Profesor Margarito Filomeno Nicolas 2022-01-04T01:09:33Z 2022-12-31T02:13:55Z 16.00 836318a7-025e-496d-8d66-beb15bdd159a 6540 21765 32767 32767 False False Universidad Autónoma Metropolitana. Unidad Lerma. Ajuste de curvas: tablas equiespaciadas ejercicio 04 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 4 - Ajuste de curvas - Equiespaciadas Hallar los valores solicitados con las curva solicitada x y P1 y( 19.068200000000001 ) 13 15.7552 P2 y( 12.9795 ) 13.291700000000001 15.7692 P3 x( 15.9818 ) 13.583299999999999 15.7827 P4 x( 15.755699999999999 ) 13.875 15.7956 14.166700000000001 15.8079 Ajustar a la curva: 14.458299999999999 15.819800000000001 14.75 15.831200000000001 Mejor curva 15.041700000000001 15.8421 15.333299999999999 15.852600000000001 15.625 15.8628 15.916700000000001 15.8725 16.208300000000001 15.8819 16.5 15.891 16.791699999999999 15.899800000000001 17.083300000000001 15.908300000000001 17.375 15.916399999999999 17.666699999999999 15.924300000000001 17.958300000000001 15.932 18.25 15.939399999999999 18.541699999999999 15.9466 18.833300000000001 15.9535 19.125 15.9603 19.416699999999999 15.966799999999999 19.708300000000001 15.9732 Criterio de Convergencia ND Tol NCSINV TolINV NumPtos MaxIter 4 5.0000000000000002E-5 6 4.9999999999999996E-6 24 22 Ajuste a curva polinomial Ajuste a curva exponencial Ajuste a curva potencial n 1 n 2 n 3 n 4 n 5 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 ∑x⁹ ∑x¹⁰ ∑yx⁵ 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 13 15.7552 13 169 15.7552 204.8176 15.771189248135116 2.556560559262905E-4 2197 28561 2662.6288 15.756995288804262 3.2230618907078707E-6 371293 4826809 34614.174400000004 15.755368171838654 2.8281767316239708E-8 62748517 815730721 449984.2672 15.755205028215642 2.5282952534303781E-11 10604499373 137858491849 5849795.4736000001 15.756995283870069 3.2230441741275261E-6 2.7571704695114008 35.84321610364821 15.771374266072641 2.6160688298857663E-4 2.5649493574615367 6.5789652063423505 7.072002624185191 15.763379408729255 6.6902727160213625E-5 13.291700000000001 15.7692 13.291700000000001 176.66928889000002 15.7692 209.59947564000001 15.780525670267503 1.2827080700820342E-4 2348.2351871392134 31212.037636898283 2785.9333503641883 15.770034884330066 6.9703184459023422E-7 414861.04065836093 5514208.4941187361 37029.790313035686 15.769256785266242 3.2245664621847706E-9 73293205.04127802 974191293.447155 492188.86390377639 15.769239887732791 1.5910312272380745E-9 12948658415.111551 172109683056.13821 6542026.7223498253 15.77003488193002 6.9702783707375977E-7 2.7580586704554557 36.659288430092779 15.780654291876276 1.3120080238693512E-4 2.587139780270745 6.6932922426593588 7.1354833026559508 15.774850180941208 3.1924544668389548E-5 13.583299999999999 15.7827 13.583299999999999 184.50603888999999 15.7827 214.38114891000001 15.789858891706668 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15.946474780151386 1.5680010487057641E-8 753436837.46250045 13969999809.178442 1884804.4598229316 15.946588737531652 1.2684319329307885E-10 259027545461.8439 4802811039689.8701 34947478.852698848 15.94715919355143 3.1269742796086319E-7 2.7692456403635211 51.346521889928297 15.948612317858153 4.0494231622407222E-6 2.9200222495694876 8.5265299379808503 8.0862588843847849 15.947930485411643 1.7701914305940776E-6 18.833300000000001 15.9535 18.833300000000001 354.69318889000004 15.9535 300.45705155000002 15.957895285930306 1.9318538409144153E-5 6680.0432343220382 125807.25824495725 5658.5977889566157 