Show that if xn+1 is the x-intercept of the tangent to f at (xn, f(xn)), then Xn+1 Xn- f(xn) f'(xn) ✓ provided that f'(xn) 0. (1) 2. Let k be the final digit in your student number and let y = 3k + 2. The purpose of this question is to use Newton's method to obtain an approximation to √√7, so let f(x) = x² - y. (a) Rewrite the equation f(x) = 0 to express x in terms of y. (b) Let the initial guess x0 = k + 1. Use this value of xo and equation (1) to calculate x1 and x2. (c) Compare your value of x2 to the value you get for √ by using a calculator. Without changing the initial guess, how could you use Newton's Method to obtain a better approximation? [3 marks]
Show that if xn+1 is the x-intercept of the tangent to f at (xn, f(xn)), then Xn+1 Xn- f(xn) f'(xn) ✓ provided that f'(xn) 0. (1) 2. Let k be the final digit in your student number and let y = 3k + 2. The purpose of this question is to use Newton's method to obtain an approximation to √√7, so let f(x) = x² - y. (a) Rewrite the equation f(x) = 0 to express x in terms of y. (b) Let the initial guess x0 = k + 1. Use this value of xo and equation (1) to calculate x1 and x2. (c) Compare your value of x2 to the value you get for √ by using a calculator. Without changing the initial guess, how could you use Newton's Method to obtain a better approximation? [3 marks]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
My last digit of student number is 4
The equation (1) is in the first image.
Transcribed Image Text:Show that if xn+1 is the x-intercept of the tangent to f at (xn, f(xn)), then
Xn+1 Xn-
f(xn)
f'(xn)
✓
provided that f'(xn) 0.
(1)
![2. Let k be the final digit in your student number and let y = 3k + 2. The purpose of this question is to
use Newton's method to obtain an approximation to √√7, so let f(x) = x² - y.
(a) Rewrite the equation f(x) = 0 to express x in terms of y.
(b) Let the initial guess x0 = k + 1. Use this value of xo and equation (1) to calculate x1 and x2.
(c) Compare your value of x2 to the value you get for √ by using a calculator. Without changing
the initial guess, how could you use Newton's Method to obtain a better approximation?
[3 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78d1386b-6fe1-438f-8c94-3f41a9b64a70%2Fed12961c-27fc-4833-9f90-37d97bef598b%2Fqayxur6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let k be the final digit in your student number and let y = 3k + 2. The purpose of this question is to
use Newton's method to obtain an approximation to √√7, so let f(x) = x² - y.
(a) Rewrite the equation f(x) = 0 to express x in terms of y.
(b) Let the initial guess x0 = k + 1. Use this value of xo and equation (1) to calculate x1 and x2.
(c) Compare your value of x2 to the value you get for √ by using a calculator. Without changing
the initial guess, how could you use Newton's Method to obtain a better approximation?
[3 marks]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning