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Apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the process until two successive approximations differ by less than 0.001. [Hint: Let h(x) = f(x) - g(x).] x = -8 f(x) = 2x + 2 g(x)=√x + 8 Need Help? -1.0 -0.5 Read It Watch It 0.5 1.0 1.5 X 2.0

Apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the process until two successive approximations differ by less than 0.001. [Hint: Let h(x) = f(x) - g(x).] x = -8 f(x) = 2x + 2 g(x)=√x + 8 Need Help? -1.0 -0.5 Read It Watch It 0.5 1.0 1.5 X 2.0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
### Applying Newton's Method for Intersection Points **Objective:** Use Newton's Method to approximate the x-value(s) at the intersection point(s) of the given graphs. The process should continue until the difference between two successive approximations is less than 0.001. **Functions:** - \( f(x) = 2x + 2 \) - \( g(x) = \sqrt{x} + 8 \) **Hint:** Let \( h(x) = f(x) - g(x) \). **Initial Guess:** - \( x = -8 \) **Graph Description:** The graph contains two functions: - The line \( f \) (depicted as a straight, upward-sloping line). - The curve \( g \), which begins at a higher y-value and is relatively horizontal due to the nature of the square root function. Both graphs intersect at a point in the given coordinate grid: - The x-axis ranges from -1.0 to 2.0, incremented by 0.5. - The y-axis ranges from 0 to 4, incremented by 1. **Additional Resources:** - **Need Help?** - **Read It:** Provides textual explanations or additional readings. - **Watch It:** Offers video explanations or visual guides. Continue using Newton's Method with the starting estimate \( x = -8 \) until the desired precision is achieved.
Transcribed Image Text:### Applying Newton's Method for Intersection Points **Objective:** Use Newton's Method to approximate the x-value(s) at the intersection point(s) of the given graphs. The process should continue until the difference between two successive approximations is less than 0.001. **Functions:** - \( f(x) = 2x + 2 \) - \( g(x) = \sqrt{x} + 8 \) **Hint:** Let \( h(x) = f(x) - g(x) \). **Initial Guess:** - \( x = -8 \) **Graph Description:** The graph contains two functions: - The line \( f \) (depicted as a straight, upward-sloping line). - The curve \( g \), which begins at a higher y-value and is relatively horizontal due to the nature of the square root function. Both graphs intersect at a point in the given coordinate grid: - The x-axis ranges from -1.0 to 2.0, incremented by 0.5. - The y-axis ranges from 0 to 4, incremented by 1. **Additional Resources:** - **Need Help?** - **Read It:** Provides textual explanations or additional readings. - **Watch It:** Offers video explanations or visual guides. Continue using Newton's Method with the starting estimate \( x = -8 \) until the desired precision is achieved.
Expert Solution
Step 1: Introduction of the given problem

f open parentheses x close parentheses equals 2 x plus 2 g open parentheses x close parentheses equals square root of x plus 8 end root h open parentheses x close parentheses equals f open parentheses x close parentheses minus g open parentheses x close parentheses

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