微积分,斜渐进线y=(x^3)/(x-1)求斜渐进线,答案是y=x^2+x+1,还有这种题的求法是什么

Question

微积分,斜渐进线
y=(x^3)/(x-1)
求斜渐进线,答案是y=x^2+x+1,
还有这种题的求法是什么

Answer 1

y=(x^3)/(x-1)
=(x^3-1+1)/(x-1)
=(x^3-1)/(x-1)+1/(x-1)
=(x-1)(x^2+x+1)/(x-1)+1/(x-1)
=x^2+x+1 + 1/(x-1)
因为1/(x-1)不可能为0
所以斜渐进线是y=x^2+x+1