Profesor Margarito Filomeno Nicolas 2022-01-04T01:09:33Z 2022-12-31T02:13:44Z 16.00 836318a7-025e-496d-8d66-beb15bdd159a 6540 21765 32767 32767 False False Universidad Autónoma Metropolitana. Unidad Lerma. Ajuste de curvas: tablas equiespaciadas ejercicio 05 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 5 - Ajuste de curvas - Equiespaciadas Hallar los valores solicitados con las curva solicitada x y P1 y( 6.0229200000000001 ) 4.8402399999999997 17.3718 P2 y( 5.8646000000000003 ) 4.8982299999999999 17.3825 P3 x( 17.376999999999999 ) 4.9562200000000001 17.392700000000001 P4 x( 17.368600000000001 ) 5.0141999999999998 17.402200000000001 5.07219 17.411300000000001 Ajustar a la curva: 5.1301800000000002 17.419799999999999 5.1881700000000004 17.427800000000001 Mejor curva 5.2461599999999997 17.435400000000001 5.3041400000000003 17.442599999999999 5.3621299999999996 17.449300000000001 5.4201199999999998 17.4557 5.47811 17.4617 5.5361000000000002 17.467400000000001 5.5940799999999999 17.4727 5.6520700000000001 17.477799999999998 5.7100600000000004 17.482600000000001 5.7680499999999997 17.487100000000002 5.8260399999999999 17.491299999999999 5.8840199999999996 17.4953 5.9420099999999998 17.499099999999999 Criterio de Convergencia ND Tol NCSINV TolINV NumPtos MaxIter 4 5.0000000000000002E-5 6 4.9999999999999996E-6 20 18 Ajuste a curva polinomial Ajuste a curva exponencial Ajuste a curva potencial n 1 n 2 n 3 n 4 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 ∑x⁵ ∑x⁶ ∑yx³ y_p ∑(y-y_p)² σ_xy Checa σ_xy Checa OSC Checa n ∑x⁷ ∑x⁸ ∑yx⁴ 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 4.8402399999999997 17.3718 4.8402399999999997 23.427923257599996 17.3718 84.083681231999989 17.383709934396045 1.4184653731807824E-4 113.3967712683658 548.86758816399481 406.98519724637561 17.372918652987259 1.2513845059032239E-6 2656.6508549348941 12858.827734090071 1969.906031119797 17.371862962846674 3.96432006120382E-9 62239.812351652115 301255.62933696061 9534.8179680672856 17.372224856333876 1.8050290443418753E-7 2.8548482018271182 13.81815046041169 17.383761629979336 1.4308059176254252E-4 1.5769643062760161 2.4868164232685968 4.5019937141176332 17.381449757834226 9.3117826259190038E-5 4.8982299999999999 17.3825 4.8982299999999999 23.9926571329 17.3825 85.143482974999998 17.390299115922513 6.082620917279286E-5 117.52155294808476 575.64759629689729 417.05236261263423 17.382915715644724 1.7281949726845863E-7 2819.654325609351 13811.315407329492 2042.8183941200834 17.38252679174855 7.1779779033806212E-10 67650.999467643531 331370.15512239566 10006.194342630817 17.382995800849987 2.4581848284707679E-7 2.8554639529910357 13.98671919845928 17.390330357870361 6.1314504377926431E-5 1.5888739153695035 2.5245203189416161 4.5369721911853471 17.38872940621323 3.880550176942277E-5 4.9562200000000001 17.392700000000001 4.9562200000000001 24.564116688400002 17.392700000000001 86.202047594000007 17.396888297448985 1.7541835521163758E-5 121.74516641338187 603.39582868133152 427.23631232633477 17.392534110993299 2.7519162544577018E-8 2990.5624740269891 14821.885545022044 2117.4771558780271 17.39262673253889 5.3681208577208146E-9 73460.525575949156 364086.52607003076 10494.682629505796 17.393163246021757 2.1459687667251639E-7 2.8560505779589733 14.155214995491823 17.396901567858595 1.7653172470370561E-5 