NOMBRE: FERNANDA ABAHONZAPROGRAMA: ING. AGROINDUSTRIAL

EJERCICIO 5.1 determine las raices reales de f(x)= -4.4*X^2 + 2.2X + 4.7

a) METODO DE BISECCION

x f(x) a f(a) b-10 -57.3 -2 -1.3 -1

-9 -47.5 -2 -1.3 -1.5-8 -38.5 -1.75 -0.375 -1.5-7 -30.3 -1.75 -0.375 -1.625-6 -22.9 -1.6875 -0.1515625 -1.625-5 -16.3 -1.65625 -0.04101563 -1.625-4 -10.5 -1.65625 -0.04101563 -1.640625-3 -5.5 -1.6484375 -0.01350098 -1.640625-2 -1.3 -1.6484375 -0.01350098 -1.64453125-1 2.1 -1.64648438 -0.00662994 -1.644531250 4.7 -1.64550781 -0.00319557 -1.644531251 6.5 -1.64501953 -0.00147867 -1.644531252 7.5 -1.64477539 -0.00062029 -1.644531253 7.7 -1.64465332 -0.00019112 -1.644531254 7.1 -1.64465332 -0.00019112 -1.644592295 5.7 -1.6446228 -8.383E-005 -1.644592296 3.5 -1.64460754 -3.019E-005 -1.644592297 0.5 -1.64459991 -3.364E-006 -1.644592298 -3.3 -1.64459991 -3.364E-006 -1.64459619 -7.9 -1.64459991 -3.364E-006 -1.64459801

10 -13.3 -1.64459896 -1.077E-008 -1.64459801-1.64459896 -1.077E-008 -1.64459848-1.64459896 -1.077E-008 -1.64459872-1.64459896 -1.077E-008 -1.64459884-1.64459896 -1.077E-008 -1.6445989-1.64459896 -1.077E-008 -1.64459893-1.64459896 -1.077E-008 -1.64459895-1.64459896 -1.077E-008 -1.64459895-1.64459896 -1.077E-008 -1.64459896-1.64459896 -4.226E-009 -1.64459896-1.64459896 -9.519E-010 -1.64459896-1.64459896 -9.519E-010 -1.64459896

b) empleando la formula cuadraruca

f(x)= -4.4*X^2 + 2.2X + 4.7 a b c-0.4 2.2 4.7=( ^2 )) ( 4

/2

=( ^2 )) ( 4/2

f(b) xi f(xi) error a2.1 -1.5 0.5 70.5 -1.75 -0.375 14.2857143 70.5 -1.625 0.06875 7.69230769 7

0.06875 -1.6875 -0.1515625 3.7037037 7.1250.06875 -1.65625 -0.04101563 1.88679245 7.1250.06875 -1.640625 0.01396484 0.95238095 7.125

0.01396484 -1.6484375 -0.01350098 0.47393365 7.1406250.01396484 -1.64453125 0.00023804 0.23752969 7.1406250.00023804 -1.646484375 -0.00662994 0.11862396 7.144531250.00023804 -1.645507813 -0.00319557 0.05934718 7.144531250.00023804 -1.645019531 -0.00147867 0.0296824 7.144531250.00023804 -1.644775391 -0.00062029 0.0148434 7.144531250.00023804 -1.64465332 -0.00019112 0.00742225 7.144531250.00023804 -1.644592285 2.3459E-005 0.00371126 7.14453125

