Question

What is the oblique asymptote of the function f(x) = the quantity of x squared plus x minus 2, all over x plus 1

Answer 1

Hello,

y=ax+b is the asymptote
with
$a= \lim_{n \to \infty} \frac{f(x)}{x}=\lim_{n \to \infty} \dfrac{x^2+x-2}{x^2+x}=1$
$b= \lim_{n \to \infty} f(x)-ax= \lim_{n \to \infty} \frac{x^2+x-2}{x+1}-x= \lim_{n \to \infty} \frac{-2}{x+1}=0$