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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 4.7 / Problem 12E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Theory and ExamplesLocating a planet To calculate a

Chapter 4, Problem 12E

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QUESTION:

Problem 12E

Theory and Examples

Locating a planet To calculate a planet’s space coordinates, we have to solve equations like x = 1 + 0.5 sin x. Graphing the function ƒ(x) = x - 1 - 0.5 sin x suggests that the function has a root near x = 1.5. Use one application of Newton’s method to improve this estimate. That is, start with x0 = 1.5 and find x1 (The value of the root is 1.49870 to five decimal places.) Remember to use radians.

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QUESTION:

Problem 12E

Theory and Examples

Locating a planet To calculate a planet’s space coordinates, we have to solve equations like x = 1 + 0.5 sin x. Graphing the function ƒ(x) = x - 1 - 0.5 sin x suggests that the function has a root near x = 1.5. Use one application of Newton’s method to improve this estimate. That is, start with x0 = 1.5 and find x1 (The value of the root is 1.49870 to five decimal places.) Remember to use radians.

ANSWER:

Solution:

Step 1 of 2

In this problem, we have to use Newton’s method to find ${x}_{1}$ .

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