Profesor Margarito Filomeno Nicolas 2022-01-04T01:09:33Z 2022-12-31T02:05:09Z 16.00 836318a7-025e-496d-8d66-beb15bdd159a 11340 16170 2340 2340 False False Universidad Autónoma Metropolitana. Unidad Lerma. Ajuste de curvas: tablas equiespaciadas ejercicio 01 Autores: Dra. Blanca Rafaela Silva López, M. en C. Hugo Pablo Leyva Colaborador: Iván Córdova de la Fuente Revisor: Margarito Filomeno Nicolás Fecha: 10/11/2022 Ejercicio 1 - Ajuste de curvas - Equiespaciadas Hallar los valores solicitados con las curva solicitada x y P1 y( 21.041599999999999 ) 20.846 4.9031599999999997 P2 y( 20.911300000000001 ) 20.851299999999998 4.9046000000000003 P3 x( 4.90381 ) 20.8567 4.9060499999999996 P4 x( 4.9023700000000003 ) 20.861999999999998 4.9074900000000001 20.8674 4.9089400000000003 Ajustar a la curva: 20.872699999999998 4.91038 20.8781 4.9118300000000001 Mejor curva 20.883400000000002 4.9132699999999998 20.8887 4.91472 20.894100000000002 4.9161599999999996 20.8994 4.9176000000000002 20.904800000000002 4.9190500000000004 20.9101 4.92049 20.915400000000002 4.9219299999999997 20.9208 4.9233700000000002 20.926100000000002 4.9248099999999999 20.9315 4.9262499999999996 20.936800000000002 4.9276900000000001 20.9421 4.9291299999999998 20.947500000000002 4.9305700000000003 20.9528 4.93201 20.958200000000001 4.9334499999999997 20.9635 4.9348900000000002 20.968800000000002 4.9363299999999999 20.9742 4.9377599999999999 20.979500000000002 4.9391999999999996 20.9849 4.9406400000000001 20.990200000000002 4.9420799999999998 20.9955 4.9435099999999998 21.000900000000001 4.9449500000000004 21.0062 4.9463800000000004 21.011600000000001 4.9478200000000001 21.0169 4.9492500000000001 21.022200000000002 4.9506899999999998 21.0276 4.9521199999999999 21.032900000000001 4.9535600000000004 Criterio de Convergencia ND Tol NCSINV TolINV NumPtos MaxIter 5 4.9999999999999996E-6 6 4.9999999999999996E-6 36 34 Ajuste a curva polinomial Ajuste a curva exponencial Ajuste a curva potencial n 1 n 2 A*exp(B*x) A*x^B x y ∑x ∑x² ∑y ∑yx y_p ∑(y-y_p)² σ_xy Checa σ_xy Checa n ∑x³ ∑x⁴ ∑yx² y_p ∑(y-y_p)² σ_xy Checa σ_xy Checa OSC Checa n ∑ln(y) ∑ln(y)x y_p ∑(y-y_p)² σ_xy Checa σ_xy ∑ln(x) ∑ln(x)² ∑ln(y)ln(x) y_p ∑(y-y_p)² σ_xy Checa σ_xy 20.846 4.9031599999999997 20.846 434.55571600000002 4.9031599999999997 102.21127335999999 4.9031898809770933 8.9287279206555029E-10 9058.7484557360003 188838.67030827267 2130.6962044625598 4.9032530246076584 8.6535776300547393E-9 1.5898798952184354 33.142636295723506 4.9032314030026605 5.0983887889682737E-9 3.0371620833171304 9.2243535203392515 4.8287229347856444 4.9031950686827779 1.2298125117937285E-9 20.851299999999998 4.9046000000000003 20.851299999999998 434.77671168999996 4.9046000000000003 102.26728598 4.9046189881182185 3.6054863346873972E-10 9065.6596484616948 189030.78902796935 2132.405860154774 4.9046877140257132 7.6937503067717529E-9 1.5901735402526425 33.157185539869921 4.9046534328052127 2.8550646728680616E-9 3.0374162964210267 9.2258977577640273 4.8300190253008939 4.9046232787117727 5.4189842178406827E-10 20.8567 4.9060499999999996 20.8567 435.00193488999997 4.9060499999999996 102.32401303499999 4.9060750595450253 6.2798079689712567E-10 9072.7048554202629 189226.68335804378 2134.141242667084 4.9061491388401297 9.8285096223476217E-9 1.5904691373864832 33.171937657728662 4.9061027175206045 2.7791369787251511E-9 3.0376752395508899 9.2274708609805565 