3. Prove each of the following statements without using limits. Justify your answer. (a) n³ + 3n² = Q(n²) (b) 2(n-1) (2-2) (c) (log n²) = o(log n)² (d) 2(n+1) = O(4") (e) 22 € (2")

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A: - We have to get the complexity according to master's theorem.

Q: 1 g(n) = 4 · g(n/3) + log(n)

A: The solution for the above given question is given below:

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A: limn→∞f(n)g(n)=x Case 1: x is constant f(n)=θ(g(n)) Case 2: x is ∞ f(n)=ω(g(n)) Case 3: x is 0…

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A:

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A: Option a is correctCorrect Answer:a. True

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A:

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A: Below are the answers with reason:

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Q: Could you help me on this? Thank you

A: Part (a):   Part (b):   Part (c):   Part (d):   Part (e):

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A: The above question s solved in step 2 :-

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A: This question comes from Algorithms which is a paper of Computer Engineering. Let's discuss it in…