Generalidades

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Biseccin

CLCULO DE RAICES: A'(x)= 7(x)^2-70x-1825CLCULO DE RAICES: A'(x)= 7(x)^2-70x-1825ITERXLXUf(XL)f(XU)Xrf(Xr)f(XL)*f(Xr)EaEs (0.5*10^(2-n))ITERXLXUf(XL)f(XU)Xrf(Xr)f(XL)*f(Xr)EaEs (0.5*10^(2-n))1030-1825237515-130023725000.0510-30-18256575-15800-14600000.0521530-1300237522.5143.75-18687533.3333333333FALSE20-15-1825800-7.5-906.251653906.25100FALSE31522.5-1300143.7518.75-676.5625879531.2520FALSE3-7.5-15-906.25800-11.25-151.5625137353.51562533.3333333333FALSE418.7522.5-676.5625143.7520.625-291.015625196890.2587890639.0909090909FALSE4-11.25-15-151.5625800-13.125299.609375-45409.545898437514.2857142857FALSE520.62522.5-291.015625143.7521.5625-79.7851562523218.72711181644.347826087FALSE5-11.25-13.125-151.5625299.609375-12.187567.87109375-10286.71264648447.6923076923FALSE621.562522.5-79.78515625143.7522.0312530.4443359375-2429.00609970092.1276595745FALSE6-11.25-12.1875-151.562567.87109375-11.71875-43.38378906256575.35552978524FALSE721.562522.03125-79.7851562530.444335937521.796875-25.05493164061999.01163578031.0752688172FALSE7-11.71875-12.1875-43.383789062567.87109375-11.95312511.8591308594-514.49403166771.9607843137FALSE821.79687522.03125-25.054931640630.444335937521.91406252.5985717773-65.10703824460.5347593583FALSE8-11.71875-11.953125-43.383789062511.8591308594-11.8359375-15.8584594727688.00006061790.9900990099FALSE921.79687521.9140625-25.05493164062.598571777321.85546875-11.2522125244281.9234156050.2680965147FALSE9-11.8359375-11.953125-15.858459472711.8591308594-11.89453125-2.023696899432.09271526430.4926108374FALSE1021.8554687521.9140625-11.25221252442.598571777321.884765625-4.332828521748.75390735830.1338688086FALSE10-11.89453125-11.953125-2.023696899411.8591308594-11.9238281254.9117088318-9.93980993370.2457002457FALSE1121.88476562521.9140625-4.33282852172.598571777321.8994140625-0.86863040923.7636266120.0668896321FALSE11-11.89453125-11.923828125-2.02369689944.9117088318-11.90917968751.4425039291-2.91919072880.12300123FALSE1221.899414062521.9140625-0.86863040922.598571777321.90673828120.8645951748-0.75101366050.0334336342TRUE12-11.89453125-11.9091796875-2.02369689941.4425039291-11.9018554688-0.29097199440.58883912290.0615384615FALSE1321.899414062521.9067382812-0.86863040920.864595174821.9030761719-0.00211149450.00183410840.0167196121TRUE13-11.9018554688-11.9091796875-0.29097199441.4425039291-11.90551757810.5756720901-0.16750445620.0307597662TRUE1421.903076171921.9067382812-0.00211149450.864595174821.90490722660.4312183708-0.00091051520.0083591072TRUE14-11.9018554688-11.9055175781-0.29097199440.5756720901-11.90368652340.1423265785-0.04141304840