Write a programme that calculates the root of a given number a > 0, and approximates it with a given accuracy € > 0. In order to achieve this you can use the following recursion: 1 2k+1=(k+aiền), with xoa. Stop the recursion whenever |x² − a ≤ € or k > 100. The input is a single string composed of an integer a and a float e separated by a space. The float is always of the form 10-n for some positive integer n. The output should have accuracy of at least €.
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I have the following question in the attached image, Now I have made an attempt at a code but it won't work and Im lost, its in python 3:
import math
a>0
epsilon>0
while a and epsilon:
x=a
x=0.5(x+ax**(-1))
if abs(x**2-a)<=epsilon or k>=100:
break
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- Given a string str and number n, write a program that recursively appends a copy of string str n times and returns the resulting string. For example: RecuriveCopy("a", 10) // -> "aaaaaaaaaaa" RecursiveCopy("blah", 5) // -> "blahblahblahblahblahblah" For this exercise, complete the following function. n is the number of copies to add to str: function RecursiveCopy(str, n) { // your code here } Part 2: Call RecursiveCopy Write another function that calls RecursiveCopy() and returns the following string output: "The resulting string [x] has [y] characters". [x] should be replaced by the result from RecursiveCopy) and [y] should be replaced by the number of characters in the resulting string. You may pick the arguments to RecursiveCopy in CountChars or have the user provide input. I will leave this up to you. function CountChars() { } // your code here // call RecursiveCopy(..) // returns a formatted string For example: console.log(CountChars()) // -> "The resulting string blahblahblahblah…Help me please: A palindrome is a string that reads the same both forward and backward. For example, the string madam is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Prompt the user for a string. If the string is a palindrome output a message in the following format: madam is a palindrome else Hello is not a palindrome Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameters.Consider a network of streets laid out in a rectangular grid, In a northeast path from one point in the grid to another, one may walk only to the north (up) and to the east (right). Write a program that must use a recursive function to count the number of northeast paths from one point to another in a rectangular grid. Your program should prompt the user to input the numbers of points to the north and to east respectively, and then output the total number of paths. Notes: 1. Here is a file (timer.h download and timer.cpp download) which should be included in your program to measure time in Window or Unix (includes Mac OS and Linux) systems (use start() for the beginning of the algorithm, stop() for the ending, and show() for printing). 2. The computing times of this algorithm is very high, and the number of paths may be overflow, don't try input numbers even over 16. 3. Name your recursive function prototype as calcPath(int north, int east) to ease grading. 4. Paste your output
- Fibonacci numbers are a sequence of integers, starting with 1, where the value of each number is the sum of the two previous numbers, e.g. 1, 1, 2, 3, 5, 8, etc. Write a function called fibonacci that takes a parameter, n, which contains an integer value, and have it return the nth Fibonacci number. (There are two ways to do this: one with recursion, and one without.)In C++ Write a recursive function called PrintNumPattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until 0 or a negative value is reached, and then continually add the second integer until the first integer is again reached. For this lab, do not end output with a newline. Ex. If the input is: 123 the output is: 12 9 6 3 0 3 6 9 12 #include <iostream> using namespace std; // TODO: Write recursive PrintNumPattern() function int main(int argc, char* argv[]) { int num1; int num2; cin >> num1; cin >> num2; PrintNumPattern(num1, num2); return 0;}Write a recursive function that finds the number of occurrences of a specified letter in a string using the following function header. def count(s, a):For example, count("Welcome", 'e') returns 2. Write a test program thatprompts the user to enter a string and a character, and displays the number of occurrences for the character in the string.
- PHP A factorial of any given integer, n , is the product of all positive integers between 1 and n inclusive. So the factorial of 4 is 1 × 2 × 3 × 4 = 24, and the factorial of 5 is 1 × 2 × 3 × 4 × 5 = 120. This can be expressed recursively as follows: ❑ If n == 0, return 1. (This is the base case) ❑ If n > 0, multiply numbers from n down to 1. Write a PHP function to display the factorials of the integers up to the given value(argument). Any format could be used for displaying. Write the recursive version of the same function to display the factorials of the integers up to the given value(argument). Any format could be used for displaying.A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare letters, make sure that you do it in a case-insensitive way.Use your function in a program that prompts a user for a phrase andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"main.py Load default template.. 1 # TODO: Write recursive print_num_pattern () function 2 == " main ": 3 if name_ num1 = int (input ()) num2 = int(input ()) print_num_pattern (num1, num2) 4 5
- Write a program to enter a natural number n and find all sphenic numbers from 1 to n using Recursion (combined with iteration if necessary). Note: A sphenic number is a product of p*q*r where p, q, and r are three distinct prime numbers.Example: 30 = 2 * 3* 5; 42 = 2*3*7; 66 = 2*3*11.30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, … are sphenic numbers.The word ladder game was invented by Lewis Carroll in 1877. The idea is to begin with a start word and then change one letter at a time until you arrive at an end word. Each word along the way must be an English word. For example, starting from FISH, you can arrive at MAST through the following word ladder:FISH, WISH, WASH, MASH, MAST Write a program that uses recursion to find the word ladder given a start word and an end word, or that determines no word ladder exists. Use the file words.txt that is available online with the source code for the book as your dictionary of valid words. This file contains 87,314 words. Your program does not need to find the shortest word ladder between words; any word ladder will do if one exists. list aalii aardvark aardvarks aardwolf aba abaca abaci abacist aback abacus abacuses abaft abalone abalones abamp abampere abandon abandoned abandonee abandoner abandonersWrite a recursive function called print_num_pattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until 0 or a negative value is reached, and then continually add the second integer until the first integer is again reached. For coding simplicity, output a space after every integer, including the last. Do not end output with a newline. Ex. If the input is: 12 3 the output is: 12 9 6 3 0 3 6 9 12 # TODO: Write recursive print_num_pattern() function if __name__ == "__main__": num1 = int(input()) num2 = int(input()) print_num_pattern(num1, num2)if (num1<=0): print(num1,end= '')