How to find the limit of two divided functions How can I find a $c$ such that $f_{2}(n) \leq c \cdot f_{3}(n)$?
where $f_{2}(n) = 2n + 20$ and $f_{3}(n) = n + 1$.
This was from the textbook, Algorithms (explaining something else), but I was wondering how they got the following: $$\frac{f_{2}(n)}{f_{3}(n)} = \frac{2n+20}{n+1} \leq 20$$

your RHS is $2+\frac{18}{n+1}$ so $\frac{18}{n+1}\leq 18 \ \forall n\geq 0$
I hope it's now clear where the result comes from!