.0153822489TRUE1521.903076171921.9049072266-0.00211149450.431218370821.90399169920.2145475708-0.0004530160.0041797283TRUE15-11.9018554688-11.9036865234-0.29097199440.1423265785-11.9027709961-0.07432857530.02162753380.007691716TRUE1621.903076171921.9039916992-0.00211149450.214547570821.90353393550.1062165713-0.00022427570.0020899078TRUE16-11.9027709961-11.9036865234-0.07432857530.1423265785-11.90322875980.0339975348-0.00252698830.0038457101TRUE1721.903076171921.9035339355-0.00211149450.106216571321.90330505370.0520521717-0.00010990790.0010449648TRUE17-11.9027709961-11.9032287598-0.07432857530.0339975348-11.9029998779-0.0201658870.00149890160.001922892TRUE1821.903076171921.9033050537-0.00211149450.052052171721.90319061280.0249702469-0.00005272450.0005224851TRUE18-11.9029998779-11.9032287598-0.0201658870.0339975348-11.90311431880.0069157322-0.00013946190.0009614368TRUE1921.903076171921.9031906128-0.00211149450.024970246921.90313339230.0114293533-0.0000241330.0002612433TRUE19-11.9029998779-11.9031143188-0.0201658870.0069157322-11.9030570984-0.00662510030.0001336010.0004807207TRUE2021.903076171921.9031333923-0.00211149450.011429353321.90310478210.0046589236-0.00000983730.0001306218TRUE20-11.9030570984-11.9031143188-0.00662510030.0069157322-11.90308570860.0001453102-0.00000096270.0002403598TRUE2121.903076171921.9031047821-0.00211149450.004658923621.9030904770.0012737131-0.00000268940.0000653109TRUE21-11.9030570984-11.9030857086-0.00662510030.0001453102-11.9030714035-0.00323989650.00002146460.00012018TRUE2221.903076171921.903090477-0.00211149450.001273713121.9030833244-0.00041889110.00000088450.0000326555TRUE22-11.9030714035-11.9030857086-0.00323989650.0001453102-11.9030785561-0.00154729350.00000501310.00006009TRUE2321.903083324421.903090477-0.00041889110.001273713121.90308690070.0004274109-0.0000001790.0000163277TRUE23-11.9030785561-11.9030857086-0.00154729350.0001453102-11.9030821323-0.00070099170.00000108460.000030045TRUE2421.903083324421.9030869007-0.00041889110.000427410921.90308511260.0000042599-0.00000000180.0000081639TRUE24-11.9030821323-11.9030857086-0.00070099170.0001453102-11.9030839205-0.00027784080.00000019480.0000150225TRUE2521.903083324421.9030851126-0.00041889110.000004259921.9030842185-0.00020731560.00000008680.0000040819TRUE25-11.9030839205-11.9030857086-0.00027784080.0001453102-11.9030848145-0.00006626530.00000001840.0000075112TRUE2621.903084218521.9030851126-0.00020731560.000004259921.9030846655-0.00010152780.0000000210.000002041TRUE26-11.9030848145-11.9030857086-0.00006626530.0001453102-11.90308526160.0000395225-0.00000000260.0000037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Regla falsa