2.3459E-005 -1.644622803 -8.383E-005 0.0018556 7.144592292.3459E-005 -1.644607544 -3.019E-005 0.00092781 7.144592292.3459E-005 -1.644599915 -3.364E-006 0.00046391 7.144592292.3459E-005 -1.6445961 1.0048E-005 0.00023195 7.144592291.0048E-005 -1.644598007 3.3420E-006 0.00011598 7.14459613.3420E-006 -1.644598961 -1.077E-008 5.7988E-005 7.144598013.3420E-006 -1.644598484 1.6656E-006 2.8994E-005 7.144598011.6656E-006 -1.644598722 8.2743E-007 1.4497E-005 7.144598488.2743E-007 -1.644598842 4.0833E-007 7.2485E-006 7.144598724.0833E-007 -1.644598901 1.9878E-007 3.6243E-006 7.144598841.9878E-007 -1.644598931 9.4001E-008 1.8121E-006 7.14459899.4001E-008 -1.644598946 4.1613E-008 9.0607E-007 7.144598934.1613E-008 -1.644598953 1.5419E-008 4.5303E-007 7.144598951.5419E-008 -1.644598957 2.3223E-009 2.2652E-007 7.144598952.3223E-009 -1.644598959 -4.226E-009 1.1326E-007 7.144598962.3223E-009 -1.644598958 -9.519E-010 5.6629E-0082.3223E-009 -1.644598958 6.8521E-010 2.8315E-0086.8521E-010 -1.644598958 -1.334E-010 1.4157E-008

X1 = -1.64459896X2 = 7.14459896

f(a) b f(b) xi f(xi) error0.5 8 -3.3 7.5 -1.30.5 7.5 -1.3 7.25 -0.375 3.448275860.5 7.25 -0.375 7.125 0.06875 1.75438596

0.06875 7.25 -0.375 7.1875 -0.1515625 0.869565220.06875 7.1875 -0.1515625 7.15625 -0.04101562 0.436681220.06875 7.15625 -0.04101562 7.140625 0.01396484 0.21881838

0.01396484 7.15625 -0.04101562 7.1484375 -0.01350098 0.109289620.01396484 7.1484375 -0.01350098 7.14453125 0.00023804 0.054674690.00023804 7.1484375 -0.01350098 7.14648438 -0.00662994 0.027329870.00023804 7.14648438 -0.00662994 7.14550781 -0.00319557 0.01366680.00023804 7.14550781 -0.00319557 7.14501953 -0.00147867 0.006833870.00023804 7.14501953 -0.00147867 7.14477539 -0.00062029 0.003417050.00023804 7.14477539 -0.00062029 7.14465332 -0.00019112 0.001708550.00023804 7.14465332 -0.00019112 7.14459229 2.3459E-005 0.00085428

2.3459E-005 7.14465332 -0.00019112 7.1446228 -8.383E-005 0.000427142.3459E-005 7.1446228 -8.383E-005 7.14460754 -3.019E-005 0.000213572.3459E-005 7.14460754 -3.019E-005 7.14459991 -3.364E-006 0.000106792.3459E-005 7.14459991 -3.364E-006 7.1445961 1.0048E-005 5.3393E-0051.0048E-005 7.14459991 -3.364E-006 7.14459801 3.3420E-006 2.6696E-0053.3420E-006 7.14459991 -3.364E-006 7.14459896 -1.077E-008 1.3348E-0053.3420E-006 7.14459896 -1.077E-008 7.14459848 1.6656E-006 6.6741E-0061.6656E-006 7.14459896 -1.077E-008 7.14459872 8.2743E-007 3.3370E-0068.2743E-007 7.14459896 -1.077E-008 7.14459884 4.0833E-007 1.6685E-0064.0833E-007 7.14459896 -1.077E-008 7.1445989 1.9878E-007 8.3426E-0071.9878E-007 7.14459896 -1.077E-008 7.14459893 9.4001E-008 4.1713E-0079.4001E-008 7.14459896 -1.077E-008 7.14459895 4.1613E-008 2.0857E-0074.1613E-008 7.14459896 -1.077E-008 7.14459895 1.5419E-008 1.0428E-0071.5419E-008 7.14459896 -1.077E-008 7.14459896 2.3223E-009 5.2141E-0082.3223E-009 7.14459896 -1.077E-008 7.14459896 -4.226E-009 2.6071E-008

