Hoja1

SEGUNDA PRCTICA DIRIGIDA

2usando el mtodo de la secante, encontrar la raz de la ecuacin y el de regla falsa.En el intervalo de -1 a 2.5.Se pide calcular el valor del error aproximado .Grafique los valores de error contra el nmero de iteraciones

1Encontrar la raz real para el mtodo grfico, mtodo de biseccin,regla falsa,punto fijo,mtodo de Newton Rapson, y graficar el comparativo de los errores relativos para los diferentes mtodosantes indocados, de la siguiente ecuacin.

MTODO DE LA SECANTE

MTODO GRFICOITERACINXiXsf(Xi)f(Xs)Xrf(Xr)e1-12.5-53.751-922.513.75-92.0588235294-1.4013840831.0588235294xf(x)312.0588235294-9-1.4013840832.25409836070.73468153720.19527483120142.05882352942.2540983607-1.4013840830.73468153722.1869352493-0.02581314510.06716311140.050.901229424552.25409836072.18693524930.7346815372-0.02581314512.189214938-0.0004437420.00227968870.10.80483741862.18693524932.189214938-0.0258131451-0.0004437422.18925481250.00000027750.00003987460.150.71070797640.20.6187307531Xr=2.1892540.250.52880078310.30.4408182207MTODO DE LA REGLA FALSA0.350.35468808970.40.2703200460.450.18762815160.50.1065306597ITERACINXiXsf(Xi)f(Xs)Xrf(Xr)e0.550.02694981041-12.5-53.751-90.6-0.0511883639212.5-93.752.0588235294-1.4013840831.05882352940.65-0.127954223232.05882352942.5-1.4013840833.752.1788413098-0.11563425950.12001778040.7-0.203414696242.17884130982.5-0.11563425953.752.1884482578-0.00897918420.0096069480.75-0.277633447352.18844825782.5-0.00897918423.752.1891924706-0.00069392080.00074421280.8-0.350671035962.18919247062.5-0.00069392083.752.1892499735-0.00005360710.00005750290.85-0.422585068172.18924997352.5-0.00005360713.752.1892544157-0.00000414120.00000444220.9-0.493430340382.18925441572.5-0.00000414123.752.1892547589-0.00000031990.00000034320.95-0.563258976592.18925475892.5-0.00000031993.752.1892547854-0.00000002470.00000002651-0.6321205588102.18925478542.5-0.00000002473.752.1892547874-0.00000000190.000000002112.18925478742.5-0.00000000193.752.1892547876-0.00000000010.0000000002122.18925478762.5-0.00000000013.752.1892547876-00MTODO DE BISECCIN132.18925478762.5-03.752.1892547876-00142.18925478762.5-03.752.1892547876-00

ITERACINXiXsf(Xi)f(Xs)Xrf(Xr)e1011-0.63212055880.50.10653065970.5120.510.1065306597-0.63212055880.75-0.27763344730.25133.333333333330.50.750.1065306597-0.27763344730.625-0.08973857150.12512040.50.6250.1065306597-0.08973857150.56250.00728282470.06250.7511.111111111150.56250.6250.0072828247-0.08973857150.59375-0.04149754980.031250.6255.263157894760.56250.593750.0072828247-0.04149754980.578125-0.01717583920.0156250.6252.702702702770.56250.5781250.0072828247-0.01717583920.5703125-0.00496376040.00781250.593751.369863013780.56250.57031250.0072828247-0.00496376040.566406250.0011552020.003906250.5781250.689655172490.566406250.57031250.001155202-0.00496376040.568359375-0.00190535960.0019531250.57031250.3436426117100.566406250.5683593750.001155202-0.00190535960.5673828125-0.00037534920.00097656250.57031250.1721170396110.566406250.56738281250.001155202-0.00037534920.56689453120.00038985880.00048828120.5683593750.0861326443120.56689453120.56738281250.0003898588-0.00037534920.56713867190.00000723790.00024414060.56738281250.043047783130.56713867190.56738281250.0000072379-0.00037534920.5672607422-0.00018405990.00012207030.56738281250.0215192597140.56713867190.56726074220.0000072379-0.00018405990.567199707-0.0000884120.00006103520.56738281250.0107607877