15.953800108832747 9.0065311492502446E-8 2369365.8367047533 44622977.612411641 106570.06973875663 15.953440861380827 3.4973762777225172E-9 840397924.26783216 15827466227.113363 2007066.0944109254 15.953549494422326 2.4496978413780389E-9 298083419695.09412 5613894468143.6162 37799677.875869282 15.953800107597269 9.0064569938609178E-8 2.7696782408950309 52.162181214248392 15.957993414150483 2.0190770727759759E-5 2.9356265795712151 8.6179034146849922 8.1307410608315003 15.956090300617431 6.7096572886636304E-6 19.125 15.9603 19.125 365.765625 15.9603 305.24073750000002 15.967231708062693 4.8048576666399275E-5 6995.267578125 133784.49243164063 5837.7291046874998 15.960106664594456 3.7378579037079127E-8 2558628.417755127 48933768.489566803 111646.56912714844 15.960228894690598 5.0559650251885359E-9 935858322.36296511 17898290415.191708 2135240.634556714 15.960297620858958 5.6603120996168455E-12 342304804190.54138 6546579380144.1045 40836477.135897152 15.960106664887617 3.7378465680343704E-8 2.7701043888374826 52.978246436516855 15.967383248426128 5.0172408266236255E-5 2.9509963797125995 8.7083796330768681 8.1745680228853939 15.964131556819707 1.468082766264096E-5 19.416699999999999 15.966799999999999 19.416699999999999 377.00823888999997 15.966799999999999 310.02256555999998 15.97656813019508 9.5416367508047617E-5 7320.2558720554616 142135.21219093929 6019.6151487088509 15.96607652796949 5.2341177892968017E-7 2759796.7745478107 53586146.032362476 116881.06145793514 15.966854839581671 3.0073797179800969E-9 1040466121.6665723 20202418544.563335 2269444.5060102893 15.966837098354 1.3762878696006081E-9 392264300154.2229 7616478236804.5 44065123.139849983 15.966076530371907 5.2340830277125471E-7 2.7705115664445814 53.794191932184503 15.976778607769079 9.9572613009139192E-5 2.9661335205144241 8.7979480615192909 8.2177072262041975 15.972055049956634 2.7615550046723151E-5 19.708300000000001 15.9732 19.708300000000001 388.41708889000006 15.9732 314.80461756000005 15.985901351634245 1.6132433333674139E-4 7655.0405129707888 150867.8349417822 6204.263844257749 15.971707825497953 2.226584744560124E-6 2973348.5513831265 58599645.255224071 122275.49312178501 15.973334877803259 1.8192021811866685E-8 1154899388.5835328 22761103620.02084 2409842.1010920755 15.973170864835099 8.4885783381465274E-10 448582658474.45673 8840801608012.1367 47493891.080952957 15.97170783065711 2.226569347862708E-6 2.7709123178588366 54.609971234057312 15.986176271689526 1.683836269603962E-4 2.981039866810633 8.8865986875143577 8.2602000869738497 15.979861577549398 4.4376615446641997E-5 ∑ 392.5 6516.8401222399998 381.08510000000001 6235.4604683400012 1.25743296246987E-3 7.5601616218590496E-3 109777.33605088001 1874529.2169373995 103579.73396099766 1.5187973414139365E-5 8.5043331851752588E-4 32414864.214988239 567030519.93435824 1745609.1228950261 1.9629763230258618E-7 9.9070084360160457E-5 10023266066.168978 178852222272.34955 29820076.096132115 2.2224992813490187E-8 3.4201410261389876E-5 AJUSTA 3218311686451.4897 58345881369073.922 515854686.41598678 1.5187880222373754E-5 9.1857015162980806E-4 OSCILA 66.359051693984043 1085.4442726825166 1.2983189537733556E-3 7.6820894227279659E-3 66.882139022969369 186.75796253426535 184.93872432478034 3.3772420113605222E-4 3.918047989961166E-3 Ecuaciones Normales 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 ∑x² ∑x³ ∑x⁴ ∑x⁵ ∑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 ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑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 ∑x² ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑yx² 24 392.5 381.08510000000001 ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑yx³ ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑yx³ ∑x³ ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑x⁸ ∑yx³ 24 392.5 66.359051693984043 24 66.882139022969369 66.359051693984043 392.5 6516.8401222399998 6235.4604683400012 24 392.5 6516.8401222399998 381.08510000000001 ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑x⁸ ∑yx⁴ ∑x⁴ ∑x⁵ ∑x⁶ ∑x⁷ ∑x⁸ ∑x⁹ ∑yx⁴ 392.5 6516.8401222399998 1085.4442726825166 66.882139022969369 186.75796253426535 184.93872432478034 392.5 6516.8401222399998 109777.33605088001 6235.4604683400012 24 392.5 6516.8401222399998 109777.33605088001 381.08510000000001 ∑x⁵ ∑x⁶ ∑x⁷ ∑x⁸ ∑x⁹ ∑x¹⁰ ∑yx⁵ Matriz Inversa 6516.8401222399998 109777.33605088001 1874529.2169373995 103579.73396099766 392.5 6516.8401222399998 109777.33605088001 1874529.2169373995 6235.4604683400012 24 392.5 6516.8401222399998 109777.33605088001 1874529.2169373995 381.08510000000001 a A B Matriz Inversa 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 103579.73396099766 392.5 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 6235.4604683400012 24 392.5 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 381.08510000000001 2.7319810002466625 15.363291578651658 2.0165800969778047E-3 2.7755884933108708 -0.1671697422661424 Matriz Inversa 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 1745609.1228950261 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 103579.73396099766 392.5 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 6235.4604683400012 2.0165800969778047E-3 20.818938285503378 -7.4557202586004001 -0.1671697422661424 1.0221844113088961E-2 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 10023266066.168978 1745609.1228950261 6516.8401222399998 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 10023266066.168978 103579.73396099766 -7.4557202586003992 2.6754121327512723 221.36419548725499 -27.312740814317525 0.82992830520237915 Matriz Inversa 1874529.2169373995 32414864.214988239 567030519.93435824 10023266066.168978 178852222272.34955 29820076.096132115 109777.33605088001 1874529.2169373995 32414864.214988239 567030519.93435824 10023266066.168978 3218311686451.4897 1745609.1228950261 a -27.312740814317625 3.3813125837517308 -0.1030651967794578 1874529.2169373995 32414864.214988239 567030519.93435824 10023266066.168978 3218311686451.4897 3218311686451.4897 29820076.096132115 a A B 15.355099129105156 0.82992830520238503 -0.10306519677945815 3.1510379303308364E-3 18614.439610764057 -3464.6252454630126 212.94472846617418 -4.3233595309873509 Matriz Inversa 32414864.214988239 567030519.93435824 10023266066.168978 3218311686451.4897 3218311686451.4897 58345881369073.922 515854686.41598678 2.6736083536029582 14.492167826594049 3.2780817712193766E-2 3.2006932233073826E-2 -3464.6252454605315 645.7489964998681 -39.74324708872529 0.80795285412691353 3.2780817712193766E-2 a 212.94472846587004 -39.743247088697046 2.449326429017773 -4.9858358226295009E-2 1607095.3408373352 -399787.86922617565 37045.114648894611 -1515.5765185498667 23.101968435949459 Matriz Inversa 14.834003550786292 -4.3233595309781458 0.80795285412577666 -4.9858358226260412E-2 1.0162214426966193E-3 -399787.86935921904 99527.714559153159 -9229.306092522942 377.86300853394368 -5.7639012649472638 9.6719532082715887E-2 37045.114673554461 -9229.306095590684 856.47831784112134 -35.091345567690595 0.53566626255143357 