EJERCICIO 5,3: f(x)= -26 + 82.3X - 38X^2 + 45.4 *X^3 -9*X^4 + 0.65 * x^3

a) METODO DE BISECCON

x f(x) a f(a) b-10 -205049 0 -26 1

-9 -134372.15 0 -26 0.5-8 -84524.4 0.25 -7.1251464844 0.5-7 -50569.85 0.25 -7.1251464844 0.375-6 -28412.6 0.3125 -2.6905829906 0.375-5 -14718.75 0.34375 -0.4780563846 0.375-4 -6838.4 0.34375 -0.4780563846 0.359375-3 -2727.65 0.34375 -0.4780563846 0.3515625-2 -870.6 0.34765625 -0.2012473476 0.3515625-1 -201.35 0.34960938 -0.062808138 0.35156250 -26 0.34960938 -0.062808138 0.350585941 55.35 0.35009766 -0.0281944672 0.350585942 226.6 0.3503418 -0.0108870354 0.350585943 533.65 0.35046387 -0.0022331691 0.350585944 962.4 0.35046387 -0.0022331691 0.35052495 1516.75 0.35049438 -6.96868E-005 0.35052496 2296.6 0.35049438 -6.96868E-005 0.350509647 3575.85 0.35049438 -6.96868E-005 0.350502018 5880.4 0.35049438 -6.96868E-005 0.35049829 10066.15 0.35049438 -6.96868E-005 0.35049629

10 17397 0.35049534 -2.07785E-006 0.350496290.35049534 -2.07785E-006 0.350495820.35049534 -2.07785E-006 0.350495580.35049534 -2.07785E-006 0.350495460.35049534 -2.07785E-006 0.35049540.35049534 -2.07785E-006 0.350495370.35049535 -1.02146E-006 0.350495370.35049536 -4.93270E-007 0.350495370.35049536 -2.29172E-007 0.350495370.35049537 -9.71235E-008 0.350495370.35049537 -3.10992E-008 0.350495370.35049537 -3.10992E-008 0.350495370.35049537 -1.45931E-008 0.350495370.35049537 -6.34004E-009 0.35049537

b) METODO DE FALSA POSICION

a f(a) b0 -26 1

0.31960664 -2.1875662417 10.34547505 -0.355824754 10.34965587 -0.0595119387 10.35035437 -0.0099957968 10.35047167 -0.001680104 10.35049138 -0.0002824269 1

0.3504947 -4.74772E-005 10.35049526 -7.98114E-006 10.35049535 -1.34167E-006 10.35049536 -2.25541E-007 10.35049537 -3.79145E-008 10.35049537 -6.37362E-009 10.35049537 -1.07144E-009 10.35049537 -1.80110E-010 10.35049537 -3.02829E-011 10.35049537 -5.09046E-012 10.35049537 -8.55552E-013 10.35049537 -1.44685E-013 10.35049537 -2.88350E-014 10.35049537 -4.03323E-015 1

f(b) Xi f(Xi) error55.35 0.5 10.7828125

10.7828125 0.25 -7.12514648 10010.7828125 0.375 1.73973236 33.33333331.73973236 0.3125 -2.69058299 201.73973236 0.34375 -0.47805638 9.090909091.73973236 0.359375 0.62979489 4.347826090.62979489 0.3515625 0.0756562 2.22222222

0.0756562 0.34765625 -0.20124735 1.123595510.0756562 0.34960938 -0.06280814 0.558659220.0756562 0.35058594 0.0064208 0.278551530.0064208 0.35009766 -0.02819447 0.139470010.0064208 0.3503418 -0.01088704 0.069686410.0064208 0.35046387 -0.00223317 0.034831070.0064208 0.3505249 0.0020938 0.01741250.0020938 0.35049438 -6.969E-005 0.008707010.0020938 0.35050964 0.00101206 0.00435332

0.00101206 0.35050201 0.00047118 0.00217670.00047118 0.3504982 0.00020075 0.001088360.00020075 0.35049629 6.5531E-005 0.00054419

