Use Newton's method to approximate all the intersection points of the following pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. y=25√√x and y=x² +4 The graphs intersect when x (Do not round until the final answer. Then round to six decimal places as needed. Use a comma to separate answers as needed.)
Use Newton's method to approximate all the intersection points of the following pair of curves. Some preliminary graphing or analysis may help in choosing good initial approximations. y=25√√x and y=x² +4 The graphs intersect when x (Do not round until the final answer. Then round to six decimal places as needed. Use a comma to separate answers as needed.)
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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![**Finding Intersection Points Using Newton's Method**
In this exercise, we will use Newton's method to approximate all the intersection points of the following pair of curves. It is recommended to conduct some preliminary graphing or analysis to help in choosing good initial approximations.
### Given Functions
\[ y = 25\sqrt{x} \]
\[ y = x^2 + 4 \]
### Task
Determine the x-values where these graphs intersect. Use Newton's method for approximation. For the final answer, do not round until the end. Then, round to six decimal places as needed. Use a comma to separate multiple answers.
\[ \text{The graphs intersect when } x \approx \_\_\_\_\_\_ . \]
Note: This approach involves iterative calculations and relies on an initial guess for convergence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3efc033e-df22-4370-9c84-9e7910492c5d%2F9c16fd23-9d67-4c47-a1a0-870de876a1e3%2Fadvjgwh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding Intersection Points Using Newton's Method**
In this exercise, we will use Newton's method to approximate all the intersection points of the following pair of curves. It is recommended to conduct some preliminary graphing or analysis to help in choosing good initial approximations.
### Given Functions
\[ y = 25\sqrt{x} \]
\[ y = x^2 + 4 \]
### Task
Determine the x-values where these graphs intersect. Use Newton's method for approximation. For the final answer, do not round until the end. Then, round to six decimal places as needed. Use a comma to separate multiple answers.
\[ \text{The graphs intersect when } x \approx \_\_\_\_\_\_ . \]
Note: This approach involves iterative calculations and relies on an initial guess for convergence.
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