 ∴曲线斜渐近线为y=x+2
见图
