1. Arrange the following functions so that each function is the big-Oh of the next function. In other word, order them by their speed of growth in non-decreasing order. Group together those functions that are of the same order. 6n x lgn 2!gn en 2100 lg lgn
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- Let f,g:Z+⟶R, and f(n)=nlog2(n) forn∈Z+. For which function g(n)below is f∉O(g)Consider the function f : N × N → N given byf(m, n) = 2m-1(2n − 1), (m, n) ∈ N × NShow that f is bijectiveI need secant and regula falsi functions that finds the root of a function in a given interval. figurex=1:0.000001:3;plot(x,myfun2(x))hold on %a=1;%b=3;a=x(1);b=x(length(x));c=(a+b)/2;epsilon=10^-5while (abs(myfun2(c))>epsilon)if(myfun2(c)*myfun2(a))<0b=c;elsea=c;end plot(c,myfun2(c),'ro');fprintf("c=%d, f(c)=%d, (%d,%d )\n",c,myfun2(c),a,b);c=(a+b)/2;pause(4)end plot(c,myfun2(c),'g+');
- GROWTH OF FUNCTIONS. Arrange the following mathematical terms from lowest to highest order. n3 n2 n! 2n 7n – 2 log n n log n 10n n5 + log n n2 + n log n Example: a < b < c < d < … < x < y < zSimplify the complement of the following function: F(A,B,C,D)=(0,2,4,5,8,9,10,11) Your answer: F=((A'B'D)' (BC)'(AB)')' F=((A'BD)'(BC)'(AB)')' F=((A'B'D)'(B'C)'(AB)') F=((A'B'D')' (BC)'(AB)')Using foldl, define a function num2int :: [Int] -> Int -> Int that converts a list of numbers and the number n into an integer of base n. >num2int [3,4,5,6] 10 3456 >num2int [1,1,0,1,0,0,0,1,0,1,0,1,1,0] 2 3456 num2int :: [Int] -> Int -> Int num2int x y = foldl (\acc (a,b) -> ___a___ + b*y^a) 0 (___b___ (\x y ->(x,y)) [0..] (___c___ x)) fill in blank spaces of a , b , and c
- The sequence of values: n, c(n), c(c(n)), c(c(c(n))), c(c(c(c(n)))),... is known as the hailstone sequence starting at n. Implement c(n) as a function. Use predicates to test the parity of each input n.% Define the function f(x) f = @(x) -1*(x < 0) + 1*(x >= 0 & x <= 2); % Set the maximum value of N Nmax = 512; % Initialize the x-axis values for plotting x = linspace(-1,3,1000); % Compute the Fejér sums for various values of N F = zeros(length(x), Nmax); for N = 1:Nmax % Compute the Nth Fejér sum Sn = @(x) 0; for n = 1:N bn = (-1)^(n+1) / (n*pi); Sn = @(x) Sn(x) + bn*sin(n*pi*x); end FN = @(x) (1/N) * Sn(x); % Evaluate the Fejér sum at each point on the x-axis I tried to submit this to MATLAB, but can't seem to get it right.These two functions make way more sense now but I'm still confused about how I can write a function "newtinterp" out of these two. (Input arguments (x,y,z) where (xi, yi), i = 1,..., n+1, (interpolation data points) and z=(z1, ..., zm)(vectors containing m points on which we want to evaluate the interpolating polynomial)).
- I need help with this question of Data Structures and Algorithmns 1 True of False a) For two functions f(n) and g(n) if f(n) =O(g(n)) then g(n) = Ω(f(n)) (True or False) b) For two positive functions g and h if f(n) =O(g(n)) then g(n) = O(h(n)) , then f(n)= O(h(n)) (True or False) c) If g1(n) = O(f(n)) and g2(n) = O(f(n)), then g1 + g2 = O(f(n)) (True or False)Please help me with these question. SHow all you work. Thank you 1. Prove that∀k ∈ N, 1k + 2k + · · · + nk ∈ Θ(nk+1). 2. Suppose that the functions f1, f2, g1, g2 : N → R≥0 are such that f1 ∈ Θ(g1) and f2 ∈ Θ(g2).Prove that (f1 + f2) ∈ Θ(max{g1, g2}).Here (f1 + f2)(n) = f1(n) + f2(n) and max{g1, g2}(n) = max{g1(n), g2(n)}Suppose n integers between 1 and 366 are presented as input, and youwant to know if there are any duplicates. How would you solve this problem?What is the rate of growth of the function T(n), describing the time it takes foryou to determine if there are duplicates? (Hint: Pick an appropriate n0.)