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I have this question in my homework. Its an a multiple choice question and goes as following: Let $f (x) = 3x^3 + 2x + 4$. One has that $O(x^3)$

** the answers have been checked with the teachers note **

C and K are the constants

  1. $(C,K) = (10,0)$
  2. $(C,K) = (6,1)$
  3. $(C,K) = (9, 1)$
  4. $(C,K) = (12,1)$
  5. $(C,K) = (3,2)$
  6. $(C,K) = (5,2)$

I know that $(10,0)$ is false since $K = 1$.

$(6,1)$ I also know is wrong because it's smaller than the statement.

But since $3x^3 + 2x^3 + 4x^3 = 9$, then $(9,1)$ is true.

$(12,1)$ is true because I assume its okay that is bigger just not smaller?

$(3,2)$ is false $(5,2)$ is true.

My question here is :Why is it that $(5,2)$ is true? And can anyone tell me whether my thinking is correct or not?

Thank you for any kind of help

Raphael
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New2Math
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    What are $C$ and $K$? I guess you mean the two constants from the definition of $O(\cdot)$, but you should be explicit in the question - not everyone uses the same notation. Further, what is $k$? – Luke Mathieson Aug 20 '15 at 10:55
  • I thought that was the universal use of the constants. :) But it's the two constants. K and k are the same. Just with and without capslock. I will correct this now. Thanks for the heads up. – New2Math Aug 20 '15 at 10:57
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    @New2Math Very little notation of the form "this letter means this thing" is universal. So, $C$ and $K$ are the two constants in the definition of $O(-)$, but which is which? However, I'm not sure this question is really a good fit for the site. If you understand the definition of $O(-)$, you should be able to answer the question yourself; the fact that you can't answer this specific question about $O(-)$ suggests that there's some underlying problem. If we knew what that problem was, we could try to help you but, at the moment, we're left trying to guess what your real problem is. – David Richerby Aug 20 '15 at 11:21
  • The constant C i find by adding all of the values on top together. I just do not understand how (5,2) can be true. Since 5 is smaller than 9. What is it that 2 does such that 5 is seen as to be true. – New2Math Aug 20 '15 at 12:00
  • That is my question ^^ – New2Math Aug 20 '15 at 12:00

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