# vertical and horizontal asymptotes

• October 20th 2009, 07:22 AM
discobob
vertical and horizontal asymptotes
How to find the Vertical and Horizontal Asymptotes of
f(x)= $\frac{x^2}{x^2-1}$
• October 20th 2009, 07:29 AM
tonio
Quote:

Originally Posted by discobob
How to find the Vertical and Horizontal Asymptotes of
f(x)= $\frac{x^2}{x^2-1}$

As $\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow-\infty}f(x)=1$, the line $y=1$ is a horizontal asymptote in both zones $\infty$ and $-\infty$.

As for vertical asymptotes put $x^2-1=(x-1)(x+1)$ and check what are the limits of $f(x)$ when $x\rightarrow 1$ and $x\rightarrow -1$

Tonio