1.6006433534192719 2.5620591448452923 4.5715183746393011 17.395926371442954 1.0409472687899843E-5 5.0141999999999998 17.402200000000001 5.0141999999999998 25.142201639999996 17.402200000000001 87.258111240000005 17.40347634271377 1.6290507229917165E-6 126.06802746328798 632.13030330641845 437.52962137960793 17.40177227834544 1.8294581377978937E-7 3169.6277668390435 15893.147548484329 2193.8610275216301 17.402182974051104 2.8988293581181437E-10 79691.420437610126 399588.72035826457 11000.457964198955 17.40275841615826 3.118286058055102E-7 2.8565966350096366 14.32354684726532 17.403474127077022 1.6233998083989628E-6 1.6122738872533084 2.5994270875188938 4.6056161610417075 17.403041323487798 7.0782521112017343E-7 5.07219 17.411300000000001 5.07219 25.7271113961 17.411300000000001 88.313421747000007 17.410065524240238 1.5239304014410344E-6 130.49279715218447 661.88426078733846 447.94245465091592 17.410633404374956 4.4434972732929263E-7 3357.2027287229303 17028.370108601161 2272.0492390558293 17.411220601087745 6.304187267374482E-9 86371.12858114572 438090.77467800147 11524.265429846586 17.411816068460496 2.6632665591792057E-7 2.8571194207224924 14.491852554594418 17.410050303645288 1.5617409789808881E-6 1.6237726770011185 2.6366377065753785 4.639312450298446 17.410078542154515 1.4919592682973925E-6 5.1301800000000002 17.419799999999999 5.1301800000000002 26.318746832400002 17.419799999999999 89.36670956399999 17.41665470576671 9.8928758139569727E-6 135.01990862464186 692.67643482796518 458.46730607104155 17.419115863095577 4.6804330399171456E-7 3553.5547924257307 18230.375725006634 2352.0198042595362 17.419759710879759 1.6232132096425203E-9 93525.108936914548 479800.6433659803 12066.284959416187 17.420364571694421 3.1874119814281681E-7 2.8576074903021915 14.660040794598498 17.416628965125351 1.0055462176228815E-5 1.6351407462864169 2.6736852601661005 4.6725904442863806 17.417038557635884 7.6255639303273042E-6 5.1881700000000004 17.427800000000001 5.1881700000000004 26.917107948900004 17.427800000000001 90.418389126000008 17.423243887293182 2.0758162997237493E-5 139.65053194724453 724.53070033273571 469.1059739118395 17.427219654507304 3.3680089089363188E-7 3758.9884435452896 19502.271073148368 2433.8015406701884 17.427822094968715 4.8818764244189577E-10 101181.09771357616 524944.7357246445 12626.976139258852 17.428432617754705 4.0020522356647911E-7 2.8580666324032569 14.828135560235607 17.423210112456182 2.1067067664905363E-5 1.6463810338433238 2.7105705085990115 4.7054666970491805 17.423923075368233 1.5030544600413123E-5 5.2461599999999997 17.435400000000001 5.2461599999999997 27.522194745599997 17.435400000000001 91.468898064000001 17.429833068819654 3.0990722766719778E-5 144.38583718657688 757.47120361473208 479.8604742674342 17.434944778610141 2.0722651378595381E-7 3973.8151295554626 20847.269980068686 2517.4248256828428 17.435429544896195 8.7290089108801577E-10 109368.11387863713 573762.62430555094 13206.8134235043 17.43604751847392 4.1928017406606844E-7 2.8585026222217698 14.996162116594959 17.429793746577094 3.1430077441865084E-5 1.6574963804077194 2.7472942510646914 4.7379577497185581 17.430733744572017 2.1773939719197818E-5 5.3041400000000003 17.442599999999999 5.3041400000000003 28.133901139600002 17.442599999999999 92.517992363999994 17.436421114084435 3.8178631157547388E-5 149.22615039059798 