Question

What are the asymptotes and removable discontinuities, if any, of `f(x)=(2x^3-x+1)/(x^2+1)`?

Answer 1

Asymptote `y=2x`

Explanation:

`x^2+1ne 0` so no vertical asymptotes.
The only Asymptote is `y=2x`
We get

`(2x^3-x+1)/(x^2+1)-2x=(1-2x)/(x^2+1)`
and we have
`lim_(xto pm infty)(1-3x)/(x^2+1)=0`