Metodos

METODOS

Encontrar la raíz de: f (x)= e-x - 0.5x
(1 , 2)


MÉTODO DE BISECCIÓN

X1 | X2 | f (X1) | Xr | f (Xr) | f (X1). f (Xr) |
-1 | 2 | 3.2183 | 0.5 | 0.3565 | 1.1473 |
0.5 | 2 | 0.3565 | 1.25 | -0.3385 | -0.1207 |
0.5 | 1.25 | 0.3565 | 0.875 | -0.0206 | -0.0073 |
0.5 | 0.875 | 0.3565 | 0.6875 | 0.1591 | 0.0567 |
0.6875 | 0.875 | 0.1591 | 0.78125 |0.0672 | 0.0107 |
0.78125 | 0.875 | 0.0672 | 0.8281 | 0.0228 | 0.0015 |
0.8281 | 0.875 | 0.0228 | 0.8516 | 0.009 | 0.0000 |

Encontrar la raíz de: f (x)=x3 –e x +3

X1=-1 X2=5

X1 | X2 | f (X1) | Xr | f (Xr) | f (X1). f (Xr) |
-1 | 5 | 1.6321 | 2 | 3.6109 | 5.8933 |
2 | 5 | 3.6109 | 3.5 | 12.7595 | 46.0732 |
3.5 | 5 | 12.7595 | 4.25 | 9.6602 | 123.2593 |4.25 | 5 | 9.6602 | 4.625 | -0.0711 | -0.6868 |
4.25 | 4.625 | 9.6602 | 4.4375 | 5.8173 | 56.1963 |
4.4375 | 4.625 | 5.8173 | 4.5312 | 3.1636 | 18.4036 |
4.5312 | 4.625 | 3.1636 | 4.5781 | 1.6231 | 5.1348 |
4.5781 | 4.625 | 1.6231 | 4.6016 | 0.7940 | 1.2887 |
4.6016 | 4.625 | 0.7940 | 4.6133 | 0.3664 | 0.2909 |
4.6133 | 4.625 | 0.3664 | 4.6192 | 0.1470 | 0.0539 |
4.6192| 4.625 | 0.1470 | 4.6221 | 0.0383 | 0.0056 |
4.6221 | 4.625 | 0.0383 | 4.6236 | -0.0182 | -0.0007 |
4.6221 | 4.6236 | 0.0383 | 4.6228 | 0.0119 | 0.0004 |
4.6228 | 4.6236 | 0.0119 | 4.6232 | -0.0032 | -0.00006 |
4.6228 | 4.6232 | 0.0119 | 4.623 | 0.0044 | 0.0000 |

MÉTODO DE LA REGLA FALSA
Encontrar la raíz de: f (x)=e-x –x

X1 | X2 | f (X1) | f (X2) | (X1- X2) | Xr | f(Xr) | r (X1). f (Xr) |
0 | 1 | 1 | -0.6321 | -1 | 0.6127 | -0.0708 | -0.0708 |
0 | 0.6127 | 1 | -0.0708 | -0.6127 | 0.5722 | -0.0079 | -0.0079 |
0 | 0.5722 | 1 | -0.0079 | -0.5722 | 0.5677 | -0.0009 | -0.0009 |
0 | 0.5677 | 1 | -0.0009 | -0.5677 | 0.5672 | -0.00009 | -0.00009 |
0 | 0.5672 | 1 | -0.00009 | -0.5672 | 0.5671 | 0.00007 | 0.0000 |

METODO DE INCREMENTO


Encontrar laraiz de la sig. Ecuacion, utilizando el metodo de incrementos,Considerando 5 decimales.

f (x)=3 x3+6x-40

X | Y |
-4 | -208 |
-3 | -103 |
-2 | -52 |
-1 | -37 |
0 | -40 |
1 | -43 |
2 | -28 |
3 | 23 |
2.1 | -24.817 |
2.2 | -21.256 |
2.3 | -17.299 |
2.4 | -12.928 |
2.5 | -8.125 |
2.6 | -2.872 |
2.7 | 2.849 |
2.61 | -2.32 |
2.62 | -1.76 |
2.63 | -1.20 |2.64 | -0.64 |
2.65 | -0.07 |
2.66 | 0.50 |
2.651 | -0.013 |
2.652 | 0.043 |
2.6511 | -0.0081 |
2.6512 | -0.0024 |
2.6513 | 0.0032 |
2.65121 | -0.00187 |
2.65122 | -0.00130 |
2.65123 | -0.00072 |
2.65124 | -0.00015 |
2.65125 | 0.00041 |

f (x)=x7 + x6- x3+ x -3

X | Y |
-7 | -705,561 |
-6 | -233,073 |
-5 | -62,383 |
-4 | -12,231 |
-3 | -1,437 |-2 | -61 |
-1 | -3 |
0 | -3 |
1 | -1 |
2 | 1.83 |
1.01 | -0.88 |
1.02 | -0.76 |
1.03 | -0.63 |
1.04 | -0.50 |
1.05 | -0.36 |
1.06 | -0.20 |
1.07 | -0.04 |
1.08 | 0.12 |
1.071 | -0.031 |
1.072 | -0.015 |
1.073 | 0.001 |
1.0721 | -0.0137 |
1.0722 | 0.0120 |
1.0723 | -0.0103 |
1.0724 | -0.0087 |
1.0725 | -0.0070 |
1.0726 | -0.0053 |
1.0727 | -0.0036 |1.0728 | -0.0020 |
1.0729 | -0.0003 |
1.0730 | 0.0013 |
1.07291 | -0.00016 |
1.07292 | 0.0000002 |
1.072911 | -0.000150516 |
1.072912 | -0.000133762 |
1.072913 | -0ooo117007 |
1.072914 | -0.000100252 |
1.072915 | -0.000083497 |
1.072916 | -0.000066742 |
1.072917 | -0.000049986 |
1.072918 | -0.000033231 |
1.072919 | -0.000016475 |

METODO DE PUNTO FIJO

f (x)=e-x – x e-x – x=0
Xi=0 -x= -e –x X= e –x

Xi | Xi + 1 |
0 | 1 |
1 | 0.3679 |
0.3679 | 0.6922 |
0.6922 | 0.5005 |
0.5005 | 0.6062 |
0.6062 | 0.5454 |
0.5454 | 0.5796 |
0.5796 | 0.5601 |
0.5691 | 0.5712 |
0.5712 | 0.5648 |
0.5648 | 0.5685 |
0.5685...