791.51639333278627 490.72838401758696 17.442290001198916 9.6099256672525798E-8 4198.3137625321651 22268.443960397359 2602.8920508030442 17.442602651128524 7.0284824592459649E-12 118114.94434810207 626498.20091454207 13806.103842346456 17.443234001550451 4.019579659755557E-7 2.8589154899379392 15.164088006799421 17.436378732479184 3.8704169565540422E-5 1.668487647708669 2.7838510305564075 4.770065180804429 17.437471004845658 2.6306591293246152E-5 5.3621299999999996 17.449300000000001 5.3621299999999996 28.752438136899997 17.449300000000001 93.565415008999992 17.443010295610907 3.9560381302181873E-5 154.17431110701557 826.70269881626132 501.70991878220912 17.449257855982694 1.7761181947783127E-9 4432.8873424036392 23769.718205322824 2690.233806799647 17.449365676414004 4.3133913563243353E-9 127456.31908030766 683437.35223009007 14425.383402454589 17.450019094235994 5.1709652023888443E-7 2.8592995332306432 15.331935806122027 17.442967342570402 4.0102550120658056E-5 1.679361284204689 2.8202543228856221 4.8017969360520807 17.444138723974941 2.663877020685803E-5 5.4201199999999998 17.4557 5.4201199999999998 29.377700814399997 17.4557 94.611988683999996 17.449599477137379 3.7216379197358468E-5 159.23066373814569 863.04930514039825 512.80833210592209 17.455847043457577 2.1621778416261261E-8 4677.8307997775755 25354.404274490429 2779.4826970139497 17.455739138404908 1.5318147387504774E-9 137423.91369625105 744854.10310332419 15065.12975573925 17.456424692828705 5.2517969597584019E-7 2.8596662428752051 15.499734196332756 17.44955844227162 3.7718731331028038E-5 1.690117955427866 2.8564987032596703 4.833173263614329 17.450737228543002 2.4629100534400386E-5 5.47811 17.4617 5.47811 30.0096891721 17.4617 95.65711338700001 17.456188658663848 3.0374883323583198E-5 164.39637835057272 900.58144420605595 524.02018941645861 17.462057563623574 1.2785174490319279E-7 4933.4842153196369 27026.169214784659 2870.6402398441955 17.461744828642814 2.009607216532145E-9 148052.32783720398 811046.93764826551 15725.683004292887 17.462472589150682 5.9689399575086737E-7 2.8600099110783965 15.667448893977674 17.456152032523583 3.0779943119382705E-5 1.7007601509605645 2.8925850910954023 4.864190888114404 17.457267966141259 1.964292412502784E-5 5.5361000000000002 17.467400000000001 5.5361000000000002 30.648403210000001 17.467400000000001 96.701273140000012 17.46277784019032 2.1364361306233922E-5 169.67262501088101 939.32461932273839 535.34791823035403 17.467889416480674 2.3952849155349681E-7 5200.1950250326126 28788.799678083044 2963.739610115063 17.467404538669292 2.0599518933660004E-11 159377.67389783554 882330.74046580738 16407.558855558003 17.468183194961941 6.1339434840839499E-7 2.860336286510377 15.835107715750098 17.462748114267388 2.164004086929245E-5 1.7112902817360389 2.9285144283642115 4.8948656896021587 17.463732339157414 1.3451736056252217E-5 5.5940799999999999 17.4727 5.5940799999999999 31.293731046399998 17.4727 97.743681616000003 17.469365885455105 1.1116319798480877E-5 175.0596349720453 979.29760280441906 546.78597445443324 17.473341694306075 4.1177158244989108E-7 5478.2691338961449 30645.875796545741 3058.764483976056 17.472739166644825 1.5340260668612216E-9 171435.48087594062 959023.79485848173 17110.973224520774 17.473574638486951 7.6499248285732591E-7 2.8606396628625137 16.002647125225931 