Let f(x) = x²-6. Use Newton's method Pn=Pn-1-Pn-1/pn-1 with po=3 to find p3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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This is a two part question please help. Part a is one image, b is the second image
![Let \( f(x) = x^2 - 6 \). Use Newton's method
\[ p_n = p_{n-1} - \frac{p_{n-1}}{p'_{n-1}} \]
with \( p_0 = 3 \) to find \( p_3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba13667f-f60c-45eb-87f2-7662478f2e6d%2F40526319-500a-4e6f-a41f-8c1d8e4f945d%2F3qiusn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( f(x) = x^2 - 6 \). Use Newton's method
\[ p_n = p_{n-1} - \frac{p_{n-1}}{p'_{n-1}} \]
with \( p_0 = 3 \) to find \( p_3 \).
![The question presented is: "Which of these is a fixed point equation for \( f(x) = x^4 + 2x^2 - x - 3 \)."
A fixed point equation is derived from setting \( f(x) = x \).
Mathematically, this means finding \( x \) such that:
\[ x = x^4 + 2x^2 - x - 3 \]
Rearranging the equation, we have:
\[ 0 = x^4 + 2x^2 - 2x - 3 \]
To explore fixed points further, you can rewrite the function as:
\[ x = g(x) \]
where \( g(x) \) is any transformation of \( f(x) \) that equals \( x \) when solved. Here, \( f(x) \) and the related transformations could be analyzed to identify \( g(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba13667f-f60c-45eb-87f2-7662478f2e6d%2F40526319-500a-4e6f-a41f-8c1d8e4f945d%2Ffix6ixg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The question presented is: "Which of these is a fixed point equation for \( f(x) = x^4 + 2x^2 - x - 3 \)."
A fixed point equation is derived from setting \( f(x) = x \).
Mathematically, this means finding \( x \) such that:
\[ x = x^4 + 2x^2 - x - 3 \]
Rearranging the equation, we have:
\[ 0 = x^4 + 2x^2 - 2x - 3 \]
To explore fixed points further, you can rewrite the function as:
\[ x = g(x) \]
where \( g(x) \) is any transformation of \( f(x) \) that equals \( x \) when solved. Here, \( f(x) \) and the related transformations could be analyzed to identify \( g(x) \).
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