Write a program that implements n-point Lagrange interpolation. Treat n as an input parameter.
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Kindly do this in wofram mathematica please
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- In this question, we are going to write a Racket functionwordMaxIndex that calculates the maximum index of each word thatappears in an input word list. For example, if the input is’(time is long but life is short)Then one output can be((time 0) (long 2) (but 3) (life 4) (is 5) (short 6))The index of the first word in a word list is 0; the index for the secondword is 1; etc. Therefore, in the previous example, the maximum indexfor word “time” is 0; the maximum index for word “is” is 5, since “is”appears twice, at index 1 and 5. Note that you are not asked to sortthe words in the output. Therefore, the output is correct as long asthe indexes are correct.Do the following steps to implement the word-index program. In ourdiscussion, we call a word with an index a word-index pair, for example,(short 6) and (is 5) are word-index pairs. We call a list of word-index pairs a word-index list.(a) Write a function initialWIList that takes a list ofwords and creates a word-index list. The resulting…a) Implement a function start( ) that takes as input a positive number a, rounds its logarithm base 4 to the nearest integer n, and returns the value of 1.0 x 2^n.c++ Implement a function that recursively calculates the nth number in the Fibonacci sequence of numbers. The Fibonacci sequence starts at 0 and 1. Each number thereafter is the sum of the two preceding numbers. This gives us the following first ten numbers: 0,1,1,3,5,8,13,21,34, .... Input Expected output0 01 17 139 34
- Using a pseudo random number generation function (e.g., rand() in C or other equivalentfunctions in other languages) that generates uniformly distributed random numbers,write functions that generate the following:(a) uniformly distributed integers between 0 and 99. (b) uniformly distributed floating numbers between 0.25 and 0.5. (c) the number 1 with probability 0.5, the number 2 with probability 0.2, otherwise a floatuniformly distributed between 3 and 4.PLEASE DO IT IN WOLFRAM MATHEMATICA ONLY. Write a program that implements n-point Lagrange interpolation. Treat n as aninput parameter.Implement *IN LEGV8 CODE* in DS-5 that accepts a number n, and produces the nth Fibonacci number using the efficient O(n) version. The number should be in the .data segment of your program. Your code must print the nth Fibonacci numberusing printf
- Implement the quadratic_formula() function. The function takes 3 arguments, a, b, and c, and computes the two results of the quadratic formula: x1=−b+b2−4ac2a x2=−b−b2−4ac2a The quadratic_formula() function returns the tuple (x1, x2). Ex: When a = 1, b = -5, and c = 6, quadratic_formula() returns (3, 2). Code provided in main.py reads a single input line containing values for a, b, and c, separated by spaces. Each input is converted to a float and passed to the quadratic_formula() function. Ex: If the input is: 2 -3 -77 the output is: Solutions to 2x^2 + -3x + -77 = 0 x1 = 7 x2 = -5.50 code: # TODO: Import math module def quadratic_formula(a, b, c):# TODO: Compute the quadratic formula results in variables x1 and x2return (x1, x2) def print_number(number, prefix_str):if float(int(number)) == number:print("{}{:.0f}".format(prefix_str, number))else:print("{}{:.2f}".format(prefix_str, number)) if __name__ == "__main__":input_line = input()split_line = input_line.split(" ")a =…Write a c++ code and test the “digit” function:Function Prototype: int digit(int n,int k)This function returns the kth digit of the positive integer n. For example, if n is the integer29,415, then the call digit(n,0) would return the digit 2, and the call digit(n,2) would returnthe digit 4. Examples:Input: n = 29415 , k = 1 output: 9Input: n = 2 , k = 0 output: 2 Input: n = 2 , k = 1 output: index out of bound (return -1) Note: The digits are numbered from left to right beginning with the “zeroth” digit. Take input and display output in main function. do not use string libruary. so do it using while , do while or for loop.Write a c++ code and test the “digit” function:Function Prototype: int digit(int n,int k)This function returns the kth digit of the positive integer n. For example, if n is the integer29,415, then the call digit(n,0) would return the digit 2, and the call digit(n,2) would returnthe digit 4. Examples:Input: n = 29415 , k = 1 output: 9Input: n = 2 , k = 0 output: 2 Input: n = 2 , k = 1 output: index out of bound (return -1) Note: The digits are numbered from left to right beginning with the “zeroth” digit. Take input and display output in main function.
- for C++ write a progam for the greatest common divisor of integers x and y is the largest integer that evenly divides both x and y. Write a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows. If y is 0 the answer is x; otherwise gcd(x, y) is gcd(y, x%y).// Description: Write a program that outputs a root of a given function f(x) by using a bi-section method. // f(x) = x3 + 5x2 +7x +2Write a function triple_riffle_repeat(mylist,n) which takes as input a list (again with length a multiple of 3) and outputs the result of doing a 3-way riffle shufffle n times Write a function period(m) which takes as input a number m (which we will always take as a multiple of 3) and outputs the smallest positive integer n so that triple_riffle_repeat(list(range(m)),n) == list(range(m)) Discuss, with evidence, the outputs of your function period for different values of m, writing your answer as a comment.