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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: Xk+1 = with xo=a. Stop the recursion whenever 1 2 (² (xk + ax=¹), |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-" for some positive integer n. The output should have accuracy of at least €.

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: Xk+1 = with xo=a. Stop the recursion whenever 1 2 (² (xk + ax=¹), |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-" for some positive integer n. The output should have accuracy of at least €.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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

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 €.
Transcribed Image Text: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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