Homework Help is Here – Start Your Trial Now!
Math
Calculus
In the video, we introduced Newton's Method by considering the function )-x +1 and trying to approximate the right-most root of the function, as shown in the graph below. From the graph, we determined a rough estimate for this root to be x1, but we know we can make this approximation better, by bringing in some of the other ideas for approximation that we discussed previously. We know that if we "zoom in" enough near a point, any "nice" function will look roughly linear, so it can be approximated by its tangent line, or the linearization at that point at x = 1 , and use this Since our initial approximation for the root was 1, we create the linearization to approximate the zero that we are looking for. Then we continue to repeat this process with each new value to refine our approximation. Let's run through this one more time: a) Calculate the linearization ofx) - -3x+1 atx-1 b) Use the linearization found in part (a) to estimate the value where x)-0 To find each successive approximation, we just set the linearization at the previous approximation, X equal to zero, and solve forx c) Solve the general linearization equation below for x to show where Newton's formula comes from

In the video, we introduced Newton's Method by considering the function )-x +1 and trying to approximate the right-most root of the function, as shown in the graph below. From the graph, we determined a rough estimate for this root to be x1, but we know we can make this approximation better, by bringing in some of the other ideas for approximation that we discussed previously. We know that if we "zoom in" enough near a point, any "nice" function will look roughly linear, so it can be approximated by its tangent line, or the linearization at that point at x = 1 , and use this Since our initial approximation for the root was 1, we create the linearization to approximate the zero that we are looking for. Then we continue to repeat this process with each new value to refine our approximation. Let's run through this one more time: a) Calculate the linearization ofx) - -3x+1 atx-1 b) Use the linearization found in part (a) to estimate the value where x)-0 To find each successive approximation, we just set the linearization at the previous approximation, X equal to zero, and solve forx c) Solve the general linearization equation below for x to show where Newton's formula comes from

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
In the video, we introduced Newton's Method by considering the function )-x +1 and trying to approximate the right-most root of the function, as shown in the graph below. From the graph, we determined a rough estimate for this root to be x1, but we know we can make this approximation better, by bringing in some of the other ideas for approximation that we discussed previously. We know that if we "zoom in" enough near a point, any "nice" function will look roughly linear, so it can be approximated by its tangent line, or the linearization at that point at x = 1 , and use this Since our initial approximation for the root was 1, we create the linearization to approximate the zero that we are looking for. Then we continue to repeat this process with each new value to refine our approximation. Let's run through this one more time: a) Calculate the linearization ofx) - -3x+1 atx-1 b) Use the linearization found in part (a) to estimate the value where x)-0 To find each successive approximation, we just set the linearization at the previous approximation, X equal to zero, and solve forx c) Solve the general linearization equation below for x to show where Newton's formula comes from
Transcribed Image Text:In the video, we introduced Newton's Method by considering the function )-x +1 and trying to approximate the right-most root of the function, as shown in the graph below. From the graph, we determined a rough estimate for this root to be x1, but we know we can make this approximation better, by bringing in some of the other ideas for approximation that we discussed previously. We know that if we "zoom in" enough near a point, any "nice" function will look roughly linear, so it can be approximated by its tangent line, or the linearization at that point at x = 1 , and use this Since our initial approximation for the root was 1, we create the linearization to approximate the zero that we are looking for. Then we continue to repeat this process with each new value to refine our approximation. Let's run through this one more time: a) Calculate the linearization ofx) - -3x+1 atx-1 b) Use the linearization found in part (a) to estimate the value where x)-0 To find each successive approximation, we just set the linearization at the previous approximation, X equal to zero, and solve forx c) Solve the general linearization equation below for x to show where Newton's formula comes from
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS