vertical and horizontal asymptotes

**discobob** · October 20th 2009, 07:22 AM

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

**tonio** · October 20th 2009, 07:29 AM

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

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