17.469345550348162 1.1252332466712047E-5 1.7217088957143343 2.9642815215818725 4.9251887549836439 17.470130608641576 6.6017719527447283E-6 5.6520700000000001 17.477799999999998 5.6520700000000001 31.945895284900001 17.477799999999998 98.785749045999992 17.475955066981577 3.4037778424630206E-6 180.56043636292475 1020.5402255537961 558.34396861042524 17.478416277844119 3.7979838115332514E-7 5768.1647926458445 32602.071179569797 3155.7991946639258 17.477772341141012 7.6501248042164809E-10 184269.18845191106 1041502.3519733929 17836.797954184134 17.478666428703725 7.5069869864204219E-7 2.8609315041830214 16.170185126847731 17.475946617470292 3.4350268014202938E-6 1.732021849742049 2.9998996879838691 4.9551958758603796 17.476466298957394 1.7787584710435792E-6 5.7100600000000004 17.482600000000001 5.7100600000000004 32.604785203600002 17.482600000000001 99.826694956000011 17.482544248508045 3.108228855359774E-9 186.17527979966823 1063.0720181728936 570.01641780045748 17.483112194073268 2.6234276868924097E-7 6070.2050080883137 34661.234808484754 3254.8279466256799 17.482524906292678 5.6390648795880214E-9 197917.73043053647 1130122.115822189 18585.262864909433 17.4834738806302 7.6366735583602707E-7 2.8612061005852456 16.33765850670779 17.482550178909513 2.4821410574809973E-9 1.7422295314936223 3.0353637404084863 4.984877764129326 17.482739578622464 1.9482191848590962E-8 5.7680499999999997 17.487100000000002 5.7680499999999997 33.270400802499999 17.487100000000002 100.86646715500001 17.489133430034517 4.1348377052697254E-6 191.90533534886012 1106.9195695589926 581.80282587339775 17.487429442993523 1.0853268598051709E-7 6384.7674231947467 36827.657735358465 3355.8677897790521 17.487018653641393 6.6172300589642898E-9 212423.77120043439 1225270.9334726655 19356.813204835064 17.488011886015901 8.3153610599251467E-7 2.8614634662489395 16.505064346497196 17.489156235608338 4.2281048769889615E-6 1.7523340684610267 3.0706746874891739 5.0142399175645957 17.48895168696821 3.4287446282343342E-6 5.8260399999999999 17.491299999999999 5.8260399999999999 33.942742081599995 17.491299999999999 101.90501345199999 17.495722611560989 1.9559493019404345E-5 197.75177307708483 1152.1097400180192 593.7026845718899 17.491368024604888 4.627346870361186E-9 6712.2374297345805 39105.763755130851 3458.9355884232136 17.491275374728737 6.0640398473320071E-10 227831.74386794254 1327356.8530443879 20151.89709557718 17.492293956548316 9.8794961994272776E-7 2.8617036144558434 16.672399725964322 17.495764788509643 1.9934336435847523E-5 1.7623375242877894 3.1058335495128149 5.0432876631455299 17.495103826561731 1.4469096511740878E-5 5.8840199999999996 17.4953 5.8840199999999996 34.621691360399993 17.4953 102.94269510599999 17.502310656825774 4.9149309128764693E-5 203.71472439842074 1198.6615126547954 605.71687685760605 17.494927357666921 1.3886230840304747E-7 7052.9483136910685 41499.688936724517 3564.0502177676904 17.495316181470564 2.6183998959680441E-10 244184.99969746577 1436789.4219198823 20970.942762349441 17.496331547859544 1.0640909865292622E-6 2.8619322734291321 16.83966673550248 17.502374698308561 5.0051356157149595E-5 1.7722402017816807 3.1408353328111724 5.0720314297475495 17.50119611889658 3.476421804260297E-5 5.9420099999999998 17.499099999999999 5.9420099999999998 35.3074828401 17.499099999999999 103.97982719099998 