1 for each of the following functions find a function g n such that f n t g n you mu 5346607

1. For each of the following functions, find a function g(n) such that f(n) ∈ Θ(g(n)). You must use the simplest g(n) possible in your answers such as n, log(n), nlog(n), n^2, n^3, an, and product of them. Prove your assertion. (20pts) Hints: You can either use the definition of big- Θ or use the limit.

a. (n^3 + 1)^2

b. sqrt(9n) + 9 log(n)

c. 2n * log(n^2) + (n +1)^2 * log(n)

d. 3^(n+2) + 4^(n−2)

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3. Find the order of growth of the following sums. You need to indicate the class Θ(g(n)) the function belongs to. You must use the simplest g(n) possible in your answers. (20pts)

a. ∑ (i^2 + 1)^2 //sum is n with i = 0

b. ∑ n lg( i^2 ) //sum is n with i = 0

c. ∑ (i + 1)*2^i //sum is n with i = 0

d. ∑ ∑ (i + j) //first sum is n with i = 0 //second sum is i-1 j=0

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