## Miyuki 2 years ago Big-O notation, how to find constants a and b? Any guide or video online? I am not sure if I should post this in math or computer science. I am having trouble with big-o, omega, theta etc. But I want to work on them 1 by 1. I am having trouble finding guides or videos on how to find constants a and b. I kind of have an idea with a, but have a huge trouble for b :( A lot of videos I have watched focused on the concept, but none that I saw explained how to find a and b. By finding I mean I need to know the number for a and b. It is for calculating algorithm running time. Does anyone have a good guide on how to learn big-o? Thanks! Example problem: Using the big-o definition (must specify two positive constants), prove that 4n^2 - 2n + 5 = O(n^2) The a I found is 7. Which came from: 4n^2 - 2n + 5 <= 4n^2 -2n^2 + 5n^2 = 7n^2 But I don't know how to find constant b.

1. satellite73

$$g=O(f)$$ means $\lim_{x\to \infty}\frac{f}{g}=c$ where $$c\neq 0$$ if $$c=1$$ you say $g=o(f)$

2. satellite73

"finding the constants $$a$$ and $$b$$" must be part of a specific problem

3. Miyuki

@satellite73, thanks for your quick response. I will find an example shortly and post it.

4. satellite73

i still don't know what $$a$$ and $$b$$ mean in your definition, but there is a good example here http://en.wikipedia.org/wiki/Big_O_notation

5. satellite73

maybe your $$a$$ corresponds to the $$x_0$$ and this example and your $$b$$ is their 13