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0 0.5 10
5
10
15
20
25
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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
8/17/2019 Taller 3 Elementos Aproximacion de Funciones
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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$4./&*2)(2./c
8/17/2019 Taller 3 Elementos Aproximacion de Funciones
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LOGARIMO
6 'ANALITICO
1.1 ' 1.43/405/21
1./ .033/443
2.1 10 11.11/43014
2./ 12.4 14.40031103/
3.1 14. 1.05121/014
3./ 1/. 1.30405
4.1 1. 21.2/404//2
4./ 22 22.2
22.x #5%31e*0%34x
0.02 #Log1%0/$ ,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
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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
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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
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1.5 2 2.5 3 3.
APROXIMACION DE FUNCIONES
8/17/2019 Taller 3 Elementos Aproximacion de Funciones
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%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
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"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
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"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
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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
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,2210310/341 A5
15/524454 A/
2542550504 A
35001154/ A
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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
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5 4 4.5 5
ExponecialVALOR REAL
ALGEBRAICA
TRIGONOMETRICA
logai!"ica
polino"io
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"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/
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"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
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"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/
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"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
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MARI$
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MARI$
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MARI$
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MARI$
MIN#ERSA
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