CLCULO DE RAICES: A'(x)= 7(x)^2-70x-1825CLCULO DE RAICES: A'(x)= 7(x)^2-70x-1825ITERXLXUf(XL)f(XU)Xrf(Xr)f(XL)*f(Xr)EaEs (0.5*10^(2-n))ITERXLXUf(XL)f(XU)Xrf(Xr)f(XL)*f(Xr)EaEs (0.5*10^(2-n))1030-1825237513.0357142857-1547.99107142862825083.705357140.0510-30-18256575-6.5178571429-1071.37276785711955255.301339290.05213.035714285730-1547.9910714286237519.7297297297-481.2454346238744963.63596342533.9285714286FALSE2-6.5178571429-30-1071.37276785716575-9.8080614203-465.0492187989498241.06873441133.5459183673FALSE319.729729729730-481.2454346238237521.4601554908-103.442968538249781.45635296378.0634353362FALSE3-9.8080614203-30-465.04921879896575-11.1418937517-176.074862757281883.47737536611.9713251723FALSE421.460155490830-103.4429685382237521.8165836507-20.4176002222112.05717738741.6337487376FALSE4-11.1418937517-30-176.07486275726575-11.6337322422-63.232661866611133.68225993034.2276930587FALSE521.816583650730-20.417600222237521.8863358824-3.961623256280.88683987610.3187021897FALSE5-11.6337322422-30-63.23266186666575-11.8086806144-22.27779201041408.68408932931.4815234485FALSE621.886335882430-3.9616232562237521.8998473574-0.76611506863.03505927270.0616966628FALSE6-11.8086806144-30-22.27779201046575-11.8701093495-7.7958737473173.67485388140.5175077437FALSE721.899847357430-0.7661150686237521.9024594197-0.14805896080.11343020090.0119258856TRUE7-11.8701093495-30-7.79587374736575-11.8915802171-2.721624383721.21744008270.1805552096FALSE821.902459419730-0.1480589608237521.9029641939-0.0286102230.00423599990.0023045931TRUE8-11.8915802171-30-2.72162438376575-11.8990728292-0.94936258542.58380836140.0629680332FALSE921.902964193930-0.028610223237521.9030617329-0.00552837280.0001581680.0004453215TRUE9-11.8990728292-30-0.94936258546575-11.9016860402-0.33106298810.31429881430.0219566451TRUE1021.903061732930-0.0055283728237521.9030805804-0.00106824630.00000590570.0000860495TRUE10-11.9016860402-30-0.33106298816575-11.9025972767-0.1154371020.03821695190.0076557789TRUE1121.903080580430-0.0010682463237521.9030842223-0.00020641680.00000022050.0000166273TRUE11-11.9025972767-30-0.1154371026575-11.9029150068-0.04024991340.00464633340.0026693465TRUE1221.903084222330-0.0002064168237521.903084926-0.00003988580.00000000820.0000032129TRUE12-11.9029150068-30-0.04024991346575-11.9030257903-0.01403392550.00056486430.0009307173TRUE1321.90308492630-0.0000398858237521.903085062-0.00000770710.00000000030.0000006208TRUE13-11.9030257903-30-0.01403392556575-11.9030644171-0.00489318380.00006867060.0003245112TRUE1421.90308506230-0.0000077071237521.9030850883-0.000001489200.00000012TRUE14-11.9030644171-30-0.00489318386575-11.903077885-0.00170609520.00000834820.0001131465TRUE1521.903085088330-0.0000014892237521.9030850934-0.000000287800.0000000232TRUE15-11.903077885-30-0.00170609526575-11.9030825808-0.000594860.00000101490.0000394505TRUE1621.903085093430-0.0000002878237521.9030850943-0.000000055600.0000000045TRUE16-11.9030825808-30-0.000594866575-11.9030842181-0.00020740830.00000012340.0000137551TRUE1721.903085094330-0.0000000556237521.9030850945-0.000000010700.0000000009TRUE17-11.9030842181-30-0.00020740836575-11.903084789-0.00007231650.0000000150.000004796TRUE1821.903085094530-0.0000000107237521.9030850946-0.000000002100.0000000002TRUE18-11.903084789-30-0.00007231656575-11.903084988-0.00002521440.00000000180.0000016722TRUE1921.903085094630-0.0000000021237521.9030850946-0.000000000400TRUE19-11.903084988-30-0.00002521446575-11.9030850574-0.00000879140.00000000020.000000583TRUE2021.903085094630-0.0000000004237521.9030850946-0.000000000100TRUE20-11.9030850574-30-0.00000879146575-11.9030850816-0.000003065300.0000002033TRUE2121.903085094630-0.0000000001237521.9030850946-000TRUE21-11.9030850816-30-0.00000306536575-11.9030850901-0.000001068800.0000000709TRUE2221.903085094630-0237521.9030850946-000TRUE22-11.9030850901-30-0.00000106886575-11.903085093-0.000000372600.0000000247TRUE2321.903085094630-0237521.9030850946000TRUE23-11.903085093-30-0.00000037266575-11.903085094-0.000000129900.0000000086TRUE2421.903085094621.9030850946-0021.9030850946000TRUE24-11.903085094-30-0.00000012996575-11.9030850944-0.000000045300.000000003TRUE2521.903085094621.9030850946-0021.9030850946000TRUE25-11.9030850944-30-0.00000004536575-11.9030850945-0.000000015800.000000001TRUE2621.903085094621.9030850946-0021.9030850946000TRUE26-11.9030850945-30-0.00000001586575-11.9030850945-0.000000005500.0000000004TRUE2721.903085094621.9030850946-0021.9030850946000TRUE27-11.9030850945-30-0.00000000556575-11.9030850946-0.000000001900.0000000001TRUE2821.903085094621.9030850946-0021.9030850946000TRUE28-11.9030850946-30-0.00000000196575-11.9030850946-0.000000000700TRUE2921.903085094621.9030850946-0021.9030850946000TRUE29-11.9030850946-30-0.00000000076575-11.9030850946-0.000000000200TRUE3021.903085094621.9030850946-0021.9030850946000TRUE30-11.9030850946-30-0.00000000026575-11.9030850946-0.000000000100TRUE

