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.
May someone help me to find the vertical and horizonal asymptotes of this function?
2
$\begingroup$
calculus
2 Answers
2
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.
-
1Yes, they are the vertical ones. – 2012-12-29
1
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.
-
0Always good to know! +1 – 2013-02-28