100n +5 € 0 (√) 100n +5 € O(n) _©_1+2+…+n-1+ne0(n) 4logn+n² FQ (n.)

Q: Q1) If y₁ =sin(x), y2 = cos(x), y₁ = tan(x), where -π<x< MATLAB script to plot y₁, y2 and y, as…

A: Algorithm:1. Define the range for x as .2. Define the functions , , and .3. Create separate plots…

Q: O(1) if n = 1 , T(n) = 8T (п/2) + Ө(n?) if n > 1.

A:

Q: What is the Theta notation for the ff. : foo(n): 1: if n == 1 then 2: return 1 3: else 4: return n·…

A: The algorithm is linear, running in O(n) time because it executes once every time it decrements the…

Q: True or False FOR ALL x, x is any integer: x^4 is greater or equal x.

A: For ALL x, x is any integer : x^4 is greater or equal x

Q: f(n) — 103л+2 А. f(n) — О(9(n)) В. f(n) — N(9(п)) С. f(n) %3D Ө(9(n)) g(n) = 10"+7

A: Let's calculate value of f(n) and g(n) for different values of n.  For n=5,  F(n) = 1017 g(n) = 1012…

Q: Factorial of a number is defined as: n! = n(n-1)(n-2)(n-3)...(2)(1) For example, 4! = 4*3*2*1 The n!…

A: 1. Start the program.2. Declare an integer variable n to store the user input.3. Request a positive…

Q: Lab Exercises: 1. Write a script that will generate a random number between 1 and 20 and the user…

A: Program Approach: Create file passwd.txt using open function with a as argument. Using write…

Q: Order the following in big O :  n², 1.01n, log n²,  n √n,  n log n,  n0.1,  1000

A: Big O complexity: It is used to analyze how complex to solve the program. Using the this complexity…

Q: 3-1 Asymptotic behavior of polynomials Let p(n) = d [a¡n², Sain', i=0 where ad > 0, be a degree-d…

A: Using the definition of the asymptotic notations proved the given property

Q: rder the following functions by asymptotic growth rate: 4n log n +2n 3n + 100 n log n n2 +…

A: The correct order for the asymptotic growth rate is :

Q: 0,1 Start 1 2.

A: DFA stands for Deterministic Finite Automata. NFA stands for Nondeterministic Finite Automata.

Q: Define terms swap and incsnd such that   swap ⟨N1, N2⟩ →∗ β ⟨N2, N1⟩…

A: "swap" is a function or operation that takes two inputs, represented by "N1" and "N2", and returns a…

Q: Which of the following statements is/are true, for arbitrarily large values of n? (Check all that…

A: Given :

Q: P(0,x) = 1 9986 The Legendre polynomial P(n,x) ca 0078 4643998 be defined by: P(1,x) = x P(n,x) =…

A: #include&lt;stdio.h&gt;float p(float x, int n){    if(n==0){        return 1;    }else if(n==1){…

Q: Q2: Design a full state controller with minimal state observer for the system below, then simulate…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: The Euler function ø is often useful for public key cryptography. It is true that: O if n is…

A: n is divisible by 3  examples of n are 3,6,9,12,15...  ∅(3) is 2 which is not divisible by 3 so,…

Q: Convolution is associative if O xn)*[y(n)+h(n)]=[x(n)+y[n]*h(n) O x(n)"[yln)"h(n)]=[x(n)*y(n)]*h(n)…

A: Associative Property : Consider the set of variables as A, B, and C. The operation is named op. The…

Q: List the functions below from the lowest order to the highest order of growth. Indicate any that are…

A: List the functions below from the lowest order to the highest order of growth. Indicate any that…

Q: Define P(n) to be the assertion that: Σ; = j=1 n(n+1) (2n+1) True 14 = 36 6 What does P(3) evaluate…

A: The above question s solved in step 2 :-

Q: c(n)=10*c(n-1),c(1)=3

A: Given Recursive sequence is,c(n)=10*c(n-1),c(1)=3

Q: If lim n-&gt;oo (f(n))/(g(n)) = 0 then f(n) = ω( g(n) ) true false

A: The question is asking whether the statement 'If the limit as n approaches infinity of the ratio of…

Q: Master theorem: if n<d T(n)={ |aT(n/b)+ f (n) if n2 d 1. if f(n) is O(n" 2. if f(n) is O(n™" log*…

A: Theorem:

Q: Order the following functions by asymptotic growth rate (number 1 is the best algorithm, and numbe…

A: When analyzing algorithms, one important aspect to consider is their growth rate or time complexity.…

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

A: Given Recurrence relation is, T(n)=nT(n)+n Asymptotic upper bound of the function is the worst case…

Q: Question 1 T(n) is 3 n³ + 20 n² + 5. Please identify it is O(n³)

A: Please refer below for your reference: T(n) = 3n^3 + 20n^2+5

Q: Legendre's formula finds the exponent of the largest power of some prime p that divides (is a factor…

A: I give the code in c++ along with output and code screenshot

Q: a = 0; for i in range(N): for j in reversed(range(i,N)): a = a + i + j; O(N^N) O(N*N) O(N/2) O(logN)

A: Big Oh complexity is the worst case time complexity which calculates the time taken to run an…

Q: n log2n - 2n <= log2 n! <= n log2n - n

A: Given :- In the above question, a sequence or relation is mention in the above given question   Need…

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.