Punto Fijox=((70x+1825)/7)^1/2ITXiXi+1EaEs1016.14664936490.05216.146649364920.547038213921.4161710469FALSE320.547038213921.59131000784.8365374474FALSE421.591310007821.8317975851.1015473016FALSE521.83179758521.88680565010.251329801FALSE621.886805650121.89936853460.0573664237FALSE721.899368534621.9022366680.013095162TRUE821.90223666821.90289141630.0029893236TRUE921.902891416321.9030408820.0006823969TRUE1021.90304088221.90307500180.0001557764TRUE1121.903075001821.90308279060.0000355604TRUE1221.903082790621.90308456860.0000081177TRUE1321.903084568621.90308497450.0000018531TRUE1421.903084974521.90308506720.000000423TRUE1521.903085067221.90308508830.0000000966TRUE1621.903085088321.90308509310.000000022TRUE1721.903085093121.90308509420.000000005TRUE1821.903085094221.90308509450.0000000011TRUE1921.903085094521.90308509460.0000000003TRUE2021.903085094621.90308509460.0000000001TRUE

Newton-Raphsonf(Xi)=7x^2-70x-1825 f'(Xi)=14x-70f(Xi)=7x^2-70x-1825 f'(Xi)=14x-70ITXif(Xi)f'(Xi)Xi+1EaEsITXif(Xi)f'(Xi)Xi+1EaEs10-1825-70-26.07142857140.05110-18257036.07142857140.052-26.07142857144758.0357142857-435-15.133415435172.2772277228FALSE236.07142857144758.035714285743525.133415435143.5198040016FALSE3-15.1334154351837.4809195874-281.867816092-12.162232235924.4295877734FALSE325.1334154351837.4809195874281.86781609222.162232235913.4065159486FALSE4-12.162232235961.7955072254-240.2712513022-11.90504163612.1603502752FALSE422.162232235961.7955072254240.271251302221.90504163611.174116005FALSE5-11.90504163610.4630290322-236.6705829057-11.90308520780.0164363129TRUE521.90504163610.4630290322236.670582905721.90308520780.0089322043TRUE6-11.90308520780.0000267933-236.6431929091-11.90308509460.0000009512TRUE621.90308520780.0000267933236.643192909121.90308509460.0000005169TRUE7-11.90308509460-236.643191324-11.90308509460TRUE721.90308509460236.64319132421.90308509460TRUE8-11.90308509460-236.643191324-11.90308509460TRUE821.90308509460236.64319132421.90308509460TRUE

Secante

f(Xi)=7x^2-70x-1825 f'(Xi)=14x-70f(Xi)=7x^2-70x-1825 f'(Xi)=14x-70ITXi-1Xif(Xi-1)f(Xi)Xi+1EaEsITXi-1Xif(Xi-1)f(Xi)Xi+1EaEs105-1825-2000-52.14285714290.051011-1825-1748260.71428571430.0525-52.1428571429-200020857.14285714290ERROR:#DIV/0!ERROR:#DIV/0!211260.7142857143-1748455728.57142857111.95414847162080.9523809524FALSE3-52.1428571429020857.1428571429-1825-4.1954022989100FALSE3260.714285714311.9541484716455728.571428571-1661.478733243112.85777476957.0278591285FALSE40-4.1954022989-1825-1408.1120359361-18.366107576677.1568238869FALSE411.954148471612.8577747695-1661.4787332431-1567.78762970527.978678229554.0443809962FALSE5-4.1954022989-18.3661075766-1408.11203593611821.8248829798-10.373213556677.0532099479FALSE512.857774769527.9786782295-1567.7876297051696.13757223720.120920806239.052673081FALSE6-18.3661075766-10.37321355661821.8248829798-345.6501346122-11.647851036410.9431128183FALSE627.978678229520.12092080621696.137572237-399.504277807921.61889036846.9289844976FALSE7-10.3732135566-11.6478510364-345.6501346122-59.9433910966-11.91527942122.2444155558FALSE720.120920806221.6188903684-399.5042778079-66.687380465621.91904239471.3693665119FALSE8-11.6478510364-11.9152794212-59.94339109662.8867452846-11.90299236160.1032266442FALSE821.618890368421.9190423947-66.68738046563.77796886821.90294987510.0734719279FALSE9-11.9152794212-11.90299236162.8867452846-0.0219445566-11.90308506110.0007787854TRUE921.919042394721.90294987513.777968868-0.031998632121.90308503080.0006170621TRUE10-11.9029923616-11.9030850611-0.0219445566-0.0000079129-11.90308509460.0000002809TRUE1021.902949875121.9030850308-0.0319986321-0.000015097121.90308509460.0000002913TRUE11-11.9030850611-11.9030850946-0.00000791290-11.90308509460TRUE1121.903085030821.9030850946-0.00001509710.000000000121.90308509460TRUE12-11.9030850946-11.903085094600-11.90308509460TRUE1221.903085094621.90308509460.0000000001021.90308509460TRUE

