Chapter 2.5, Problem 43E

Algebraic functions Determine $\underset{x\to \infty }{\lim }f(x)$ and $\underset{x\to -\infty }{\lim }f(x)$ for the following functions. Then give the horizontal asymptote(s) of f (if any).

43. $f(x)=\frac{\sqrt[3]{x^6+8}}{4x^2+\sqrt{3x^4+1}}$