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 $\displaystyle y=ax+b$ is a slant asymptote in the $\displaystyle +\infty$ zone to the function $\displaystyle y=f(x)$, when:
$\displaystyle a=\lim_{x\rightarrow \infty}\frac{f(x)}{x}$
$\displaystyle b=\lim_{x\rightarrow \infty}(f(x)-ax)$
Do as above for $\displaystyle x\rightarrow -\infty$ for asymptotes in the $\displaystyle -\infty$ 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