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Problem 1 1. Back in the day before calculator has square root function. People use the "divide and average" method to calculate √√a where a is a postive number. The method goes • Start with a number æ, then the next guess for a can be obtained by xn+1 xn+a/xn 2 • Then you repeat and keep making the next guess. 1.1) Calculate √17 using this method. Pick a sensible value for x and do it for 5 iterations. 1 1.2) Show that this method is equivalent to Newton's method. Hint find equation where the answer is sqrt. 1 1.3) Find an equivalent formula for finding cube root (a) xn+1 = H(xn) Find H(xn) 1 1.4) Use the above method to find v/17 1 Python Python Python Python

Problem 1 1. Back in the day before calculator has square root function. People use the "divide and average" method to calculate √√a where a is a postive number. The method goes • Start with a number æ, then the next guess for a can be obtained by xn+1 xn+a/xn 2 • Then you repeat and keep making the next guess. 1.1) Calculate √17 using this method. Pick a sensible value for x and do it for 5 iterations. 1 1.2) Show that this method is equivalent to Newton's method. Hint find equation where the answer is sqrt. 1 1.3) Find an equivalent formula for finding cube root (a) xn+1 = H(xn) Find H(xn) 1 1.4) Use the above method to find v/17 1 Python Python Python Python

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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%matplotlib inline
import numpy as np
from matplotlib import pyplot as plt
import math
 
 
Problem 1 1. Back in the day before calculator has square root function. People use the "divide and average" method to calculate √√a where a is a postive number. The method goes • Start with a number æ, then the next guess for a can be obtained by xn+1 xn+a/xn 2 • Then you repeat and keep making the next guess. 1.1) Calculate √17 using this method. Pick a sensible value for x and do it for 5 iterations. 1 1.2) Show that this method is equivalent to Newton's method. Hint find equation where the answer is sqrt. 1 1.3) Find an equivalent formula for finding cube root (a) xn+1 = H(xn) Find H(xn) 1 1.4) Use the above method to find v/17 1 Python Python Python Python
Transcribed Image Text:Problem 1 1. Back in the day before calculator has square root function. People use the "divide and average" method to calculate √√a where a is a postive number. The method goes • Start with a number æ, then the next guess for a can be obtained by xn+1 xn+a/xn 2 • Then you repeat and keep making the next guess. 1.1) Calculate √17 using this method. Pick a sensible value for x and do it for 5 iterations. 1 1.2) Show that this method is equivalent to Newton's method. Hint find equation where the answer is sqrt. 1 1.3) Find an equivalent formula for finding cube root (a) xn+1 = H(xn) Find H(xn) 1 1.4) Use the above method to find v/17 1 Python Python Python Python
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