P(0,x) = 1 9986 The Legendre polynomial P(n,x) ca 0078 4643998 be defined by: P(1,x) = x P(n,x) = (2*n-1)/n *x* P(n-1,x) - (n-1)/n *P(n-2,x) where n is a non-negative integer. Please complete the Legendre polynomial function below: float p(int n, int x)
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- Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined re-cursively by f(0) = 3 and for n = 0, 1, 2, ... a) f(n + 1) = −2f(n).b) f(n + 1) = 3f(n) + 7.1) For IEEE 754 single precision floating point numbers, if X is a negative denormalized floating point number with mantisa 010 0000 0000 0000 0000 0000, what is the decimal value of X? Question options: a. –1.25 × 2^(–126 ) b. –1.25 × 2^(–127 ) c. –0.25 × 2^(–127) d. –0.25 × 2^(–126 ) e. None of the above 2) Which of following recursive C++ functions correctly computes a[0]+a[1]+...+a[n-1] (where n is the size of array a) ? Question options: int sum(int n, int a[] ){ return n>0? sum(n-1) + a[n] : a[0]; } int sum(int n, int a[] ){ return n>0? sum(n-1, a) + a[n-1] : a[0]; } int sum(int n, int a[] ){ return sum(n-1, a) + a[n-1] ; } int sum(int n, int a[] ){ return n>0? sum(n-1, a) + a[n] : a[0]; } int sum(int n, int a[] ){ return n>0? sum(n-1) + a[n-1] : a[0]; }Given the function T(n) = n3 + 20n + 5, show that T(n) is O(n3)
- Q1. Write a Java program to implement Horner's Rule for Polynomial Evaluation. Evaluate the following polynomial using the Program: P(x) = x2 + 100x3 - 50 x2 + 1000 for x = - 4Consider the following intermediate code:r1 = 5vl1 = r1jmp Simple.f@0jmp Simple.f@1Simple.f@0:write vl1r2 = 7r3 = vl1 + r2vl1 = r3jmp Simple.f@0Simple.f@1:r0 = vl1return(i) Describe briefly what the optimisation dead code elimination involves.(ii) Show the result of applying dead code elimination to the intermediate code above.Find t(4)(n) for the function t(n)=5n−1/5+7n8/5.
- Write Algorithm to Conversion from an Arabic number to a modern Roman number.in: decimal number n (0 ≤ n)out: sequence R = s0, s1,...,s12 representing the structure of the Roman number (Ri = number of primitives Vi in n for i ∈ [0, 12])constant: sequence P = 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 of primitive Roman numberslocal: remainder x to be converted (0 ≤ x ≤ n); coefficient c for a primitive Romannumbers (for other than P0, 0 ≤ c ≤ 3)Let N = {0, 1, 2, . . .} be the set of Natural Numbers. Given an n ∈ N, which of the followingconditions are necessary, and which of these conditions are sufficient, for the Natural Number,n, to be a factor of 10.(a) 1 is a factor of n.(b) 1 is a factor of 2n.(c) −n is a factor of 10.(d) 10 is a multiple of n.(e) n is divisible by 2.(f) n^2 is divisible of 5.(g) n = 10.procedure Horner(c, a_(0), a_(1), a_(2),… , a_(n): real numbers)y := a_(n)for i := 1 to ny := y ∗ c + a_(n−i)return y {y = a_(n)c^(n) + a_(n−1)c^(n−1) + ⋯ + a_(1)c + a_(0)}a) Evaluate 3x^(2) + x + 1 at x = 2 by working througheach step of the algorithm showing the values assigned at each assignment step.b) Exactly how many multiplications and additions areused by this algorithm to evaluate a polynomial ofdegree n at x = c? (Do not count additions used toincrement the loop variable.)
- A certain company has encoded the accounts of its customers and requires that you provide an algorithm that, given an account code, informs if it is valid according to the following description: The account codes are made up of 4 digits counted from right to left, plus the verification digit. The verifying digit is obtained by adding the digits of the account number of the even positions and multiplying the digits of the odd positions, from the new result the residue of the division is extracted for 10, which represents the verifying digit. No use CHATGPT Develop the code in python as a check digit class that returns 1 if it is correct or 0 if notA certain company has encoded the accounts of its customers and requires that you provide an algorithm that, given an account code, informs if it is valid according to the following description: The account codes are made up of 4 digits counted from right to left, plus the verification digit. The verifying digit is obtained by adding the digits of the account number of the even positions and multiplying the digits of the odd positions, from the new result the residue of the division is extracted for 10, which represents the verifying digit. Develop the code in python as a check digit class that returns 1 if it is correct or 0 if not Heading: Extract digits, verifier calculation, Account verification, Integral algorithm Code in python no use chat gptA certain company has encoded the accounts of its customers and requires that you provide an algorithm that, given an account code, informs if it is valid according to the following description: The account codes are made up of 4 digits counted from right to left, plus the verification digit. The verifying digit is obtained by adding the digits of the account number of the even positions and multiplying the digits of the odd positions, from the new result the residue of the division is extracted for 10, which represents the verifying digit. Develop the code in python as a check digit class that returns 1 if it is correct or 0 if not Heading: Extract digits, verifier calculation, Account verification, Integral algorithm Code in python no use chatgpt
