Question

What is the oblique asymptote of the function f(x) x^2+x-2/x+1

Answer 1

`f(x)=\displaystyle(x^2+x-2)/(x+1)=(x(x+1)-2)/(x+1)=x-(2)/(x+1)`


`\displaystyle\lim_(x\to\infty)\left\{f(x)-x \right\}=\lim_(x\to\infty)(2)/(x+1)=\lim_(x\to\infty)(\displaystyle(2)/(x))/(1+\displaystyle(1)/(x)) =0`

Consequently, the limit of
`f(x)` as x approaches infinity is
`x`.

In other words,
`f(x)` approaches the line y=x,

so oblique asymptote is y=x.

I'm Japanese, if you find some mistakes in my English, please let me know.