Metodo De Newton-Raphson

METODO METODO DE NEWTON-RAPHSON
1. LOCALIZAMOS LAS RAICES
x | y1=senx | y2=3-x^2 |
-3 | -0.141120008 | -6 |
-2 | -0.909297427 | -1 |
-1 | -0.841470985 | 2 |
-0.5 | -0.479425539 | 2.75 |0 | 0 | 3 |
1 | 0.841470985 | 2 |
2 | 0.909297427 | -1 |
3 | 0.141120008 | -6 |

2. DEL GRAFICO APRECIAMOS QUE TIENE 2 RACES
RAICES: |   |   |
PRIMERA | -2 | -1 |
SEGUNDA | 1 | 2 |3. VERIFICAMOS LA EXISTENCIA DE LA RAIZ PARA ESTE INTERVALO
  | x |   | y= seno(x)+x^2-3 |
a | -2 | f(a) | 0.090702573 |
b | -1 | f(b) | -2.841470985 |
f(a)*f(b)<0 |   | -0.25772873| ok |

4. COMPROVANDO CRITERIO DE CONVERGENCIA
x= | -2 |
f(x)= seno(x)+x^2-3 | 0.090702573 |
f`(x)=cos(x)+2x | -4.416146837 |
f"(x)=-seno(x)+2 | 1.909421743 |
(f(x)*f(x)")<1 |0.00888044 | <1 ok |
(f`(x))^2 |   |   |

5. DETERMINAMOS LA RAIZ
* consideramos valor inicial x= -2
I | X | F(X)=seno(x)+x^2-3 | f`(x)=cos(x)+2x | Xn= Xn-1-F(Xn-1)/f`(x-1) |
0 | -2 |0.0907025732 | -4.416146837 | -1.979461151 |
1 | -1.979461151 | 0.0006142295 | -4.356306757 | -1.979320153 |
2 | -1.979320153 | 0.0000000290 | -4.355895371 | -1.979320147 |
3 | -1.979320147 |0.0000000000 | -4.355895352 | -1.979320147 |

la raiz x = | =-1.979320147 |

Para x = -1
* COMPROVANDO CRITERIO DE CONVERGENCIA
x= | -1 |
f(x)= seno(x)+x^2-3 | -2.841470985 |f`(x)=cos(x)+2x | -1.459697694 |
f"(x)=-seno(x)+2 | 2.295636439 |

(f(x)*f(x)")<1 | -3.061402916 | <1 ok |
(f`(x))^2 |   |   |

DETERMINAMOS LA RAIZ
* consideramos valor inicial x= -1
I | X |F(X)=seno(x)+x^2-3 | f`(x)=cos(x)+2x | Xn= Xn-1-F(Xn-1)/f`(x-1) |
0 | -1 | -2.8414709848 | -1.459697694 | -2.946616067 |
1 | -2.946616067 | 5.4888026832 | -6.874284341 | -2.148161652 |
2 |-2.148161652 | 0.7766948737 | -4.842141535 | -1.987758478 |
3 | -1.987758478 | 0.0368603252 | -4.380501704 | -1.979343842 |
4 | -1.979343842 | 0.0001032159 | -4.355964488 | -1.979320147 |
5 |...