Hello,

I am currently taking a class which is covering a topic which I have not yet had experience with. I have done a lot of research on the topic, and believe to understand the definition well, however, I'm not sure how to go about truly applying the definition.

I will type up the question below with modified numbers so I can see how to really solve the problem rather than simply receiving the answer.

The questions are as follow:

So for the first one I get to a point similar to this:Code:`Indicate for each of the following pairs of expressions (A,B) whether A is O, Ω, Θ of B.`

(1)

and

(2)

and

But I'm not sure how to draw the proof from here. I understand that Big O is the upper-bound of a function and to prove it, some numbers and (k is the same as ) must make this statement true (where f(x) = original and g(x) = bound equation):Code:

so new question:

is

My biggest issue is finding my numbers c and k. Are these arbitrary values which make the statement true or is there a better way to find them?Code:

for every number

As for the second set of numbers, I'm just not exactly sure where to begin. Again, I have changed the numbers so there arenotmy homework problems, but do highly resemble them. So I appreciate concept explanations over answers - the answers are irrelevant if I don't understand the concept.

Thank you for your help!