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] 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)
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...
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Question
The equation in the first image is the equation (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%2F909fc9c1-4a77-4cee-9536-10ad45046ec4%2Fe2403j_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]
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)
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