Question
Download Solution PDFThe iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Newton Raphson method:
The iteration formula is \(x_{n+1} = x_n - \frac {f(x)}{f'(x)} \)
Calculation:
Given
\(f(x)=x^3 -5x+7\)
\(x_{n+1} = x_n - \frac {f(x)}{f'(x)} \)
\(f'(x) = 3x^2 -5\)
\(x_{k+1} = x_k- (\frac{x_k^3-5x+7}{3x_k^2 -5})\) ⇒\(x_{k+1} =\frac{3x_k^3 -5x_k-x_k^3+5x_k-7}{3x_k^2-5}\) ⇒ \(x_{k+1} = \frac{2x_k^3-7}{3x_k^2-5}\)
Last updated on Apr 16, 2025
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