Chapter 2.5, Problem 47E

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).

41. $f(x)=\frac{4x^3+1}{2x^3+\sqrt{16x^6+1}}$