1. Rank the following 10 functions by order of growth; that is, find an arrangement of the functions satisfying f₁=2(f₂) = 2(f3) = ... = n(f10). n1999, Vn, (n+1)/2, n!, nlogn, 22", (3-n)(3-n), 1/n, 3", 25

Wilson's Theorem states that for any natural number n > 1, n is prime if and only if Python (n – 1)! = -1 (mod n) Write a function wilson (n) that accepts a natural number n, and returns the remainder of (n – 1)! + 1 after division by n.

Please answer question.

1. Consider the following functions of n. (1) (2) (3) (4) (5) (6) (7) (8) (9) fi(n) = n, if n = 2.k for k = 0, 1, 2,... = n², otherwise. f2(n) = n, if n = 3.k for k= 0, 1, 2,... = n², otherwise. f3(n) = log n. Answer the following questions and prove your answ Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. fi(n) = 2(f₂(n)), f2(n) = Q(fi(n)), fi(n) = 0 (f₂(n)), f₂(n) = 0 (fi(n)), fi(n) = O(n), f₂(n) = O(n²), f3(n) = O(√n), f3(n) = O(fi(n)), 22n = 0(2¹), swer for each one.

4. Show that 6n + 3n log(n)= O(n logn). Find the appropriate values of C and no

Please solve it and explain it in words please

we are assuming  f(n) and g(n) are asymptotically positive functions. Prove/ disproveeach of the following.

Let f (f(n) and g(n)) be asymptotically nonnegative functions. Using the basic definition of Θ notation, prove that max(f(n), g(n)) = Θ(f(n) + g(n)),

b. Prove or disprove that n( 1 ) = O(log(n)³3).….....