4.8313287179087823 4.9060784904807493 8.11707493349593E-10 20.861999999999998 4.9074900000000001 20.861999999999998 435.2230439999999 4.9074900000000001 102.38005638 4.9075041666861505 2.0069499648383321E-10 9079.6231439279964 189419.09802862586 2135.8527361995598 4.9075831722059258 8.6810599570498902E-9 1.5907626094690011 33.186489558742295 4.9075255800586497 1.2659405735064642E-9 3.0379293222537793 9.2290145670093064 4.8326243760508154 4.9075068072458672 2.8248351363568809E-10 20.8674 4.9089400000000003 20.8674 435.44838276000002 4.9089400000000003 102.436814556 4.9089602381129573 4.0958121606184429E-10 9086.6755824060238 189615.29404829949 2137.5899840658744 4.9090439285897336 1.0801151763951159E-8 1.5910580325526569 33.201244388489314 4.9089757134699123 1.2754519331586501E-9 3.0381881325903835 9.2305871290130419 4.8339336327640865 4.9089621277410238 4.8963692280322794E-10 20.872699999999998 4.91038 20.872699999999998 435.66960528999994 4.91038 102.492888626 4.9103893452540825 8.7333773868020094E-11 9093.6009703365817 189808.00497354433 2139.30331642391 4.9104773059032709 9.4684388113754805E-9 1.591351331887096 33.215798945079783 4.910399409231097 3.7671825177677732E-10 3.0384420850259781 9.232130304057014 4.8352288588678949 4.9103905511954924 1.1132772631937673E-10 20.8781 4.9118300000000001 20.8781 435.89505960999998 4.9118300000000001 102.549677923 4.9118454166808894 2.3767404964017097E-10 9100.6606440435407 190004.50299240544 2141.0424306441864 4.9119373938564763 1.1533440408826121E-8 1.5916465811254108 33.230556485394438 4.9118503918352223 4.1582694372844663E-10 3.038700762705453 9.2337023252667016 4.8365376800233122 4.9118459803692005 2.5537219977992632E-10 20.883400000000002 4.9132699999999998 20.883400000000002 436.11639556000006 4.9132699999999998 102.605782718 4.9132745238220146 2.0464965621300389E-11 9107.5931350377068 190197.51047624645 2142.7576028130816 4.9133701151177505 1.0023036802227374E-8 1.5919397079150233 33.245113696272597 4.9132749213074796 2.4219267310291957E-11 3.0389545850072599 9.2352449697366481 4.837832474423478 4.9132745104663016 2.0344306259565885E-11 20.8887 4.91472 20.8887 436.33778769000003 4.91472 102.66211166399999 4.9147036309631398 2.6794536773050896E-10 9114.5291457201038 190390.66496620353 2144.4780519157971 4.914802511418559 6.8081341926139672E-9 1.5922347835124793 33.259714722357124 4.9146998639202133 4.0546170917559094E-10 3.0392083428996544 9.2367873515508627 4.839133237906152 4.9147030933691012 2.8583416834881303E-10 20.894100000000002 4.9161599999999996 20.894100000000002 436.5634148100001 4.9161599999999996 102.718738656 4.9161597023899466 8.8571743674085345E-14 9121.5996453816242 190587.61515056822 2146.21559735233 4.9162615998493653 1.0322529391120972E-8 1.5925277379601581 33.274433809713344 4.9161521172732998 6.2137380224150286E-11 3.0394668224668475 9.2383585648767141 4.8404352233880781 4.9161586849640377 1.7293195810951394E-12 20.8994 4.9176000000000002 20.8994 436.78492036 4.9176000000000002 102.77488944000001 4.9175888095310718 1.2522659483727038E-10 9128.5427645717846 190781.06665389155 2147.9335243623359 4.9176933400979124 8.7123738782545423E-9 1.5928206066106627 33.288994985798887 4.9175778943272581 4.8866076737988355E-10 3.0397204504247077 9.2399004167301886 4.8417293717723195 4.9175873744396847 1.5940477327904157E-10 20.904800000000002 4.9190500000000004 20.904800000000002 