6.5531E-005 0.35049534 -2.078E-006 0.000272096.5531E-005 0.35049582 3.1727E-005 0.000136053.1727E-005 0.35049558 1.4824E-005 6.8023E-0051.4824E-005 0.35049546 6.3733E-006 3.4012E-0056.3733E-006 0.3504954 2.1477E-006 1.7006E-0052.1477E-006 0.35049537 3.4925E-008 8.5029E-0063.4925E-008 0.35049535 -1.021E-006 4.2515E-0063.4925E-008 0.35049536 -4.933E-007 2.1257E-0063.4925E-008 0.35049536 -2.292E-007 1.0629E-0063.4925E-008 0.35049537 -9.712E-008 5.3143E-0073.4925E-008 0.35049537 -3.110E-008 2.6572E-0073.4925E-008 0.35049537 1.9130E-009 1.3286E-0071.9130E-009 0.35049537 -1.459E-008 6.6429E-0081.9130E-009 0.35049537 -6.340E-009 3.3215E-0081.9130E-009 0.35049537 -2.214E-009 1.6607E-008

f(b) Xi f(Xi) error55.35 0.31960664 -2.18756624

55.35 0.34547505 -0.35582475 7.4877804655.35 0.34965587 -0.05951194 1.1956964155.35 0.35035437 -0.0099958 0.19936855.35 0.35047167 -0.0016801 0.0334691755.35 0.35049138 -0.00028243 0.0056250555.35 0.3504947 -4.748E-005 0.0009455655.35 0.35049526 -7.981E-006 0.0001589555.35 0.35049535 -1.342E-006 2.6721E-00555.35 0.35049536 -2.255E-007 4.4919E-00655.35 0.35049537 -3.791E-008 7.5511E-00755.35 0.35049537 -6.374E-009 1.2694E-00755.35 0.35049537 -1.071E-009 2.1339E-00855.35 0.35049537 -1.801E-010 3.5872E-00955.35 0.35049537 -3.028E-011 6.0298E-01055.35 0.35049537 -5.090E-012 1.0139E-01055.35 0.35049537 -8.556E-013 1.7042E-01155.35 0.35049537 -1.447E-013 2.8508E-01255.35 0.35049537 -2.884E-014 4.7514E-01355.35 0.35049537 -4.033E-015 055.35 0.35049537 1.1349E-015 0

EJERCICIOS 6,3 f(x) = X^3 -6X^2 + 11X - 6.1

a) METODO DE NEWTON RAPHSON

a f(a) f{(a) xi f(xi) error35 35903.9 3266 24.0067667 10635.72149 45.7922279

24.0067667 10635.7215 1451.89334 16.6813515 3149.667732 43.913798916.6813515 3149.66773 645.626248 11.8028824 932.1198324 41.332862511.8028824 932.119832 287.289509 8.55835098 275.4292281 37.91070758.55835098 275.429228 128.035903 6.40716351 81.09357112 33.57472396.40716351 81.0935711 57.2692707 4.99115856 23.67082538 28.37026594.99115856 23.6708254 25.8410886 4.07514353 6.760882486 22.47810464.07514353 6.76088249 11.9186621 3.50789174 1.820658235 16.17073283.50789174 1.82065823 5.82121247 3.19512902 0.411913641 9.788735183.19512902 0.41191364 3.28500011 3.06973674 0.054402269 4.084789243.06973674 0.05440227 2.43301009 3.04737668 0.001593338 0.733748063.04737668 0.00159334 2.2909937 3.0466812 1.51948E-006 0.02282743

3.0466812 1.5195E-006 2.28662458 3.04668053 1.38733E-012 2.1811E-0053.04668053 1.3873E-012 2.28662041 3.04668053 0 1.9911E-011

b) METODO DE LA SECANTE

a f(a) b f(b) xi f(xi)2.5 -0.475 3.5 1.775 2.711111111 -0.45151715

2.71111111 -0.45151715 3.5 1.775 2.871090503 -0.310108192.8710905 -0.31010819 3.5 1.775 2.964625212 -0.16703972

