Carroll Salinas
03/21/2024 · Elementary School
Usando el método de Newtón-Rapson para encontrar las raíces de la función \( f(x)=x^{4}+2 x-1 \) El valor sucesivo \( x_{n+1} \) se expresa como (A) \( x_{n+1}=\frac{4 x_{n}^{3}+2}{x_{n}^{4}+2 x_{n}-1} \) (B) \( x_{n+1}=x_{n}-\frac{x_{n}}{x_{n}^{4}+2 x_{n}-1} \) (C) \( x_{n+1}=x_{n}-\frac{x_{n}^{4}+2 x_{n}-1}{4 x_{n}^{3+2}} \) (D) \( x_{n+1}=\frac{x_{n}^{4}+2 x_{n}{ }^{4}}{4 x_{n}^{3}+2} \) (D)
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La fórmula correcta para \( x_{n+1} \) en el método de Newton-Raphson para la función \( f(x)=x^{4}+2x-1 \) es:
\[
x_{n+1}=x_{n}-\frac{x_{n}^{4}+2x_{n}-1}{4x_{n}^{3}+2}
\]
La respuesta correcta es la opción (C).
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