This was a question on one of my previous exams. Sadly the solutions that were offered in class were torn off and lost at some point over the semester.
Could someone guide me through the solutions to this? I'm strictly doing this for review.
I understand the example from wikipedia here, but the formal definition is a little bit scratchy.
Write down the definition of $5n + 1 = O(n).$
$5n + 1 = n \text{ as } n \to \infty $
$|5n + 1| \leq Mn \qquad \forall n>n_0 $
How do I go about finding $M$?
Prove that $5n + 1 = O(n)$ is in fact true:
$ \begin{align*}| 5n + 1| &\leq |5n +1n| \\ |5n + 1| &\leq |6n| \end{align*}$