2.96462521 -0.16703972 3.5 1.775 3.010674143 -0.078308693.01067414 -0.07830869 3.5 1.775 3.031349849 -0.034321053.03134985 -0.03432105 3.5 1.775 3.040239684 -0.014597783.04023968 -0.01459778 3.5 1.775 3.043989956 -0.006129613.04398996 -0.00612961 3.5 1.775 3.045559278 -0.002559943.04555928 -0.00255994 3.5 1.775 3.046213736 -0.00106673.04621374 -0.0010667 3.5 1.775 3.046486279 -0.000444063.04648628 -0.00044406 3.5 1.775 3.046599709 -0.000184793.04659971 -0.00018479 3.5 1.775 3.046646906 -7.688E-0053.04664691 -7.688E-005 3.5 1.775 3.046666543 -3.199E-0053.04666654 -3.199E-005 3.5 1.775 3.046674712 -1.331E-0053.04667471 -1.331E-005 3.5 1.775 3.046678111 -5.536E-0063.04667811 -5.536E-006 3.5 1.775 3.046679525 -2.303E-0063.04667952 -2.303E-006 3.5 1.775 3.046680113 -9.581E-0073.04668011 -9.581E-007 3.5 1.775 3.046680357 -3.986E-0073.04668036 -3.986E-007 3.5 1.775 3.046680459 -1.658E-0073.04668046 -1.658E-007 3.5 1.775 3.046680502 -6.899E-008

3.0466805 -6.899E-008 3.5 1.775 3.046680519 -2.870E-0083.04668052 -2.870E-008 3.5 1.775 3.046680527 -1.194E-008

3.04668053 -1.194E-008 3.5 1.775 3.04668053 -4.967E-0093.04668053 -4.967E-009 3.5 1.775 3.046680531 -2.066E-0093.04668053 -2.066E-009 3.5 1.775 3.046680531 -8.597E-010

error7.786885255.572077653.155026411.529522250.682062670.292405750.123202520.051528190.021484320.008946130.003723180.001549150.000644520.000268140.00011155

4.6407E-0051.9306E-0058.0318E-0063.3414E-0061.3901E-0065.7829E-0072.4058E-007

1.0008E-0074.1637E-0081.7322E-008

EJERCICIO 5,5 f(x)=(0,9-0,4x)/x

METODO DE LA FALSA POSICION

a f(a) b (f(b) xi f(xi)1 0.5 3 -0.1 2.66666667 -0.06251 0.5 2.66666667 -0.0625 2.48148148 -0.037313431 0.5 2.48148148 -0.03731343 2.37860082 -0.02162631 0.5 2.37860082 -0.0216263 2.3214449 -0.012310421 0.5 2.3214449 -0.01231042 2.28969161 -0.006933971 0.5 2.28969161 -0.00693397 2.2720509 -0.003882111 0.5 2.2720509 -0.00388211 2.2622505 -0.002166071 0.5 2.2622505 -0.00216607 2.25680583 -0.001206281 0.5 2.25680583 -0.00120628 2.25378102 -0.000671051 0.5 2.25378102 -0.00067105 2.25210057 -0.000373091 0.5 2.25210057 -0.00037309 2.25116698 -0.000207361 0.5 2.25116698 -0.00020736 2.25064832 -0.000115221 0.5 2.25064832 -0.00011522 2.25036018 -6.402E-0051 0.5 2.25036018 -6.402E-005 2.2502001 -3.557E-0051 0.5 2.2502001 -3.557E-005 2.25011117 -1.976E-0051 0.5 2.25011117 -1.976E-005 2.25006176 -1.098E-0051 0.5 2.25006176 -1.098E-005 2.25003431 -6.100E-0061 0.5 2.25003431 -6.100E-006 2.25001906 -3.389E-0061 0.5 2.25001906 -3.389E-006 2.25001059 -1.883E-0061 0.5 2.25001059 -1.883E-006 2.25000588 -1.046E-0061 0.5 2.25000588 -1.046E-006 2.25000327 -5.811E-0071 0.5 2.25000327 -5.811E-007 2.25000182 -3.228E-0071 0.5 2.25000182 -3.228E-007 2.25000101 -1.793E-0071 0.5 2.25000101 -1.793E-007 2.25000056 -9.963E-0081 0.5 2.25000056 -9.963E-008 2.25000031 -5.535E-0081 0.5 2.25000031 -5.535E-008 2.25000017 -3.075E-0081 0.5 2.25000017 -3.075E-008 2.2500001 -1.708E-0081 0.5 2.2500001 -1.708E-008 2.25000005 -9.491E-0091 0.5 2.25000005 -9.491E-009 2.25000003 -5.273E-0091 0.5 2.25000003 -5.273E-009 2.25000002 -2.929E-0091 0.5 2.25000002 -2.929E-009 2.25000001 -1.627E-0091 0.5 2.25000001 -1.627E-009 2.25000001 -9.041E-0101 0.5 2.25000001 -9.041E-010 2.25 -5.023E-0101 0.5 2.25 -5.023E-010 2.25 -2.790E-0101 0.5 2.25 -2.790E-010 2.25 -1.550E-010

