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# Limits and Big-Oh Notation

ALGOR-XVYEW2

Let $f(n)$ and $g(n)$ be increasing functions of $n$.

Which of the following statements imply that $f(n) = O(g(n))$?

Select ALL that apply.

A

$\lim\limits_{n \to \infty} \cfrac{f(n)}{g(n)} = 0$

B

$\lim\limits_{n \to \infty} \cfrac{f(n)}{g(n)} = \infty$

C

$\lim\limits_{n \to \infty} \cfrac{g(n)}{f(n)} = \infty$

D

For some positive constants, $c$ and $n_0$, $0 \leq f(n) \leq cg(n)$ for all $n \geq n_0$.

E

For some positive constants, $c$ and $n_0$, $0 \leq cg(n) \leq f(n)$ for all $n \geq n_0$.