Horizontal Asymptotes: (x + 1)^2 / x^2 - 1

[JBen]

My question is regarding horizontal asymptotes. How do you determine what the horizontal asymptotes on a problem such as: (x+1)^2/x^2-1 ? I can figure out that the vertical asymptotes are restrictions of x (x=1 in this problem). I do not understand how horizontal asymptotes are calculated.

Thanks!

 

[galactus]

Let's say you have:

\(\displaystyle \L\\f(x)=\frac{a_{n}x^{n}+a_{n-1}x^{n-1}+.....+a_{1}x+a_{0}}{b_{k}x^{k}+b_{k-1}x^{k-1}+.....+b_{1}x+b_{0}}\)

If n<k, then the x-axis is the horizontal asymptote.

If n=k, then the line \(\displaystyle y=\frac{a_{n}}{b_{k}}\)(the ratio of leading coefficients) is the horizontal asymptote.

If n>k, then the graph has no asymptote.. Instead, either \(\displaystyle f(x)\rightarrow{\infty} \;\ or \;\ f(x)\rightarrow{-\infty} \;\ as \;\ x\rightarrow{\infty} \;\ or \;\ as \;\ x\rightarrow{-\infty}\)

 

[JBen]

Thank you!