Raices mltiples

f(Xi)=x^3+9x^2+24x+20 f'(Xi)=3x^2+18x+24 f''(Xi)=6x+18ITXif(Xi)f'(Xi)f''(Xi)Xi+1mEaEs10202418-2.22222222222.66666666670.052-2.22222222220.1371742112-1.18518518524.6666666667-2.0095693781.837320574210.582010582FALSE3-2.0095693780.0002738427-0.0571415495.9425837321-2.00001535991.99359491280.4776972348FALSE4-2.00001535990.0000000007-0.00009215885.9999078405-1.99999999982.00000210880.0007680036TRUE5-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE6-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE7-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE8-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE9-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE10-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE11-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE12-1.999999999800.00000000096.0000000009-1.9999999998ERROR:#DIV/0!0TRUE

Ejercicio

f(Xi)=2x^3-11,7x^2+17,7x-5 f'(Xi)=6x^2-23.4x+17.7 f''(Xi)=12x-23.4f(Xi)=2x^3-11,7x^2+17,7x-5 f'(Xi)=6x^2-23.4x+17.7 f''(Xi)=12x-23.4ITXif(Xi)f'(Xi)f''(Xi)Xi+1mEaEsITXif(Xi)f'(Xi)f''(Xi)Xi+1mEaEs10-517.7-23.40.45086351831.59605685470.0513-3.21.512.63.11275546160.05285412260.0520.45086351830.7852338918.3694611452-17.98963778080.37278729280.832179994620.9439074058FALSE23.1127554616-2.94790280522.997001580813.95306553913.28904984170.179230655.3600397857FALSE30.37278729280.07599457739.8105995419-18.9265524860.36515517560.98527616322.0901024313FALSE33.2890498417-2.19176130915.64332687116.06859810013.47347841040.47486498355.3096218535FALSE40.36515517560.00056681429.955398704-19.01813789250.36509824650.99989124630.0155928359TRUE43.4734784104-0.86514652248.810918802418.28174092523.55504977340.83074789842.2945209807FALSE50.36509824650.00000003089.9564814103-19.01882104250.36509824340.99999999140.000000848TRUE53.5550497734-0.084520012310.342108649819.26059728033.56309967070.9850082960.2259240023FALSE60.365098243409.9564814692-19.01882107970.3650982434ERROR:#DIV/0!0TRUE63.5630996707-0.000642004210.497543286519.35719604893.56316082140.99988723980.0017161917TRUE70.365098243409.9564814692-19.01882107970.3650982434ERROR:#DIV/0!0TRUE73.5631608214-0.000000036210.498727014519.3579298573.56316082491.0000000270.0000000968TRUE80.365098243409.9564814692-19.01882107970.3650982434ERROR:#DIV/0!0TRUE83.5631608249-010.498727081219.35792989833.56316082491.09361740430TRUE

f(Xi)=2x^3-11,7x^2+17,7x-5 f'(Xi)=6x^2-23.4x+17.7 f''(Xi)=12x-23.4ITXif(Xi)f'(Xi)f''(Xi)Xi+1mEaEs11.51.975-3.9-5.41.79768115940.5878260870.0521.79768115940.6275429618-4.9757938248-1.8278260871.91821605470.95572227596.2836975536FALSE31.91821605470.0180106626-5.1089386849-0.38140734331.92174045090.99973688650.1833960528FALSE41.92174045090.0000024576-5.1102083873-0.33911458971.92174093180.99999996830.0000250252TRUE51.92174093180-5.1102085504-0.33910881871.92174093180.99010290660TRUE61.92174093180-5.1102085504-0.33910881871.9217409318ERROR:#DIV/0!0TRUE71.92174093180-5.1102085504-0.33910881871.9217409318ERROR:#DIV/0!0TRUE81.92174093180-5.1102085504-0.33910881871.9217409318ERROR:#DIV/0!0TRUE