17.508899838352242 9.6036831730107286E-5 209.79741611070259 1246.618344503956 617.84917296719391 17.498108669959226 9.8273524973791413E-7 7407.4186692259509 44014.955806727296 3671.2659642627955 17.49916425613932 4.1288514404876371E-9 261537.30755313166 1554057.296853784 21814.699072309173 17.500136802839954 1.0749601289396696E-6 2.8621494510355454 17.00692065954772 17.50898824601401 9.7777409233605603E-5 1.7820474599740384 3.1756931495999217 5.1004861592839816 17.507231798627991 6.6126148926224553E-5 ∑ 107.82252000000001 583.52092073439997 348.92610000000002 1881.3586526480001 6.3510763845463193E-4 5.9400132737161453E-3 3169.9453216706879 17284.997390096527 10183.012366154118 5.8666371285211936E-6 5.8744897793571599E-4 94596.778431201979 519558.24647337053 55325.857608382255 4.7063480869274104E-8 5.4235298047762508E-5 2863513.6078801914 15835189.91126864 301717.73789550515 1.1249718026541689E-5 8.6601455055296034E-4 OSCILA 57.182509069869269 308.29267937292684 6.4341249979990188E-4 5.9787238502687443E-3 33.65648315134905 56.715295946528208 96.230827305238961 4.2681997638609285E-4 4.8695195769540237E-3 Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales Ecuaciones Normales NP ∑x ∑y NP ∑x ∑x² ∑y NP ∑x ∑x² ∑x³ ∑y NP ∑x ∑x² ∑x³ ∑x⁴ ∑y NP ∑x ∑ln(y) NP ∑ln(x) ∑ln(y) ∑x ∑x² ∑yx ∑x ∑x² ∑x³ ∑yx ∑x ∑x² ∑x³ ∑x⁴ ∑yx ∑x ∑x² ∑x³ ∑x⁴ ∑x⁵ ∑yx ∑x ∑x² ∑ln(y)x ∑ln(x) ∑ln(x)² ∑ln(y)ln()x ∑x² ∑x³ ∑x⁴ ∑yx² ∑x² ∑x³ ∑x⁴ ∑x⁵ ∑yx² ∑x² ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑yx² 20 107.82252000000001 348.92610000000002 ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑yx³ ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑yx³ 20 107.82252000000001 57.182509069869269 20 33.65648315134905 57.182509069869269 107.82252000000001 583.52092073439997 1881.3586526480001 20 107.82252000000001 583.52092073439997 348.92610000000002 ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑x⁸ ∑yx⁴ 107.82252000000001 583.52092073439997 308.29267937292684 33.65648315134905 56.715295946528208 96.230827305238961 107.82252000000001 583.52092073439997 3169.9453216706879 1881.3586526480001 20 107.82252000000001 583.52092073439997 3169.9453216706879 348.92610000000002 Matriz Inversa 583.52092073439997 3169.9453216706879 17284.997390096527 10183.012366154118 107.82252000000001 583.52092073439997 3169.9453216706879 17284.997390096527 1881.3586526480001 20 107.82252000000001 583.52092073439997 3169.9453216706879 17284.997390096527 348.92610000000002 a A B Matriz Inversa 583.52092073439997 3169.9453216706879 17284.997390096527 94596.778431201979 10183.012366154118 107.82252000000001 583.52092073439997 3169.9453216706879 17284.997390096527 94596.778431201979 1881.3586526480001 2.8240032425247819 16.844147086241787 6.5148191618789042E-3 13.047563848208291 -2.4109182104458866 Matriz Inversa 3169.9453216706879 17284.997390096527 94596.778431201979 519558.24647337053 55325.857608382255 583.52092073439997 3169.9453216706879 17284.997390096527 94596.778431201979 519558.24647337053 10183.012366154118 6.5148191618789042E-3 36.660030071750171 -21.755113216743048 -2.4109182104458866 0.4472012359655268 3169.9453216706879 17284.997390096527 94596.778431201979 519558.24647337053 2863513.6078801914 55325.857608382255 -21.755113216743048 12.927740024953284 4235.8064992779091 -1575.0197435924063 145.85161353120887 Matriz Inversa 