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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- T(n) = T(n-2) + 2lgn Show that T(n) = O(n lg n) using substitution method.O(nlgn) means that there is function f(n) that is O(nlgn) which is an upper bound for the running time at large n Select one: True FalseLet P(n) be the statement “the number 2^2n -1 is divisible by 3”. Use mathematicalinduction to show that P(n) is true for all n >0
- Given A={1,2,3,4,56}, B= {2,4,5,6} and C= (1,6,7} 1. B' U C'=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 notfunction iterFunc(x) {return x^3 + x - 1 }oldEst = 0 tol = 0.00005 error = 1 while (error > tol) newEst = iterFunc(oldEst) print(newEst)error = abs(newEst - oldEst) oldEst = newEst } Edit this psuedocode to make it work in python, the output should be 0.6823 as this is a method of root finding!
- Which of the following is the recursive definition for the function f(n)=2n with initial condition f(1) = 2? f(n) = 2n + f(n-1) f(n) = 2n - f(n-1) f(n) = 2n * f(n-1) f(n) = 2f(n − 1) Which of the following is the recursive definition for the function f(n)=5n+2 with initial condition f(1)=7? f(n) = 5n - f(n-1) f(n) = 5f(n-1) + 2 f(n) = 5n + f(n-1) f(n) = f(n-1) + 5A 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 gptThe following function f uses recursion:def f(n):if n <= 1return nelsereturn f(n-1) + f(n-2)5Let n be a valid input, i.e., a natural number. Which of the following functions returns the same result but without recursion? a) def f(n):a <- 0b <- 1if n = 0return aelsif n = 1return belsefor i in 1..nc <- a + ba <- bb <- creturn b b) def f(n):a <- 0i <- nwhile i > 0a <- a + i + (i-1)return a c) def f(n):arr[0] <- 0arr[1] <- 1if n <= 1return arr[n]elsefor i in 2..narr[i] <- arr[i-1] + arr[i-2]return arr[n] d) def f(n):arr[0..n] <- [0, ..., n]if n <= 1return arr[n]elsea <- 0for i in 0..na <- a + arr[i]return a