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Concept explainers
(a) Apply Newton’s method to the equation 1/x − a = 0 to derive the following reciprocal algorithm:
(This algorithm enables a computer to find reciprocals without actually dividing.)
(b) Use part (a) to compute 1/1.6984 correct to six decimal places.
(a)
![Check Mark](/static/check-mark.png)
To Derive: The square root of the given reciprocal equation by Newton’s method
Explanation of Solution
Given:
The equation is
Formula used:
The Newton’s method is
Calculation:
Let
Let the derivative of
To derive the
Hence, the derivation.
(b)
![Check Mark](/static/check-mark.png)
To Compute: The root of
Answer to Problem 24E
The root correct to six decimal places is
Explanation of Solution
Given:
The equation is
Choose the initial point
Calculation:
Calculate
Calculate
Substitute
Substitute
Substitute
Calculate
Calculate
Substitute
Substitute
Calculate
Calculate
Substitute
Substitute
Thus, the root corrected to six decimal places is
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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