calculus - Equvalent Asymptote of Radical Functions Proof

There a formula in our textbook which we can find a radical function's slant asymptote as it goes to + or - infinity.

I couldn't find It's proof anywhere on the internet As I couldnt find the formula itself.

when $$\lim_{x\to \infty} (ax^n+bx^{n-1}+...)^{1/n} $$
is equvalent to :

$$(a)^{1/n} |{x+\frac{b}{na}}| $$

Answer

The point of this is that, if $P(x)=c_1x^d + c_2 x^{d-1} ... $ is some polynomial function of degree $d$ such that $\lim_{x \to \infty}\left({P(x) \over x^{d-1}}\right)^n= \lim_{x \to \infty}ax^n+bx^{n-1} \dots$, then clearly we have ${c_1}^n=a$ and $n{c_1}^{n-1}c_2=b.$ Your equivalence follows.