437.01066304000005 4.9190500000000004 102.83175644000002 4.9190448809578786 2.6204592244234435E-11 9135.6205087185936 190978.31961066046 2149.6773020269125 4.9191517600981136 1.035511756801746E-8 1.5931154224291584 33.303759282797074 4.9190309981146374 3.6107164734738117E-10 3.0399787976735504 9.2414710903047244 4.8430371064313835 4.9190430745945299 4.7961240929805971E-11 20.9101 4.92049 20.9101 437.23228201000001 4.92049 102.887937949 4.9204739880990029 2.5638097354069851E-10 9142.570740057301 191172.06843167217 2151.397071307385 4.9205828442944028 8.6200630031568213E-9 1.5934081190410487 33.318323109960232 4.9204576100984641 1.0491057215103849E-9 3.0402322958298718 9.2430124126069728 4.8443308239461249 4.9204718705964146 3.2867527436507771E-10 20.915400000000002 4.9219299999999997 20.915400000000002 437.45395716000007 4.9219299999999997 102.944134722 4.921903095240129 7.2386610369791196E-10 9149.5244955842663 191365.96463494317 2153.1177553645189 4.9220136035302264 6.9895502663732707E-9 1.5937007300067003 33.33288824838214 4.9218846358267374 2.0579082157706668E-9 3.0404857297411638 9.244553472759657 4.8456243270634474 4.9219007193463833 8.5735667620381156E-10 20.9208 4.9233700000000002 20.9208 437.67987263999999 4.9233700000000002 103.00083909600001 4.923359166666935 1.1736110530340691E-10 9156.613079526911 191563.67091416661 2154.8599545595966 4.9234710240080268 1.0205850197755411E-8 1.5939932553762206 33.347614097074839 4.9233390122207785 9.6024246109437296E-10 3.040743879383339 9.2461233400072373 4.8469252350635665 4.923356581745252 1.8004956048785457E-10 20.926100000000002 4.9248099999999999 20.926100000000002 437.90166121000004 4.9248099999999999 103.05706654100001 4.9247882738080611 4.7202741616389806E-10 9163.5739526465823 191757.86489047765 2156.5824801436202 4.924901127191589 8.3041650469169191E-9 1.5942856951996727 33.36218188631787 4.9247668736101389 1.8598855024461363E-9 3.0409971836915837 9.2476638712201442 4.8482183091019833 4.924785536951843 5.9844072512940122E-10 20.9315 4.9262499999999996 20.9315 438.12769225 4.9262499999999996 103.11380187499999 4.926244345234867 3.1976368704755607E-11 9170.6697903308741 191955.8747163107 2158.3265439465622 4.9263578792387843 1.1637930160776492E-8 1.5945780495270763 33.376910443675996 4.9262221016817183 7.7831616292563237E-10 3.0412552013528904 9.2492331997560093 4.8495187870873675 4.9262415077922554 7.2117592369398529E-11 20.936800000000002 4.9276900000000001 20.936800000000002 438.34959424000004 4.9276900000000001 103.17005999200001 4.9276734523759931 2.7382386027856922E-10 9177.6377846840332 192150.36677037267 2160.0509120405059 4.9277873263700869 9.47242231426258E-9 1.5948703184084072 33.391480882453145 4.9276507992215288 1.536701032756285E-9 3.0415083761905746 9.2507732024374256 4.8508114323768989 4.9276705694089635 3.7754786803142546E-10 20.9421 4.9291299999999998 20.9421 438.57155240999998 4.9291299999999998 103.22633337299999 4.9291025595171174 7.5298010081876203E-10 9184.6093077254609 192345.00658331736 2161.7761961307033 4.9292164485409238 7.4733502278866036E-9 1.5951625018935971 33.406052630905897 4.9290799111106338 2.5088968379167277E-9 3.0417614869469838 9.2523129434739264 4.8521038636819389 4.9290996837162808 9.1907705852893034E-10 20.947500000000002 4.9305700000000003 20.947500000000002 438.79775625000008 4.9305700000000003 103.28311507500001 4.9305586309439242 