221.39802754627451 -27.318468555563399 0.83021385502169798 -2.2783343623138666E-6 -6.8941507315847728E-8 -1.3997019991647776E-9 -1.9784744322919323E-3 a -1515.5765200592909 377.86300878396958 -35.091345579228864 1.4387962483528556 -2.1978811823304779E-2 -27.318468555563694 3.3822779270080923 -0.10311283607568413 3.5573335067319727E-7 1.1467295811096022E-8 2.6157747113129076E-10 14.308891122229397 23.101968466471885 -5.7639012706277297 0.53566626290052832 -2.1978811830391399E-2 3.3598197240075443E-4 0.83021385502171385 -0.10311283607568503 3.1533358464676201E-3 -1.4671200310187664E-8 -5.3139947243291547E-10 -1.6141818316980753E-11 0.19485295657068491 -2.2783343623662157E-6 3.5573335067960444E-7 -1.4671200310380919E-8 -7.7179252918566747E-16 -1.8756444352218509E-17 3.2900558192233573E-13 -8.0342378059867769E-3 a -6.8941507306688205E-8 1.1467295809963213E-8 -5.3139947239841501E-10 -1.8756444470518493E-17 3.2900541209957987E-13 -6.9679626662686272E-21 1.2342958734734566E-4 13.782316088676453 -1.3997019991942761E-9 2.615774711350791E-10 -1.6141818317100138E-11 3.2900558192233699E-13 -6.9679625295687168E-21 -1.065166709263539E-22 0.32623469829559326 -2.0244203507900238E-2 a 6.2441453337669373E-4 14.834002273521682 -7.6583619375014678E-6 9.6719751057709663E-2 -1.9784856647036293E-3 Resumen Mejor curva 1.0680425440541194E-10 2.6065961910692525E-12 Curva σ_xy y= 13.782316088676453 0.32623469829559326 *x -2.0244203507900238E-2 *x^2 6.2441453337669373E-4 *x^3 -7.6583619375014678E-6 *x^4 ± 3.4201410261389876E-5 3.9960713037861428E-14 Pn(x) 3.4201410261389876E-5 A*exp(B*X) 7.6820894227279659E-3 A*x^B 3.918047989961166E-3 Evaluación de puntos Evaluando en X P1 Y( 19.068200000000001 )= 15.959000161424758 Redondeando a las cifras que representa la curva Y( 19.068200000000001 )= 15.959000161424758 P2 Y( 12.9795 )= 15.754195670391208 Redondeando a las cifras que representa la curva Y( 12.9795 )= 15.754195670391208 Evaluando en Y P3 15.9818 = 13.782316088676453 0.32623469829559326 *x -2.0244203507900238E-2 *x^2 6.2441453337669373E-4 *x^3 -7.6583619375014678E-6 *x^4 Reacomodando 0= -2.1994839113235471 0.32623469829559326 *x -2.0244203507900238E-2 *x^2 6.2441453337669373E-4 *x^3 -7.6583619375014678E-6 *x^4 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 19.416699999999999 -1.4962901646000892E-2 1 19.708300000000001 -8.6291351649010473E-3 2 20.105576379164557 -3.2084912677055044E-4 1.9759512071300462E-2 3 20.120918385777777 -7.347098318621903E-6 7.6249037539285048E-4 4 20.121277934427425 -6.5257914627636637E-9 1.7869076249513337E-5 CERO 5 20.121278254067278 -1.3322676295501878E-13 1.5885663342464363E-8 RAÍZ CERO X( 15.9818 )= 20.121277934427425 Redodeando X( 15.9818 )= 20.121277934427425 P4 15.755699999999999 = 13.782316088676453 0.32623469829559326 *x -2.0244203507900238E-2 *x^2 6.2441453337669373E-4 *x^3 -7.6583619375014678E-6 *x^4 Reacomodando 0= -1.9733839113235465 0.32623469829559326 *x -2.0244203507900238E-2 *x^2 6.2441453337669373E-4 *x^3 -7.6583619375014678E-6 *x^4 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 13 -4.9497178435764511E-4 1 13.291700000000001 1.353988773279205E-2 2 13.010287475219876 1.0393101910560754E-5 2.1630000514294461E-2 3 13.010071299440311 -2.1842591516052501E-7 1.6616033424384047E-5 CERO 4 13.010075749166425 3.4397762416205069E-12 3.4202153780472487E-7 RAÍZ CERO 5 13.010075749096352 -6.9388939039072284E-16 5.3861119606108547E-12 RAÍZ CERO X( 15.755699999999999 )= 13.010075749096352 Redodeando X( 15.755699999999999 )= 13.010075749096352