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:
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):
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?
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 are not my 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!