1.2925543606212111E-10 9191.7159990468772 192543.47089003448 2163.523053033563 4.9306722010657182 1.0445057833874423E-8 1.595454600032534 33.420785234181508 4.9305364136492917 1.1280429539212882E-9 3.0420193075053046 9.2538814672350522 4.8534036975471215 4.9305558166239347 2.0116815661891663E-10 20.9528 4.93201 20.9528 439.01982784 4.93201 103.339419128 4.9319877380850494 4.9559285726699811E-10 9198.6946487659516 192738.40923666325 2165.2501811051584 4.9321006671842955 8.2205383080763414E-9 1.5957466128750626 33.435359630248612 4.9319663624211323 1.9042382894362037E-9 3.0422722889888867 9.2554206803496797 4.8546957005976799 4.9319850372719207 6.2313779316011383E-10 20.958200000000001 4.9334499999999997 20.958200000000001 439.24614724000008 4.9334499999999997 103.39623179 4.9334438095118562 3.8322143453967143E-11 9205.8086030853701 192937.17786518382 2166.9989051011785 4.9335557512784867 1.1183332901634713E-8 1.5960385404709834 33.450094938898964 4.933423717882393 6.9074970589192378E-10 3.0425299779025314 9.2569886664355785 4.8559951052707699 4.933441278503027 7.6064509443403012E-11 20.9635 4.9348900000000002 20.9635 439.46833225 4.9348900000000002 103.452566515 4.9348729166529814 2.9184074536391931E-10 9212.7943831228749 193132.41505059641 2168.7278781372024 4.9349835613448025 8.7537252412181604E-9 1.5963303828700537 33.46467198129637 4.9348545040270464 1.2599640959386841E-9 3.0427828302452671 9.2585273520353972 4.8572866803958528 4.9348706054452878 3.7614875249416038E-10 20.968800000000002 4.9363299999999999 20.968800000000002 439.69057344000009 4.9363299999999999 103.50891650400001 4.9363020237941067 7.8266809618051003E-10 9219.7836963486752 193327.80037199613 2170.4577683890757 4.9364110464506528 6.5685271634292936E-9 1.5966221401219871 33.479250331789927 4.9362857051267328 1.9620357977457966E-9 3.0430356186698577 9.2600657764934429 4.8585780419481033 4.9362999850208205 9.0089897514142787E-10 20.9742 4.9377599999999999 20.9742 439.91706563999998 4.9377599999999999 103.565565792 4.9377580952209126 3.6281833715952631E-12 9226.908518146487 193527.02464130806 2172.2048900345662 4.9378651310224431 1.1052531879939794E-8 1.5969117870686926 33.493947204336173 4.9377443369182048 2.4533213132078627E-10 3.0432931109822738 9.2616329593521662 4.8598706404325442 4.937756388142799 1.3045512439550937E-11 20.979500000000002 4.9391999999999996 20.979500000000002 440.13942025000006 4.9391999999999996 103.6219464 4.9391872023620387 1.6377953737865657E-10 9233.9049671348766 193722.70925800616 2173.9366244988 4.9392919600760337 8.4566555841919303E-9 1.5972033747657577 33.508528200898219 4.9391763761240615 5.5808751434006215E-10 3.0435457704629965 9.2631708569031943 4.8611615758375457 4.9391858739433179 1.9954547737511169E-10 20.9849 4.9406400000000001 20.9849 440.36602800999998 4.9406400000000001 103.678836336 4.9406432737888446 1.0717693398111116E-11 9241.0370611870476 193922.23862530407 2175.6900126273263 4.9407453762172189 1.1104147155329676E-8 1.5974948774642219 33.523270254098946 4.9406358620850179 1.7122340400049901E-11 3.0438031314656464 9.2647375031200756 4.8624599105259279 4.9406423852709445 5.6895174777989808E-12 20.990200000000002 4.9420799999999998 20.990200000000002 440.58849604000005 4.9420799999999998 103.73524761600001 4.9420723809299707 5.8050228108450078E-11 9248.0406495788102 194118.22284278914 2177.4235945093633 4.9421715492185507 