Q)to establish the big O relationship ,find witnesses C and K for the function

f(n)=13n^3 +42n^2+2nlogn +4n

solution:

i try to solve it as

when nlogn>n and n^2>nlogn and n^3>n^2

13n^3 +42n^2+2nlogn +4n<=13n^3 +42n^2 +2nlogn +4nlogn<=13n^3+42n^3+2n^3+4n^3<=61n^3

so witnesses are C=61 k=nlogn

big O(n^3)

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i dont get the idea how to get different witnesses ,i try to understand through text but it a really a difficult topic to understand ,i do it as much as i understand .please explain me if i do it wrong or right