How to define asymptotes of a fuction below?

Question

Please, help. I know there is no horizontal and vertical asymptotes, but how to prove it using $k_1$ and $b_1$ formulas? $(x-1)^{2/3}(x+1)^3$

Answer 1

I assume that by $k_1$ and $b_1$ formulas you mean the formulas for computing the slope and the $y$-intercept of the asymptote. In this case what happens is that $$ \lim_{x\to\pm\infty}\frac{(x-1)^{2/3}(x+1)^3}{x}=\infty, $$ and $k_1$ is not defined.