Taller 3 Elementos Aproximacion de Funciones

8/17/2019 Taller 3 Elementos Aproximacion de Funciones

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0 0.5 10

5

10

15

20

25



Exponencial A#$0.1%2.4& '#a()*x+ 2%4#a($)*0.1&,-$a(&

Ex!e"o# B#$4./%20.4& 20%4#a($)*4%/& ,-$)(&

X Y NUMERICO

0.1 5.4 5.1711021643

0./ / 6.1185524459

a1 1.1 7.239594741a2 1./ 10 8.5660346098

a3 2.1 12.4 10.1355050334

a4 2./ 14. 11.9925341141

a5 3.1 1/. 14.1898084018

a/ 3./ 1. 16.7896676851

a 4.1 22 19.8658736605

a 4.6 22. 23.5057026558

X Y NUMERICO0.1 5.4 5.4

Ψ=4x+5 0./ / 7.4

1.1 9.4

1./ 10 11.4

2.1 12.4 13.4

2./ 14. 15.4

3.1 1/. 17.4

3./ 1. 19.4

4.1 22 21.4

4.6 22. 23.4



ALGEBRAICA

X y NUMERICO

0.1 5.4 5.305/

Ψ=4x+5 0./ / .13433/

1.1 ./1/

1./ 10 10./34/2.1 12.4 12.301/

2./ 14. 14.13545/

3.1 1/. 15.03/

3./ 1. 1./3//01/

4.1 22 1.545

4.6 22. 22./45//4

N#ax*2)xc a#0.4 #,0.04x*23.4x5.5.4#a$0.1&*2)(0.1c )#3.4

15.4#a$2./&*2)(2./c c#5.04

23.4#a$4./&*2)(2./c



LOGARIMO

6 'ANALITICO

1.1 ' 1.43/405/21

1./ .033/443

2.1 10 11.11/43014

2./ 12.4 14.40031103/

3.1 14. 1.05121/014

3./ 1/. 1.30405

4.1 1. 21.2/404//2

4./ 22 22.2

22.x #5%31e*0%34x

0.02 #Log1%0/$ ,5.55/

0.03 5.3551423 ,52.4///2

0.04 5.33105 ,4.5112//5

0.05 5.325441 ,45.142/1

0.0/ 5.4113423 ,42.4005540354

0.0 5.4302021 ,40.03/031

0.0 5.441325 ,3.0/43421

0.0 5.4/1332 ,3/.241112

0.1 5.41553 ,34.01//2202

0.11 5.50/32424 ,33.2/555/51

0.12 5.52551/3 ,31.5422124/

0.13 5.54413 ,30.4055

0.14 5.5/41113 ,2./3103/0/23

0.15 5.535022 ,2.512532/

0.1/ 5./022/ ,2./1/0142

0.1 5./22504 ,2/.04355351

0.1 5./421053 ,25.4350312

0.1 5.//1413 ,25.02//1/2

0.2 5./151142 ,24.255/3344

0.21 5.013152 ,23.52032313

0.22 5.2112/ ,22.122513

0.23 5.411311 ,22.14203

0.24 5./11510 ,21.50553

0.25 5.1234 ,20.2//541/

0.2/ 5.01354 ,20.3015511/

0.2 5.21/1254 ,1.32544

0.2 5.41005 ,1.14033215



0.2 5./2223 ,1./554/51/

0.3 5.2055 ,1.1442055/

0.31 5.0321/03 ,1./50431

0.32 5.23501 ,1.122/3/4

0.33 5.444453 ,1/.05123



POLINOMIO

! YANALIICO

0.1 y 5.3

0./ 5.4 .35544444441.1 / .310

1./ 11.2//3333334

2.1 10 13.221

2./ 12.4 15.12222224

3.1 14. 1.132//////

3./ 1/. 1.01111114

4.1 1. 21.043555555

4./ 22 22.0000004

22.