8.3812594172847883E-9 1.597786295213625 33.537853893793034 4.942068739887838 1.267901258961539E-10 3.0440556621339789 9.2662748741699374 4.8637504188251084 4.9420719772501691 6.4364514845899858E-11 20.9955 4.9435099999999998 20.9955 440.81102025000001 4.9435099999999998 103.791464205 4.943501488071095 7.2452933680893514E-11 9255.0477756588753 194314.35557384591 2179.1536867160776 4.9435973972594143 7.6382809531520277E-9 1.5980756052113034 33.552396369213923 4.9435020332523072 6.3469068798438561E-11 3.0443081290466734 9.2678119845796569 4.8650345557759538 4.9435016218054582 7.0194143778431614E-11 21.000900000000001 4.9449500000000004 21.000900000000001 441.03780081000008 4.9449500000000004 103.84840045500002 4.9449575594979018 5.7146008521764205E-11 9262.1907510307319 194514.3417433213 2180.9098731154099 4.9450498138782013 9.9628102815051054E-9 1.5983668538000988 33.567142459970498 4.944962797409338 1.6377368575339227E-10 3.0445652939479393 9.2693778291123028 4.8663322500765407 4.9449582948480071 6.8804503454000709E-11 21.0062 4.9463800000000004 21.0062 441.26043843999997 4.9463800000000004 103.90464755600001 4.946386666639027 4.4444075910958464E-11 9269.2050219583271 194710.77453226101 2182.6418074908474 4.9464750058668034 9.026114726989303E-9 1.5986559959093929 33.581687581271886 4.9463969301052018 2.8662846212770203E-10 3.0448176322444711 9.2709144136268264 4.8676159642382641 4.9463880455128759 6.4730277429456371E-11 21.011600000000001 4.9478200000000001 21.011600000000001 441.48733456000008 4.9478200000000001 103.96161471200001 4.9478427380658339 5.1701963785992575E-10 9276.3552788408979 194911.06657689344 2184.3998636826595 4.9479267540549854 1.1396428255800354E-8 1.5989470755338531 33.596436372287108 4.947858549680423 1.48607786071073E-9 3.045074666169604 9.2724797225479243 4.868913232254112 4.9478448266435437 6.1636222964299219E-10 21.0169 4.9492500000000001 21.0169 441.71008560999996 4.9492500000000001 104.01789232500001 4.9492718452069591 4.7721306707781902E-10 9283.3766982568086 195107.79972959351 2186.1336412052924 4.9493512899913288 1.0259662343354892E-8 1.5992360499495037 33.610984138183724 4.9492935221991887 1.8941818222097882E-9 3.0453268759809511 9.2740157815718991 4.8701965239488381 4.9492746833718222 6.092688445052236E-10 21.022200000000002 4.9506899999999998 21.022200000000002 441.93289284000008 4.9506899999999998 104.074395318 4.9507009523480843 1.1995392856314534E-10 9290.4016598610506 195304.68177393099 2187.8727532540597 4.9507755009672074 7.3104153934364441E-9 1.5995269608055604 33.625575675446655 4.9507289108871149 1.5140571360802571E-9 3.0455790221985475 9.2755515804558613 4.8714857572704133 4.9507045926190907 2.1294453193121246E-10 21.0276 4.9521199999999999 21.0276 442.15996175999999 4.9521199999999999 104.131198512 4.9521570237748902 1.370759907130828E-9 9297.5628119045759 195505.43178360464 2189.629189830931 4.9522262496329876 1.12889845100371E-8 1.5998157677219689 33.640286037350471 4.9521918105269949 5.156751787300869E-9 3.0458358605202367 9.2771160892310505 4.8727762355532862 4.9521615352891413 1.7251802440609025E-9 21.032900000000001 4.9535600000000004 21.032900000000001 442.38288241000004 4.9535600000000004 104.18773212400002 4.9535861309160163 6.8282477182935808E-10 9304.5949274412906 195702.61464937992 2191.3701509908801 4.9536498045566066 8.0648583872419659E-9 1.6001065100052134 33.654880214288653 