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Solved: Use Theorem 3.3 to find an error bound for the approximations in Exercise 1

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 3 Chapter 3.1

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 3

Use Theorem 3.3 to find an error bound for the approximations in Exercise 1

Step-by-Step Solution:
Step 1 of 3

MTH 132 - Lecture 26 - Newtonian method Roots ● Frequently, there are issues when we attempt to solve “imperfect” equations, where the roots result in imaginary numbers or no neat solution - we have to resort to an approximation. ● Newton’s method is essentially a way to approximate by narrowing down the numbers until they reach a specific accuracy that you specify. How does this work ● The concept of the IVT or intermediate value theorem guarantees the Newtonian method. Intermediate Value Theorem - Which Intervals are continuous ● If f(x) is continuous on the closed interval on [a,b] and c is between a and b; then there exists a point (d) on the interval [a,b] such that f(d) = c. Application of IVT: ● Prove the existe

Step 2 of 3

Chapter 3.1, Problem 3 is Solved
Step 3 of 3

Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Solved: Use Theorem 3.3 to find an error bound for the approximations in Exercise 1