# Math Help - Slant asymptote

1. ## Slant asymptote

How can I find the slant asymptote of f(x)= x^3 / x^2 +1

Thanks for any help!

2. Originally Posted by DBA
How can I find the slant asymptote of f(x)= x^3 / x^2 +1

Thanks for any help!
Using polynomial long division, $\frac{x^3}{x^2 + 1} = x - \frac{x}{x^2 + 1}$ ....

3. Originally Posted by DBA
How can I find the slant asymptote of f(x)= x^3 / x^2 +1

Thanks for any help!

Provided the respective limits exists, the line $y=ax+b$ is a slant asymptote in the $+\infty$ zone to the function $y=f(x)$, when:

$a=\lim_{x\rightarrow \infty}\frac{f(x)}{x}$

$b=\lim_{x\rightarrow \infty}(f(x)-ax)$

Do as above for $x\rightarrow -\infty$ for asymptotes in the $-\infty$ zone.

You can also find slant asymptotes of rational functions (like yours) by long polynomial division, but the above method works for a larger kind of functions.

Tonio