For this question, you will need the following definition: For a discrete time model of intraspecific competition $N_{t+1} = F(N_t)$, if the limit $F_{\infty} = \lim_{N \to \infty} F(N)$ exists, one says that competition in this model undercompensates if $F_{\infty}$, overcompensates if $F_{\infty} = -$ and compensates exactly if $F_{\infty}$ is finite. The model is:
$$N_{t+1} = F(N_t) = \frac{R N_t}{(1 + a N_t)^b} \hspace{2cm} (1) $$
where $R, a ,b$ are constants. Investigate, at what values of parameters the Hassel Model $(1)$ will show undercompensation, overcompensation and exact compensation.
So I thought I would need to take limits and, for it to undercompensate, I would need
$$\lim _{N \to \infty} = \infty \implies RN_t > (1 + aN_t)^b$$
and so on. But in the answers, it says:
"In Hassell Model, $\lim _{N \to \infty} F(N) = Ra^{-b} \lim_{N \to \infty}N^{1-b}$, hence it undercompensates for $b < 1$, compensates exactly for $b = 1$ and overcompensates for $b > 1$."
Where does that limit that they use come from?