# May someone help me to find the vertical and horizonal asymptotes of this function?

I have found this question in the Leithold´s book, but there´s no any worked example of how i can compute it in order to find the horizontal and vertical asympototes.

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Thanks nameless. – Vinicius L. Beserra Dec 29 '12 at 14:15

Another hint: you can find vertical asymptotes of a function like $p(x)/q(x)$ by looking for the values of $x$ which make $q(x) = 0$ (so long as they don't also make $p(x)=0$, of course).

As Nameless notes, the best hint for getting better answers would be to accept more answers.

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thanks for your commentaries. – Vinicius L. Beserra Dec 29 '12 at 14:15
In this case i can do x^2-4=0. So, the roots are the +2 and -2. These are the Vertical assymptotes? – Vinicius L. Beserra Dec 29 '12 at 14:16
Yes, they are the vertical ones. – Old John Dec 29 '12 at 14:20
Thanks Old John. – Vinicius L. Beserra Dec 31 '12 at 11:56

You can always find the horizontal ones by taking the limit of the function when $x\to\infty$: $$\lim_{x\to\pm\infty}f(x)=\lim_{x\to\pm\infty}\frac{2}{\sqrt{x^2-4}}=0$$ so $y=0$ is the only horizontal asymptote for $f(x)$. The vertical ones can be found by @Old John's comment.

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Always good to know! +1 – amWhy Feb 28 '13 at 19:31