Chapter 2.5, Problem 56E

a.

To determine

To analyze: The value of $\underset{x\to \infty }{\lim }f\left(x\right)$ and $\underset{x\to -\infty }{\lim }f\left(x\right)$, identify the horizontal asymptote of $f\left(x\right)$ where $f\left(x\right)=16x^2\left(4x^2-\sqrt{16x^4+1}\right)$.

b.

To determine

To find: The vertical asymptotes $x=a$ of $f\left(x\right)=16x^2\left(4x^2-\sqrt{16x^4+1}\right)$ and analyze $\underset{x\to a^{+}}{\lim }f\left(x\right)$, $\underset{x\to a^{-}}{\lim }f\left(x\right)$.