Q3 (Q5, Section 2.3 in the Textbook): Order the following functions according to their order of growth (from the lowest to the highest): (n – 2)!, 5lg(n + 100)10. 2²n. 0.001n4, 3n³ + 1, ln² n, n, 3n.

CODING QUESTION.  Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n):    """Euler's totient function or Phi function.    Time Complexity: O(sqrt(n))."""    result = n.

3. Two 7-digit integers (leading zeros allowed) are considered to be equivalent if one can be obtained from the other by rearranging its digits. For example, 0012234, 0312042, 3220014 and 2100243 are all considered equivalent, whereas 0012234 and 0001234 are not equivalent. How many nonequivalent 7-digit integers are there in which the digits 0, 2, 4 and 6 can each appear at most once?

Order the following functions by asymptotic growth rate (number 1 is the best algorithm, and number 3 is the worst). 4nlog n+2n 2log n n³ + 2

Give asymptotic upper and lower bounds for each of the following recurrences. Justify your answer.

Which function grows faster f(n) = log 2n or g(n) = n0.3log3n

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

Find the maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations.

IN VISUAL BASIC, solve Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

2. If n is a positive integer, then n4 - n is divisible by 4. [Proof of Exhaustion]