4.9536280397733279 4.6294107544544982E-9 3.0460878784481289 9.2786513632286223 4.87406504435282 4.9535915505308603 9.9543599754168477E-10 ∑ 753.82080000000019 15784.716311260005 177.42213000000004 3715.1546526889997 1.1200701530329296E-8 1.8150272668774475E-5 330528.18110168685 6921229.5716807023 77794.528640303688 3.3469778188623553E-7 1.0070926981591924E-4 OSCILA 57.420297485591725 1202.3564671842919 4.9245848380915938E-8 3.8057946677678988E-5 109.4987601303864 333.05521020033916 174.65171675279504 1.4393761334320117E-8 2.057537172441E-5 Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales NP ∑x ∑y NP ∑x ∑x² ∑y NP ∑x ∑ln(y) NP ∑ln(x) ∑ln(y) ∑x ∑x² ∑yx ∑x ∑x² ∑x³ ∑yx ∑x ∑x² ∑ln(y)x ∑ln(x) ∑ln(x)² ∑ln(y)ln()x ∑x² ∑x³ ∑x⁴ ∑yx² 36 753.82080000000019 177.42213000000004 36 753.82080000000019 57.420297485591725 36 109.4987601303864 57.420297485591725 753.82080000000019 15784.716311260005 3715.1546526889997 36 753.82080000000019 15784.716311260005 177.42213000000004 753.82080000000019 15784.716311260005 1202.3564671842919 109.4987601303864 333.05521020033916 174.65171675279504 753.82080000000019 15784.716311260005 330528.18110168685 3715.1546526889997 Matriz Inversa 15784.716311260005 330528.18110168685 6921229.5716807023 77794.528640303688 a A B Matriz Inversa 0.44935529268695973 1.5673014090175557 5.4712614653908531E-2 3957.3658388903582 -188.98943913467613 Matriz Inversa 5.4712614653908531E-2 36611.059191954249 -12036.639769627884 -188.9894391346761 9.0255135024774304 -12036.639769627884 3957.2962396161033 706191501.02441788 -67451072.77597563 1610616.6942531362 a -67451072.77556923 6442521.024503178 -153836.64076719026 a A B -0.71778511221054941 1610616.6942337276 -153836.64076626339 3673.3671658046192 -1.8896358567290008 0.15112683063629739 1.1456493953010067 0.2696428568160627 1.1456493953010067 a -3.25390625 0.51188468933105469 -5.7842731475830078E-3 Resumen Mejor curva Curva σ_xy y= -0.71778511221054941 0.2696428568160627 *x ± 1.8150272668774475E-5 Pn(x) 1.8150272668774475E-5 A*exp(B*X) 3.8057946677678988E-5 A*x^B 2.057537172441E-5 Evaluación de puntos Evaluando X P1 Y( 21.041599999999999 )= 4.9559320237703153 Redondeando a las cifras que representa la curva Y( 21.041599999999999 )= 4.9559320237703153 P2 Y( 20.911300000000001 )= 4.9207975595271831 Redondeando a las cifras que representa la curva Y( 20.911300000000001 )= 4.9207975595271831 Evaluando Y P3 4.90381 = -0.71778511221054941 0.2696428568160627 *x Reacomodando 0= -5.6215951122105494 0.2696428568160627 *x Es una ecuación no lineal y se resolvera por métodos numericós Método de la Secante Es una interpolación inversa n X Y CC Checa CC Checa Y Checa n 0 20.846 -6.2011902290670662E-4 1 20.851299999999998 8.0898811821850103E-4 2 20.848299779160588 0 1.4390721887114335E-4 CERO 3 20.848299779160588 0 0 RAÍZ CERO X( 4.90381 )= 20.848299779160588 Redodeando X( 4.90381 )= 20.848299779160588 P4 4.9023700000000003 = -0.71778511221054941 0.2696428568160627 *x Reacomodando 0= -5.6201551122105498 0.2696428568160627 *x Es una ecuación no lineal y se resolvera por métodos numericós Método de la Secante Es una extrapolación inversa n X Y CC Checa CC Checa Y Checa n 0 20.846 8.1988097709295715E-4 1 20.851299999999998 2.2489881182181648E-3 2 20.842959381803123 0 4.0016477718405149E-4 CERO 3 20.842959381803123 0 0 RAÍZ CERO X( 4.90381 )= 20.842959381803123 Redodeando X( 4.90381 )= 20.842959381803123