Question: Need help with 1-3: 2. Asymptotic Notation (50 points) Show the following using the definitions of O,, and . (1) (2 points) 2n3+n2+4(n3) (2) (2

Need help with 1-3:

Need help with 1-3: 2. Asymptotic Notation (50 points) Show the following

2. Asymptotic Notation (50 points) Show the following using the definitions of O,, and . (1) (2 points) 2n3+n2+4(n3) (2) (2 points) 3n49n2+4n(n4) (Hint: careful with the negative number) (3) (4 points) Suppose f(n)O(g1(n)) and f(n)O(g2(n)). Which of the following are true? Justify your answers using the definition of O. Give a counter example if it is false. (a) f(n)O(5g1(n)+100) (b) f(n)O(g1(n)+g2(n)) (c) f(n)O(g2(n)g1(n))

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