1. Find the asymptotic upper (big O), lower (Omega) and tight (Theta) bound for the following functions: A. n + 10 B. 6 +n + log(n) C. 4 log (log (n)) + 5 D. [(n² + 1) (n² + 2)]/(n² + 4)

Q: Determine the correct running times for each recursive functions 1. If T(n) = T([n/2]) + 1, then…

A: 1. Using the Master Theorem, we can determine the time complexity of T(n) based on the recurrence…

Q: Let f(n) and g(n) be asymptotically nonnegative functions. Using the basic defi- nition of…

A: Your answer is given below.

Q: For the following questions, simplify and express your answer as (nk) or (nk (log n)) wherever…

A: Both a and b answers are given with Justification

Q: a. (n²+1) 10 b. √10n²+7+3 c. 2n Ig(n + 2)² + (n + 2)² lg d. 2+¹+34-1 e. [log₂ n]

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…

Q: 5. Consider the following functions, f(n) and g(n): f(n) 1₁ -logn n 2k logn g(n) 1 n n k

A: The different conditions for finding asymptotic bounds are as follows: If limn→∞f(n)g(n)=0, then…

Q: Solve the following recurrence equations by expanding the formulas (also called the 'iteration…

A: a) solution:-

Q: Find the closed-form equation of T(n)=*** using substitution a) T(n)= T(n-1)+4 b)…

A: T(n) = T(n-1) + 4 = T(n-1) + (1×4)=T(n-2) + 4 + 4 = T(n-2) + (2×4)=T(n-3) + (3×4)=T(n-4) +…

Q: 1.) Please prove the following using definitions. a.) 2n4 − 5n2 ∈ Θ(n4) b.) n log n − n ∈ Ω(n log…

A: Proved the given functions of the asymptotic notations

Q: Determine the growth rate of the function belo T(n) = 1+2+3+...+n T(n) = 0(n²) T(n) = O(n) T(n)= O(n…

A: The complexity of an algorithm is expressed in theta notation. It limits a function from both the…

Q: Prove by induction that T(n) = 2T(n/2) + cn is O(n logn).

A: Induction is a mathematical proof technique where a statement is proven true for a base case, often…

Q: Solve the following recursive function and describe it in terms of Big-O using expansion. T(n) =…

A:

Q: 1. Give the definition of an asymptotic upper bound of a function f(n)? What is he asymptotic upper…

A: An asymptotic upper bound of f(n)

Q: Arrange these functions under the O notation using only = (equivalent or C (strict subset of): (a)…

A: here arranging the functions as subset and equivalence in O format in step 2.

Q: If two functions f(n) and g(n) grow at the same rate asymptotically, what else can we say about…

A:

Q: The function f(n)= n4.3+ n° log n + 10 is a. O(log n) O b.O(n5) O. o(n5 log n) O d. 0(n2.5) e. O(n…

A: Here in this question we have given a function and we have asked to find complexity in term of big…