MTODO DE LA REGLA FALSA

ITERACINXiXsf(Xi)f(Xs)Xrf(Xr)e1011-0.63212055880.6126998368-0.0708139479200.61269983681-0.07081394790.5721814121-0.00788827290.0405184247300.57218141211-0.00788827290.5677032142-0.0008773920.0044781979400.56770321421-0.0008773920.5672055526-0.00009757270.0004976616500.56720555261-0.00009757270.5671502142-0.00001085060.0000553384600.56715021421-0.00001085060.5671440604-0.00000120660.0000061539700.56714406041-0.00000120660.567143376-0.00000013420.0000006843800.5671433761-0.00000013420.5671432999-0.00000001490.0000000761900.56714329991-0.00000001490.5671432915-0.00000000170.00000000851000.56714329151-0.00000000170.5671432905-0.00000000020.00000000091100.56714329051-0.00000000020.5671432904-00.00000000011200.56714329041-00.5671432904-001300.56714329041-00.5671432904-001400.56714329041-00.5671432904-00

MTODO DEL PUNTO FIJO

ITERACINXif(Xi)g(Xi)e101121-0.63212055880.3678794412130.36787944120.32432118640.69220062760.632120558840.6922006276-0.1917271270.50047350060.324321186450.50047350060.10577003450.60624353510.19172712760.6062435351-0.06084774910.5453957860.105770034570.5453957860.03421654950.57961233550.060847749180.5796123355-0.01949687410.56011546140.034216549590.56011546140.01102765370.57114311510.0194968741100.5711431151-0.00626376770.56487934740.0110276537110.56487934740.00354937760.5684287250.0062637677120.568428725-0.00201399190.56641473310.0035493776130.56641473310.00114190420.56755663730.0020139919140.5675566373-0.00064772540.56690891190.0011419042150.56690891190.00036732030.56727623220.0006477254160.5672762322-0.00020833380.56706789840.0003673203170.56706789840.00011815170.56718605010.0002083338

MTODO DE NEWTON RAPHSON

ITERACINXif(Xi)f'(Xi)e101-220.50.1065306597-1.60653065970.530.56631100320.0013045098-1.5676155130.066311003240.5671431650.0000001965-1.56714336150.000832161850.56714329040-1.56714329040.0000001254Xr=0.56714329

0.57

Hoja23Mediante el mtodo de Newton Raphson y el mtodo de la secante. Grafique la funcin y verifique que la solucin no existe en el conjunto de los nmeros reales.Como podra obtener races complejas.

xy-417-3.8515.8225-3.714.69-3.5513.6025-3.412.56-3.2511.5625-3.110.61-2.959.7025-2.88.84-2.658.0225-2.57.25-2.356.5225-2.25.84-2.055.2025-1.94.61-1.754.0625-1.63.56-1.453.1025-1.32.69-1.152.3225-12-0.851.7225-0.71.49-0.551.3025-0.41.16-0.251.0625-0.11.010.051.00250.21.040.351.12250.51.250.651.42250.81.640.951.90251.12.211.252.56251.42.961.553.40251.73.891.854.4225252.155.62252.36.292.457.00252.67.762.758.56252.99.413.0510.30253.211.243.3512.22253.513.253.6514.32253.815.443.9516.60254.117.814.2519.06254.420.364.5521.70254.723.094.8524.52255265.1527.52255.329.095.4530.70255.632.365.7534.06255.935.816.0537.60256.239.446.3541.32256.543.256.6545.22256.847.246.9549.30257.151.417.2553.56257.455.767.5558.00257.760.297.8562.62258658.1567.42258.369.898.4572.40258.674.968.7577.56258.980.219.0582.90259.285.649.3588.42259.591.259.6594.12259.897.049.95100.002510.1103.0110.25106.062510.4109.1610.55112.302510.7115.4910.85118.72251112211.15125.322511.3128.6911.45132.102511.6135.5611.75139.062511.9142.6112.05146.202512.2149.8412.35153.522512.5157.2512.65161.022512.8164.8412.95168.702513.1172.6113.25176.562513.4180.5613.55184.602513.7188.69

Hoja3