A1 A3

.3554444444 A2 22.0//3333332

,0.5523104 .310 14.10 2.32//////

,0.233/11 11.2//3333334 1./21 33.0000002

0.1//21 13.221 22.532/// 3.//5333333

1.355532 15.12222224 2/.443555/ 45.531/////2

1.55/411 1.132////// 30.3544444 51.3000000

1.154/43 1.01111114 34.2/53333 5.2/43333342

0.0/3101 21.043555555 3.1/2222 /3.130/////

,0.151324523 42.01111



1.5 2 2.5 3 3.

APROXIMACION DE FUNCIONES



%5#$)*2375&($)*,1710&

b a

1.40001 5 .00005

"1 "2 "3 "4

,1.4 /.11552445 .433/0/ .1/23325/5 11.21204242

,2.4 .235441 10.4234/402 15.152 21.51222

,1.4 .5//034/0 14./534 25.1413//3 43.0341302,1 10.1355050334 20.545/245/3 41./413/0 4.4250501

,0. 11.25341141 2./4145 /.10/402 1/5.455514

,0./ 14.10401 40.2013245 114.250255 324.33/1424

,0. 1/.///51 5/.35153 1.31555201 /35.00413

0./ 1./53//05 .305253 313./050142 124/.00521

MIN#ERSA /.0/55513 ,242.0/150// 32/.05513003/1 ,23.42/23/

,234.214/42 0.1325010 ,102.402/44 14.2103142

304.34/31 ,104/.//30150 14.203/201 ,115.305/51

,215.25405/ /1.220322/13 ,111.0125020 .30//13.32/3202 ,324.415//2 4.553/5/52 ,3.5/4

,22.023510433 1.14050245 ,124.253354 103.223/13

2.5/1/3/52 ,11.02/000 1.25/1325 ,14./1440

,0.1//5110 0./21240 ,0./21222 0.//0/005

1.4/21015 .04/00003

,/3.213512 11.530352

4.1021/0 20.2323

,/13.301/0223 41.01342325.22222/5 4.025/2

,/4.//102142 22.1025/4

.544/532/ 52.222

,0.4523 1513.155

35.20044

1045.5414



"1 "2 "3

,1.4 .43/ .20 11.41/32

,2.4 ./ 12.25/ 1/./52

,1.4 12./ 1/./444 22.44/2

,1 1/.0/ 20.442 2.1502,0. 1./ 24.3340 33.112

,0./ 23.3/ 2.304 3.332

,0. 2.4/ 32.35/ 4/.0152

0./ 33.4/ 3/.44 52.222

MIN#ERSA

1.112/04 ,2.150/105 ,0.3/3014/

./545E014 ,545/23022421 .054/E014

2.0441E014 //4433443//. ,1.0551E015

4 1.022/E013 ,141405/22 2./44E014.1510/4E013 141/0253014 ,3.0/05E014

.2/034E013 ///0345040/.3 2.0/1/E014

.00E014 1113/40234/ 3./53E014

1./20/4E014 ,1102011433,2.240E014

2.3333 45.435

./5555E013 4.125

.5201E013 52.35

2./03/E014 55.5

.032E014 5.5.004/E013 /2

.1/2E014 /5.5

2.02/25E014 /.5

3

5.5



"1 "2 "3

,1.4 ,/0.1215433 ,/.0050154 ,1/.02143,2.4 ,3.3455155121 13.133/5314 ,33.5/0/3453

,1.4 ,35./3522 ,25./242/404 50.3153/1

,1 .2010 ,2.320/2405 1./1051/2

,0. 14.020325533 3.25400 ,44.030/03

,0./ ,1./20/42 34.34/01 ,11.1440535

,0. ,4.401031 ,5./5211 11.0/4/4/3

0./ ,3/.5/34/5 ,5.4/5003 /1.1/5230

MIN#ERSA

,0.003/0/23 ,0.0112505/2 ,0.0035052,0.00354/4 0.004204 0.004233412

,0.00/2535/ ,0.0051330 0.01254424//

,0.00//411/ 0.01/35145 0.0024/3

,0.0042012 ,0.00230/15/1 0.0011552322

0.0005/434 ,0.004121/ ,0.00513114

0.00023413 ,0.00/050/51 0.003054054

0.005244412 ,0.01513/22 0.0013311

RESULADOS

0.05/0543 a1 5.5//4402

,0.0213122 a2 1.433102/23

0.03/34/55 a3 /.23244033

,0.000/5/ a4 .050554

0.022/2255 a5 13./202/521

0.011334521 a/ 1/.201//

0.005/3341 a 15.20102

0.0/305123a



C8ce apoxi"a9o 6 '

