Question

What is the equation of the slant asymptote of the rational function f(x) = 4x^2+6x-1 / x+2?

Answer 1

Hello,

y=4x-2

Explanation:

1: slope.

`\displaystyle \lim_(n \to \infty) (f(x))/(x)\\\\= \lim_(n \to \infty) (4x^2+6x-1))/(x(x+2))\\\\= \lim_(n \to \infty) (4x^2)/(x^2)\\\\=\boxed{4}\\`

2:

`\displaystyle \lim_(n \to \infty) (f(x)-4x)\\\\= \lim_(n \to \infty) ((4x^2+6x-1)/(x+2)-4x)\\\\= \lim_(n \to \infty) ((4x^2+6x-1-4x^2-8x)/(x+2))\\\\= \lim_(n \to \infty) ((-2x-2)/(x+2))\\\\= \lim_(n \to \infty) ((-2x)/(x))\\\\=\boxed{-2}\\`

Slant asymptote is y=4x-2

Answer 2

Check out the attached photo