MÉTODO DE REGULA FALSI

MÉTODO DE REGULA FALSI

PROBLEMA N°1

Sea f(x) =  y empleando el método de Regula Falsi, se pide determinar la raíz más pequeña de la función para  Se pide realizar el cálculo con una tolerancia menor a 0.0001.[pic 1][pic 2]

SOLUCIÓN PROBLEMA N°1

Dado f(x) =  , [pic 3][pic 4]

Sea:                    f (-3) = 55.012716                                 f (4) = -52.308051

Por lo tanto:     f (-3) x f (4)  0    = [[pic 5][pic 6][pic 7][pic 8][pic 9]

1. Sea i = 0

 [pic 10][pic 11]

 [pic 12][pic 13]

  = 0.588206[pic 14][pic 15]

Luego: f () f () = f (-3) f (0.588206)  0[pic 16][pic 17][pic 18]

[pic 19]

 [] = [-3,0.588206][pic 20][pic 21]

1. Sea i = 1

 [pic 22][pic 23]

 [pic 24][pic 25]

  = 0.505024[pic 26][pic 27]

Luego: f () f () = f (-3) f (0.505024)  0[pic 28][pic 29][pic 30]

[pic 31]

 [] = [-3,0.505024][pic 32][pic 33]

1. Sea i = 2

 [pic 34][pic 35]

 [pic 36][pic 37]

  = 0.455622[pic 38][pic 39]

Luego: f () f () = f (-3) f (0.455622)  0[pic 40][pic 41][pic 42]

[pic 43]

 [] = [-3,0.455622][pic 44][pic 45]

1. Sea i = 3

 [pic 46][pic 47]

 [pic 48][pic 49]

  = 0.427071[pic 50][pic 51]

Luego: f () f () = f (-3) f (0.427071)  0[pic 52][pic 53][pic 54]

[pic 55]

 [] = [-3,0.427071][pic 56][pic 57]

1. Sea i = 4

 [pic 58][pic 59]

 [pic 60][pic 61]

  = 0.410785[pic 62][pic 63]

Luego: f () f () = f (-3) f (0.410769)  0[pic 64][pic 65][pic 66]

[pic 67]

 [] = [-3,0.410785][pic 68][pic 69]

1. Sea i = 5

 [pic 70][pic 71]

 [pic 72][pic 73]

  = 0.401558[pic 74][pic 75]

Luego: f () f () = f (-3) f (0.401558)  0[pic 76][pic 77][pic 78]

[pic 79]

 [] = [-3,0.401558][pic 80][pic 81]

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