2.05 10.5

"1 "2 "3

,0.5523104 ,./5152 2.44425/ .5454

,0.233/11 1.43/405/21 11.240302 1.345322/

0.1//21 .033/443 1.52/43 23./4041040

1.355532 11.11/43014 21./25222 2.3/4/

1.55/411 14.40031103/ 24.4/23444 30.543//

1.154/43 1.05121/014 2.454/422 33./02/25//

0.0/3101 1.30405 2.51123330 35./13/254

,0.151324523 21.2/404//2 31.111343 3.21503/

.01/4/E014 /033/4/503/ ,/.534E013

3.20554/E014 ,4/121 1.0011E014

.04/55E014 /52242/344./ .4023E013

3.//0/E013 10/245420540 1.505E012

2.2501E014 ,401304021,1.0254E014

.3431E014 3/31033/0/5 ,4.44142E012

.213501E013 ,103440/3/345 3.3/0E013

.112554E014 3212/2/53120/ 3.034E013

441341531/ A1

,12250// A2

,20453143304 A3

,500354 A4



,2210310/341 A5

15/524454 A/

2542550504 A

35001154/ A



A4 A5 A/ A A

2.421/ 3/.222222 44.132//////4 51.4111110 5.43555555

3.243555555/ 4/.5544444445 55./53333334 /5.1/2222223 4.4111111

45.0/5333333/ 5/.331///// /.50000004 ./4333333 0.130/////

52.111111/ //.105 .330/////4 2.5524444453 105.422222

/0.0/ 5./111112 1.0/33333344 10/.24055555/ 121.41

/.530////// 5.//33333345 102./000001 11.2/////3 13.0/133334

/.352444445/ 5.44055555 114.52///// 133./1/ 152.04

4.14222223/ 105.215 12/.2/1333335 14.30413 1/.3444445



5 4 4.5 5

ExponecialVALOR REAL

ALGEBRAICA

TRIGONOMETRICA

logai!"ica

polino"io



"5 "6 "7 "8

13.20240021 1/.///5 20.545/245/ 25.1413// MARI$

31.134/44 4/.01353/ //.02340 /.5154

3.3//445/ 12/.423252 21/.50125 31.0/32111.131/44 34/.144103 03.2305505 1425.5135/

3/.423245 51.53540 223.2/0/2/ 54/.431/2

20.4551//55/2 2/12.21/412 413.30302 2103./041

2134.//035 1/.05/512 240/.21/25 025.105

450./0555332 1//./2103 150.4143/ 31050/.44

102.41122/ ,2/.140115/2 3./12//1/ ,0.2101101/

,35.4/211//5 2.304522 ,13.050453/ 0.//103

522.5/2000 ,13./133 1.4/35303 ,1.1220055

,411.3/420/3 111.15//0201 ,1/.2413214 0.0421521.13232 ,52.3/50/11/ .3/553 ,0.4/435

