solving the resulting problem, and then returning to the original function. 1. F(1) = 2, F(2) = 1, (n − 1)F(n) = (n − 2)F(n − 1) + 2(n − 3)F(n − 2) for all n ≥ 3

Solve the following recurrences using iteration methods and Master's Theorem (if possible) a. T(n) = 2T (n/3) +3 b. T(n) = 3T (n/6) + n

for i=1 to n/2: for j-i to n-i : for k=1 to j do print("hello") Let T(n) denote the number of times "hello" is printed as a function of n. 1- Find a function f(n) -> T(n)=0(f(n)) 2- Explain T(n) as three nested summations, and simplify them by step by step

write using python

Given the functions T( n) = n? + 3n and F( n ) = 2n², which of the following is the most accurate description of these two functions: O a. T(n) = O(F( n )) O b. T(n) = O(F( n )) O. T(n) = Q(F( n )) O d. None of them is correct

Exercise 4B (1) Write a function which takes a list of the coefficients of a polynomial P(x) = ª₁ + ª₁x + a² + ….. +anxn of arbitrary degree n, and a value of x, and returns P(x). You can use the function given in lectures, ensuring you understand how it works. (2) Use the function to evaluate (a) P₁(x) = 4x4 + 3x² + 2 at x = 2. (b) P₂(x) = 2 — ¹x¹ at x = √√/2. Are these answers exact? Explain why or why not. (Use a print statements to show the evaluation of your function, and answer the question in a comment.) (3) The power series for the sine function sin(x) is given by ∞ x2n+1 (2n + 1)! sin(x) = Σ(−1)”. n=0 = x 6 + x5 120 for all x. Use the first four terms in this series in the Horner evaluation function at a suitable value of a to give an approximation of sin(π/4). (4) (a) Use your Horner's method function to evaluate the polynomial (x − 1)³ at the point x = 1.000001. (b) Is this answer correct? (c) Briefly explain why, or why not. (5) In week 3 we wrote a function to convert from…

What is the time complexity of the following functions? a) f(n) = 5log(n) + 10 b) h(n) = 3n³+ 2n