Chapter 2.5, Problem 72E

Horizontal and vertical asymptotes

1. a. Analyze $\underset{x\to \infty }{\lim }f(x)$ and $\underset{x\to -\infty }{\lim }f(x)$, and then identify any horizontal asymptotes.
2. b. Find the vertical asymptotes. For each vertical asymptote x = a, analyze $\underset{x\to a^{-}}{\lim }f(x)$ and $\underset{x\to a^{+}}{\lim }f(x)$.

54. $f(x)=\frac{\sqrt{16x^4+64x^2}+x^2}{2x^2-4}$