,50./323501 14.4102444 ,2.21/10333 0.141554

.32/5/4 ,2.142/01/1 0.334431 ,0.02242/354

,0.441/51/24 0.132543135 ,0.021435 0.00145/

RESULADOS 5.111021/43

/.11552445

.235441

.5//034/010.135505033

11.2534114

14.10402

1/.///5

1./53//1

23.50502/5/



"4 "5 "6 "7 "8

13.541/ 15.//2 1.2/4 1.10 22.04352

20.113/ 24.542 2./04 32./3 3/.522

2.24/ 34.0512 3.5344 45./55/ 51.452

35.545/ 43.552 51.2/14 5./54 //.//1243./21/ 53.252 /2.2224 2.5/2 2.21/32

51.5// /3.2022 4.34/4 /.4/0 .052

5./3/ 3.332 /.04 100./5 114.312

/.5// 3.//2 .41544 115.144/ 130.32

0.3/3014/ 1.0534502 ,0.2523053 0.32514 ,0.0/1215/

,32205/20//5001 ,1.5405E014 ,5./2/5E013 2./2E013 .114/1E013

512313/5/2153 2.255/E014 1.1/45E014 2.101/4E013 ,1.511E014

,413411/./ ./33E013 ,1.20E014,.2355E013 1.034/E014130111/4205 ,1.0225E014 1.25153E014 5.3/221E013,.3E013

,1545/4/535 ,./053E013 ./3E013,/.0102E013 4.44541E013

,23410253/333 ,1.1053E014 ,3.41E013,/.53E012 /.04/E013

1/235013/02 1.3053E014 ,4.14E013 4.4/231E013,5.03/2E013

RESULADOS

5.305/

.13433/

./1/

10./34/

12.301/14.13545/

15.03/

1./3//01/

1.545

22./45//4



"4 "5 "6 "7 "8

1.402130/ ,.1431 ,4.401032 ,2.320/240 50.3153/1,4./30403 102.3505 ,2.3314/ ,53.2110 1/.021251

2.45443252 ,24.2152/522 ,34./1/231 //.11001/14 ,15.2/10022

.2332/// ,2/.12/35/1 15.3/3053 .13015 ,24.35/0

,35.450005 ,42.//4/4 ,12.41/11 .1143120/ ,2.//222432

4/.0125213 ,4./2240330 5.41051 1.43014323 /.04//532

,12.14240 102.522/0 .354250 10.50213 ,50.54515

,50.5035241 ,30.4004/ 0.440545 ,4.425002 ,5/.01222300

,0.01/343 ,0.0043403 ,0.00230/35 0.00251433/5 ,0.003040/0.00/54//2 0.0005/32 0.0004//3/ ,0.002/15 ,0.00010523

,0.023/3 ,0.00434252 0.000/3511 ,0.001/134 0.00223/04

0.044/31/53 ,0.0021042/ 0.0044/112 ,0.005240442 ,0.002//25

,0.01530015/ ,0.003453432 0.001312 0.005/150 ,0.0020005

,0.0005101/ 0.00202202 0.00/554342 0.005012 0.00350/15

,0.00/23// 0.0035512 0.00330032 0.00/5351045 ,0.001/04255

,0.04210220/2 ,0.003555105 0.00505040 0.00524//4/1 0.001/04/



"4 "5 "6 "7 "8

13.140///4 1/.55045//4 1.30405 21./2522 23./4041040

22.3203043 25./2041042 2.435/ 30./211 32.54055

2./030224/ 31.33222 34.0/4314 3/.4023 3.4223/2/5

32.04305/3 35.432/5/1 3.150214/ 40.5020/1 42.520/41304

35.2305/552 3./5/02453 41.403/50 43.2/5441 45.3332/

3.43233 41.30/5031 44.0545530/ 4/.3053 4.30215124

40.145/015 43.5/04240/ 4/.301/5 4./3135422 50./4312

42.15401 45.520431/ 4.2/13101 50.513/334 52./03021

,133//514/010 1.2/34E015 1.04//E015,5.0534E014 ,4.224E014

22/35/010 ,1.413E015 ,1.355/4E015 4.33//E014 5.4352E014

331543 ,4.3/0E014 ,1./5E014 2.3315E014 ,4.3220E013

,102204 ,2.000/E014 ,4.44142E012 1.143E014 /.433E013

1021///1010020 ,5.///51E014 ,.12E014 3./21/E014 2.42E014

,154/53155 /.110/E014 /./1E014,2.4251E014 ,2.5/0E014

,4003531551 3.0112E014 1.4434/E014,./230E013 ,4.1/13E013

,4453513142 4.1/53E014 3.521E014,3.041E014 ,1./25E014



MARI$



MARI$

MIN#ERSA

Taller 3 Elementos Aproximacion de Funciones

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