I tried reading up on Limits abit but I really don't understand a thing or rather I don't have time to go through everything as its not the focus of my course, so I hope someone can answer some basic Limits questions that I need to know for my course.

Firstly, if I have f(n) and f(g), I am gonna need to solve

**"Limit of n approching inifinity f(n)/g(n)"**to determine whether its Big-O/Big Omega or Big Theta. How do I solve it? Can I just plug in ANY number? I can't calculate inifinity.

Secondly, after we solve

**"Limit of n approching inifinity f(n)/g(n)"**, how do we determine whether its Big-O/Big Omega or Big Theta? What I meant is according to definition :

< inifinity means Big-Oh

> 0 means Big Omega

0 < c < inifinity means Big Theta

Which doesn't any sense to me? All positive number range between these 3 conditions afterall...

Lastly, it says to use the L Hospital Rule if both f(n) and g(n) are really big and close to inifinity... how do I tell whether they are?

I mean I have an example where :

Limit of n approching inifinity 4n + 3/n = 4 < infinity (No L Hospital Rule used)

And

Limit of n approching inifinity 4n / e^n = 0 (L Hospital Rule used)

How is 4n bigger then 4n + 3? I don't understand at all.