17284.997390096527 94596.778431201979 519558.24647337053 2863513.6078801914 15835189.91126864 301717.73789550515 a -1575.019743592389 586.10661383455465 -54.316985208637185 a A B 16.833732007310573 145.8516135312058 -54.316985208636623 5.0376290702211248 1447431.3605282924 -808390.72348473431 150147.18049013728 -9274.5834018369369 Matriz Inversa 2.7999591132120258 16.443974416056523 3.5158955862925723E-2 0.11362616876135689 -808390.72348071751 451634.8768118798 -83912.27191114919 5184.9380448349775 3.5158955862925723E-2 a 150147.18048864577 -83912.271910732889 15595.716661935132 -963.97181321323046 510133000.77241445 -380098020.398009 106028589.39590791 -13123646.651639029 608146.37993823003 15.203660516766831 -9274.5834016990175 5184.9380447836893 -963.97181320848074 59.602385162711492 -380098018.71382517 283260173.56942147 -79029723.54440254 9783613.1108601578 -453450.28064042208 0.72068540437612683 106028588.45576471 -79029723.193954527 22053265.154076122 -2730605.5350055047 126580.33694152287 -5.6301711891137529E-2 a -13123646.477108579 9783613.0241453275 -2730605.5229162574 338159.91973698448 -15678.561122232371 12.305595636367798 608146.36916289129 -453450.27461952379 126580.33582269531 -15678.561053089978 727.05426514867315 2.340843141078949 -0.35751774162054062 a 1.8624189309775829E-2 8.052703857421875 5.511749267578125 -1.2426986694335938 0.12827587127685547 -5.0848126411437988E-3 Resumen Mejor curva Curva σ_xy y= 12.305595636367798 2.340843141078949 *x -0.35751774162054062 *x^2 1.8624189309775829E-2 *x^3 ± 5.4235298047762508E-5 Pn(x) 5.4235298047762508E-5 A*exp(B*X) 5.9787238502687443E-3 A*x^B 4.8695195769540237E-3 Evaluación de puntos Evaluando en X P1 Y( 6.0229200000000001 )= 17.504251212547544 Redondeando a las cifras que representa la curva Y( 6.0229200000000001 )= 17.504251212547544 P2 Y( 5.8646000000000003 )= 17.493985358977813 Redondeando a las cifras que representa la curva Y( 5.8646000000000003 )= 17.493985358977813 Evaluando en Y P3 17.376999999999999 = 12.305595636367798 2.340843141078949 *x -0.35751774162054062 *x^2 1.8624189309775829E-2 *x^3 Reacomodando 0= -5.071404363632201 2.340843141078949 *x -0.35751774162054062 *x^2 1.8624189309775829E-2 *x^3 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 4.8402399999999997 -5.1370371533252523E-3 1 4.8982299999999999 5.5267917485504192E-3 2 4.8681752554567836 7.1768578330022592E-5 6.1737186863861501E-3 3 4.8677798426013963 -1.0230462135218943E-6 8.1230636588536191E-5 CERO 4 4.8677853999114165 1.8531665091359173E-10 1.1416505789812971E-6 RAÍZ CERO X( 17.376999999999999 )= 4.8677853999114165 Redodeando X( 17.376999999999999 )= 4.8677853999114165 P4 17.368600000000001 = 12.305595636367798 2.340843141078949 *x -0.35751774162054062 *x^2 1.8624189309775829E-2 *x^3 0 0 Reacomodando 0= -5.0630043636322029 2.340843141078949 *x -0.35751774162054062 *x^2 1.8624189309775829E-2 *x^3 0 0 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 4.8402399999999997 3.2629628466729343E-3 1 4.8982299999999999 1.3926791748548606E-2 2 4.8224959779212808 -1.160146016494501E-4 1.5704320423583624E-2 3 4.8231216543127129 4.0720057827847711E-6 1.2972436448344796E-4 CERO 4 4.8231004383092086 1.1291709789418292E-9 4.3988309544058605E-6 RAÍZ CERO X( 17.368600000000001 )= 4.8231004383092086 Redodeando X( 17.368600000000001 )= 4.8231004383092086