error

7.462686574.325259522.462083911.386793290.776422590.433214540.241255380.134210650.074617110.041471140.023044830.012804320.007114020.003952390.002195820.001219910.000677740.000376520.000209180.00011621

6.4561E-0053.5867E-0051.9926E-0051.1070E-0056.1501E-0063.4167E-0061.8982E-0061.0545E-0065.8586E-0073.2548E-0071.8082E-0071.0046E-0075.5809E-0083.1005E-008

EJERCICIO 5,10: f(x)=x^4 - 8x^3 -36x^2 + 462x -1010

METODO DE FALSA POSICION

a f(a) a f(a) b-10 8770 3 -83 4

-9 4309 3 -83 3.93258427-8 1182 3 -83 3.9028571-7 -863 3 -83 3.89015407-6 -2054 3 -83 3.88479998-5 -2595 3 -83 3.88255651-4 -2666 3 -83 3.88161877-3 -2423 3 -83 3.88122721-2 -1998 3 -83 3.88106379-1 -1499 3 -83 3.880995590 -1010 3 -83 3.880967131 -591 3 -83 3.880955262 -278 3 -83 3.88095033 -83 3 -83 3.880948244 6 3 -83 3.88094737

3 -83 3.880947013 -83 3.880946863 -83 3.88094683 -83 3.880946773 -83 3.880946763 -83 3.880946763 -83 3.88094676

f(b) xi f(xi) error6 3.93258427 2.73283018

2.73283018 3.9028571 1.18445917 0.761677141.18445917 3.89015407 0.50224906 0.3265430.50224906 3.88479998 0.21098687 0.137821660.21098687 3.88255651 0.08828349 0.057783260.08828349 3.88161877 0.0368796 0.02415847

0.0368796 3.88122721 0.01539547 0.010088510.01539547 3.88106379 0.00642502 0.004210870.00642502 3.88099559 0.00268104 0.001757220.00268104 3.88096713 0.00111869 0.000733240.00111869 3.88095526 0.00046678 0.000305950.00046678 3.8809503 0.00019476 0.000127660.00019476 3.88094824 8.1264E-005 5.3265E-005

8.1264E-005 3.88094737 3.3907E-005 2.2224E-0053.3907E-005 3.88094701 1.4148E-005 9.2731E-0061.4148E-005 3.88094686 5.9030E-006 3.8692E-0065.9030E-006 3.8809468 2.4630E-006 1.6144E-0062.4630E-006 3.88094677 1.0277E-006 6.7360E-0071.0277E-006 3.88094676 4.2879E-007 2.8106E-0074.2879E-007 3.88094676 1.7891E-007 1.1727E-0071.7891E-007 3.88094676 7.4651E-008 4.8930E-0087.4651E-008 3.88094676 3.1147E-008 2.0416E-008

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