Homework Help is Here – Start Your Trial Now!
Math
Algebra
11. Given that f(x) = x – 5 + x² In x, show that the equation: f(x): interval: 2 < x < 3. Taking x = 2 as a first approximation to the root of the equation, use one iteration of the Newton Raphson's procedure to find a second approximation of this root, giving the answer correct to two decimal places. 12. Use one iteration of the Newton-Raphson method to find, to 3 decimai places, a second approximation to the real root of the equation x+3x-1 = 0, taking 0.2 as the first approximation to the root of the 0 has a root in the equation(

11. Given that f(x) = x – 5 + x² In x, show that the equation: f(x): interval: 2 < x < 3. Taking x = 2 as a first approximation to the root of the equation, use one iteration of the Newton Raphson's procedure to find a second approximation of this root, giving the answer correct to two decimal places. 12. Use one iteration of the Newton-Raphson method to find, to 3 decimai places, a second approximation to the real root of the equation x+3x-1 = 0, taking 0.2 as the first approximation to the root of the 0 has a root in the equation(

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question

Solve Q11, 12 explaining detailly each step

2. Show that the equation xe = 1 has a root between 0.5 and 0.6. starting with 0.55 as a first estimate, use one iteration of the Newton-Raphson method to obtain a better approximation of this root giving your answer correct to 3 decimal places. 3. Show that the equation f(x) = 0, where f(x) = x° + x² – 2x – 1, has a root in the interval 1<x<2. Use Newton Raphson pròcedure method to find an approximation to this root correct to 2 decimal places. %3D 4. Show that the equation: x5 - x³ - of the Newton- Raphson method to find an approximation to this root correct to 2 decimal places. 5. Show that the equation f(x) = 0, where f(x) = 12x + 16x – 3x – 4, has a root in each of the intervals: -2 <x <-1, -1<x <0. Use Newton Raphson method with initial value -1.5 to find two further approximation to the root in the interval: -2 < x <-1, giving your final answer to two decimal places. 6. Show that x = -1 is a root of the equation f(x)= 0. where f(x) = x* + x' + 3x² – 9x – 12. Show also that another root of this equation lies in the interval 1<x<2. Starting with 1.5 as a first approximation, use the Newton-Raphson procedure twice to find another approximation to this root, giving your answver correct to three decimal places. 7. Show that a root of the equation:Inx = 1 1 = 0, has a root in the interval 1<x<2 use two iterations - lies in the interval between i and 1.6. starting - - 2 with x = 1.4 as a first approximation for the root correct to 2 decimal places 8. Taking x =-as the first approximation to the real root of the equation x'– 6x +1 = 0, use one iteration of Newton-Raphson's method to obtain the second approximation giving your answer to 2 decimal places. 9. Show that a root of the equation:e + 4x - 5 = 0 lies within the range 0 <x<1. using x = 0.6 as a first approximation to this root and applying one iteration of the Newton- Raphson method, find a second approximation giving your answer correct to 2 decimal places. 10. Show that the equation: x³ + x - 6 = 0 has a root between land 2. Using the Newton- Raphson method and taking 1.6 as the first approximation, determine by means of two iterations, two other approximations for the root, giving your answers correct to 3 decimal places. 11. Given that f(x) = x – 5+ x² In x, show that the equation: f(x) = 0 has a root in the interval: 2 < x < 3. Taking x = one iteration of the Newton Raphson's procedure to find a second approximation of this root, giving the answer correct to two decimal places. 12. Use one iteration of the Newton-Raphson method to find, to 3 decimai places, a second approximation to the real root of the equation x + 3x -1 = 0, taking 0.2 as the first approximation to the root of the 1 3 2x 2 as a first approximation to the root of the equation, use .3 equation(
Transcribed Image Text:2. Show that the equation xe = 1 has a root between 0.5 and 0.6. starting with 0.55 as a first estimate, use one iteration of the Newton-Raphson method to obtain a better approximation of this root giving your answer correct to 3 decimal places. 3. Show that the equation f(x) = 0, where f(x) = x° + x² – 2x – 1, has a root in the interval 1<x<2. Use Newton Raphson pròcedure method to find an approximation to this root correct to 2 decimal places. %3D 4. Show that the equation: x5 - x³ - of the Newton- Raphson method to find an approximation to this root correct to 2 decimal places. 5. Show that the equation f(x) = 0, where f(x) = 12x + 16x – 3x – 4, has a root in each of the intervals: -2 <x <-1, -1<x <0. Use Newton Raphson method with initial value -1.5 to find two further approximation to the root in the interval: -2 < x <-1, giving your final answer to two decimal places. 6. Show that x = -1 is a root of the equation f(x)= 0. where f(x) = x* + x' + 3x² – 9x – 12. Show also that another root of this equation lies in the interval 1<x<2. Starting with 1.5 as a first approximation, use the Newton-Raphson procedure twice to find another approximation to this root, giving your answver correct to three decimal places. 7. Show that a root of the equation:Inx = 1 1 = 0, has a root in the interval 1<x<2 use two iterations - lies in the interval between i and 1.6. starting - - 2 with x = 1.4 as a first approximation for the root correct to 2 decimal places 8. Taking x =-as the first approximation to the real root of the equation x'– 6x +1 = 0, use one iteration of Newton-Raphson's method to obtain the second approximation giving your answer to 2 decimal places. 9. Show that a root of the equation:e + 4x - 5 = 0 lies within the range 0 <x<1. using x = 0.6 as a first approximation to this root and applying one iteration of the Newton- Raphson method, find a second approximation giving your answer correct to 2 decimal places. 10. Show that the equation: x³ + x - 6 = 0 has a root between land 2. Using the Newton- Raphson method and taking 1.6 as the first approximation, determine by means of two iterations, two other approximations for the root, giving your answers correct to 3 decimal places. 11. Given that f(x) = x – 5+ x² In x, show that the equation: f(x) = 0 has a root in the interval: 2 < x < 3. Taking x = one iteration of the Newton Raphson's procedure to find a second approximation of this root, giving the answer correct to two decimal places. 12. Use one iteration of the Newton-Raphson method to find, to 3 decimai places, a second approximation to the real root of the equation x + 3x -1 = 0, taking 0.2 as the first approximation to the root of the 1 3 2x 2 as a first approximation to the root of the equation, use .3 equation(
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS