akar kelompok 9 kelas vib
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Koefsien Nilai x f(x)
p 1 0.1 -4.897755
q 3 0.29 -1.629523
r 2 0.48 0.028492
0.67 1.247467Toleransi Galat 0.86 2.287131
n 15 1.05 3.24887
T 5E-016 1.24 4.182934
1.43 5.117923
Interval Akar 1.62 6.071678
a 0.1 1.81 7.056081
b 2 2 8.079442
Interval Akar
0 0.5
-6
-4
-2
0
2
4
6
8
10
rxqpxxf ++= ln)( 2
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i Bisection
a f(a) b f(b) x f(x)
1 0.1 -4.897755 2 8.0794415417 1.05 3.24887
2 0.1 -4.897755 1.05 3.2488704925 0.575 0.670469
3 0.1 -4.897755 0.575 0.6704692854 0.3375 -1.144663
4 0.3375 -1.144663 0.575 0.6704692854 0.45625 -0.1459795 0.45625 -0.145979 0.575 0.6704692854 0.515625 0.278743
6 0.45625 -0.145979 0.515625 0.2787425749 0.4859375 0.071109
7 0.45625 -0.145979 0.4859375 0.0711094614 0.47109375 -0.036165
8 0.471094 -0.036165 0.4859375 0.0711094614 0.47851563 0.017778
9 0.471094 -0.036165 0.4785156 0.0177779599 0.47480469 -0.009116
10 0.474805 -0.009116 0.4785156 0.0177779599 0.47666016 0.00435
11 0.474805 -0.009116 0.4766602 0.0043503964 0.47573242 -0.002378
12 0.475732 -0.002378 0.4766602 0.0043503964 0.47619629 0.000987
13 0.475732 -0.002378 0.4761963 0.0009874924 0.47596436 -0.000695
14 0.475964 -0.000695 0.4761963 0.0009874924 0.47608032 0.000146
15 0.475964 -0.000695 0.4760803 0.0001463891 0.47602234 -0.000274
16 0.476022 -0.000274 0.4760803 0.0001463891 0.47605133 -6.4E-005
17 0.476051 -6.4E-005 0.4760803 0.0001463891 0.47606583 4.12E-005
18 0.476051 -6.4E-005 0.4760658 4.12405E-005 0.47605858 -1.1E-005
19 0.476059 -1.1E-005 0.4760658 4.12405E-005 0.4760622 1.50E-005
20 0.476059 -1.1E-005 0.4760622 0.000014953 0.47606039 1.81E-006
21 0.476059 -1.1E-005 0.4760604 1.80920E-006 0.47605948 -4.8E-006
22 0.476059 -4.8E-006 0.4760604 1.80920E-006 0.47605994 -1.5E-006
23 0.47606 -1.5E-006 0.4760604 1.80920E-006
0.47606016 1.66E-00724 0.47606 -1.5E-006 0.4760602 1.66225E-007 0.47606005 -6.6E-007
25 0.47606 -6.6E-007 0.4760602 1.66225E-007 0.47606011 -2.4E-007
26 0.47606 -2.4E-007 0.4760602 1.66225E-007 0.47606014 -3.9E-008
27 0.47606 -3.9E-008 0.4760602 1.66225E-007 0.47606015 6.35E-008
28 0.47606 -3.9E-008 0.4760601 6.35387E-008 0.47606014 1.22E-008
29 0.47606 -3.9E-008 0.4760601 1.21957E-008 0.47606014 -1.3E-008
30 0.47606 -1.3E-008 0.4760601 1.21957E-008 0.47606014 -6.4E-010
31 0.47606 -6.4E-010 0.4760601 1.21957E-008 0.47606014 5.78E-009
32 0.47606 -6.4E-010 0.4760601 5.77777E-009 0.47606014 2.57E-009
33 0.47606 -6.4E-010 0.4760601 2.56883E-009 0.47606014 9.64E-01034 0.47606 -6.4E-010 0.4760601 0.000000001 0.47606014 1.62E-010
35 0.47606 -6.4E-010 0.4760601 1.62121E-010 0.47606014 -2.4E-010
36 0.47606 -2.4E-010 0.4760601 1.62121E-010 0.47606014 -3.8E-011
37 0.47606 -3.8E-011 0.4760601 1.62121E-010 0.47606014 6.18E-011
38 0.47606 -3.8E-011 0.4760601 6.18416E-011 0.47606014 1.17E-011
39 0.47606 -3.8E-011 0.4760601 1.17015E-011 0.47606014 -1.3E-011
40 0.47606 -1.3E-011 0.4760601 1.17015E-011 0.47606014 -8.3E-013
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41 0.47606 -8.3E-013 0.4760601 1.17015E-011 0.47606014 5.43E-012
42 0.47606 -8.3E-013 0.4760601 5.43388E-012 0.47606014 2.30E-012
43 0.47606 -8.3E-013 0.4760601 2.30038E-012 0.47606014 7.33E-013
44 0.47606 -8.3E-013 0.4760601 7.33191E-013 0.47606014 -5.0E-014
45 0.47606 -5.0E-014 0.4760601 7.33191E-013 0.47606014 3.42E-013
46 0.47606 -5.0E-014 0.4760601 3.41505E-013 0.47606014 1.46E-013
47 0.47606 -5.0E-014 0.4760601 1.45661E-013 0.47606014 4.75E-014
48 0.47606 -5.0E-014 0.4760601 4.75175E-014 0.47606014 0
49 0.47606 0 0.4760601 0 0.47606014 0
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Regula Falsi
galat kriteria a f(a) b f(b) x f(x)
0.1 -4.897755 2 8.079442 0.817083601 2.061584
0.45238095 !E"T 0.1 -4.897755 0.817084 2.061584 0.604659974 0.856347
0.41304348 !E"T 0.1 -4.897755 0.60466 0.856347 0.529554616 0.373271
0.35185185 !E"T 0.1 -4.897755 0.529555 0.373271 0.499135426 0.1645030.13013699 !E"T 0.1 -4.897755 0.499135 0.164503 0.486165156 0.072736
0.05757576 !E"T 0.1 -4.897755 0.486165 0.072736 0.480514191 0.032198
0.03054662 !E"T 0.1 -4.897755 0.480514 0.032198 0.47802899 0.01426
0.01575456 !E"T 0.1 -4.897755 0.478029 0.01426 0.476931538 0.006317
0.0077551 !E"T 0.1 -4.897755 0.476932 0.006317 0.476446029 0.002798
0.00390786 !E"T 0.1 -4.897755 0.476446 0.002798 0.476231069 0.00124
0.00194632 !E"T 0.1 -4.897755 0.476231 0.00124 0.476135862 0.000549
0.00097506 !E"T 0.1 -4.897755 0.476136 0.000549 0.476093687 0.000243
0.00048705 !E"T 0.1 -4.897755 0.476094 0.000243 0.476075003 0.000108
0.00024365 !E"T 0.1 -4.897755 0.476075 0.000108 0.476066725 4.78E-005
0.00012179 !E"T 0.1 -4.897755 0.476067 4.78E-005 0.476063058 2.12E-005
6.090E-005 !E"T 0.1 -4.897755 0.476063 2.12E-005 0.476061433 9.37E-006
3.045E-005 !E"T 0.1 -4.897755 0.476061 9.37E-006 0.476060714 4.15E-006
1.522E-005 !E"T 0.1 -4.897755 0.476061 4.15E-006 0.476060395 1.84E-006
7.612E-006 !E"T 0.1 -4.897755 0.47606 1.84E-006 0.476060253 8.15E-007
3.806E-006 !E"T 0.1 -4.897755 0.47606 8.15E-007 0.476060191 3.61E-007
1.903E-006 !E"T 0.1 -4.897755 0.47606 3.61E-007 0.476060163 1.60E-007
9.516E-007 !E"T 0.1 -4.897755 0.47606 1.60E-007 0.476060151 7.09E-008
4.758E-007!E"T 0.1 -4.897755 0.47606 7.09E-008
0.4760601453.14E-008
2.379E-007 !E"T 0.1 -4.897755 0.47606 3.14E-008 0.476060143 1.39E-008
1.189E-007 !E"T 0.1 -4.897755 0.47606 1.39E-008 0.476060142 6.16E-009
5.947E-008 !E"T 0.1 -4.897755 0.47606 6.16E-009 0.476060141 2.73E-009
2.974E-008 !E"T 0.1 -4.897755 0.47606 2.73E-009 0.476060141 1.21E-009
1.487E-008 !E"T 0.1 -4.897755 0.47606 1.21E-009 0.476060141 5.36E-010
7.434E-009 !E"T 0.1 -4.897755 0.47606 5.36E-010 0.476060141 2.37E-010
3.717E-009 !E"T 0.1 -4.897755 0.47606 2.37E-010 0.476060141 1.05E-010
1.858E-009 !E"T 0.1 -4.897755 0.47606 1.05E-010 0.476060141 4.66E-011
9.292E-010 !E"T 0.1 -4.897755 0.47606 4.66E-011 0.476060141 2.07E-011
4.646E-010 !E"T 0.1 -4.897755 0.47606 2.07E-011 0.476060141 9.15E-0122.323E-010 !E"T 0.1 -4.897755 0.47606 9.15E-012 0.476060141 4.05E-012
1.162E-010 !E"T 0.1 -4.897755 0.47606 4.05E-012 0.476060141 1.80E-012
5.808E-011 !E"T 0.1 -4.897755 0.47606 1.80E-012 0.476060141 7.95E-013
2.904E-011 !E"T 0.1 -4.897755 0.47606 7.95E-013 0.476060141 3.53E-013
1.452E-011 !E"T 0.1 -4.897755 0.47606 3.53E-013 0.476060141 1.56E-013
7.260E-012 !E"T 0.1 -4.897755 0.47606 1.56E-013 0.476060141 6.91E-014
3.630E-012 !E"T 0.1 -4.897755 0.47606 6.91E-014 0.476060141 3.06E-014
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1.815E-012 !E"T 0.1 -4.897755 0.47606 3.06E-014 0.476060141 1.33E-014
9.075E-013 !E"T 0.1 -4.897755 0.47606 1.33E-014 0.476060141 6.22E-015
4.537E-013 !E"T 0.1 -4.897755 0.47606 6.22E-015 0.476060141 3.11E-015
2.268E-013 !E"T 0.1 -4.897755 0.47606 3.11E-015 0.476060141 0
1.133E-013 !E"T
5.667E-014 !E"T
2.834E-014 !E"T
1.411E-014 !E"T
0 #T$%
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galat kriteria
0.259978 !E"T
0.124211 !E"T
0.057443 !E"T0.025985 !E"T
0.011624 !E"T
0.005172 !E"T
0.002296 !E"T
0.001018 !E"T
0.000451 !E"T
0.0002 !E"T
8.86E-005 !E"T
3.92E-005 !E"T
1.74E-005 !E"T
7.70E-006 !E"T
3.41E-006 !E"T
1.51E-006 !E"T
6.70E-007 !E"T
2.97E-007 !E"T
1.31E-007 !E"T
5.82E-008 !E"T
2.58E-008 !E"T
1.14E-008 !E"T5.07E-009 !E"T
2.24E-009 !E"T
9.94E-010 !E"T
4.40E-010 !E"T
1.95E-010 !E"T
8.65E-011 !E"T
3.83E-011 !E"T
1.70E-011 !E"T
7.52E-012 !E"T
3.33E-012 !E"T1.48E-012 !E"T
6.54E-013 !E"T
2.90E-013 !E"T
1.28E-013 !E"T
5.69E-014 !E"T
2.52E-014 !E"T
1.12E-014 !E"T
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4.90E-015 !E"T
0 !E"T
0 !E"T
0 #T$%
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iNewton-Raphson Sec
x f(x) f'(x) galat Kriteria x f(x)
1 0.1 -4.897755279 30.2 0.1 -4.89775528
2 0.262177 -1.947465598 11.96699 1.621773 !E"T 2 8.0794415423 0.424914 -0.387055406 7.910084 0.620711 !E"T 0.817084 2.061584025
4 0.473846 -0.016091138 7.278867 0.115157 !E"T 0.411843 -0.49172638
5 0.476056 -2.7660E-005 7.253888 0.004665 !E"T 0.489886 0.099237877
6 0.47606 -8.1697E-011 7.253845 8.01E-006 !E"T 0.47678 0.005220625
7 0.47606 0 7.253845 2.37E-011 !E"T 0.476053 -5.523E-005
8 0.47606 0 7.253845 0 #T$% 0.47606 3.0788E-008
9 0.47606 0 7.253845 0 #T$% 0.47606 1.8208E-013
10 0.47606 0 7.253845 0 #T$% 0.47606 0
11 0.47606 0 7.253845 0 #T$% 0.47606 0
12 0.47606 0 7.253845 0 #T$% &'I)0*
13 0.47606 0 7.253845 0 #T$% &'I)0*
14 0.47606 0 7.253845 0 #T$% &'I)0*
15 0.47606 0 7.253845 0 #T$% &'I)0*
16 0.47606 0 7.253845 0 #T$% &'I)0*
17 0.47606 0 7.253845 0 #T$% &'I)0*
18 0.47606 0 7.253845 0 #T$% &'I)0*
19 0.47606 0 7.253845 0 #T$% &'I)0*
20 0.47606 0 7.253845 0 #T$% &'I)0*
rxqpxxf ++= ln)( 2
xqpxxf /2)( +=
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nt
galat Kriteria
0.591458 !E"T
0.49596 !E"T
0.189497 !E"T
0.026752 !E"T
0.001526 !E"T
1.60E-005 !E"T
8.92E-009 !E"T
5.27E-014 !E"T
0 #T$%
&'I)0*
&'I)0*
&'I)0*
&'I)0*
&'I)0*
&'I)0*
&'I)0*
&'I)0*
&'I)0*
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Analisis hasil perhitungan Bisection, Regula Falsi, Newton Raphson, an Secant
Ko!ponen BisectionRegula Falsi Newton Raphson Secant
Ban"ak iterasi 49 44 8 11
Nilai ha!piran 0+47606 0+47606 0+47606 0+47606
Galat 0 4.70E-16 0 0
Kesi!pulan # 1. ,eraarkan prakt/k enan ke-4 ete ntk enar/ akar: x;2 < 3 ln x < 2 aala enekat/ 0+47606.2. ,eraarkan ra=k ater paa fn/ /perle baa akar terlkrva)ar/ teraap b x.3. ,eraarkan /tera/ ternata ete ,/et/n /perle /tera/ apn enan 8 /tera/. >al /n/ /karenakan ete ,/et/n a/tera/ an kp banak ntk enekat/ n/la/ akar terebt an 4. ,eraarkan alat an /perle+ enan ete ,/et/n+ !entk ela al/ alatna aala 4.7E-16 an pre berent/ kare
#e/na apat //plkan baa ar/ kepat ete penar/an a/perlkan pal/n e/k/t /ban/nkan ete an la/nna.
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a/t ete ,/et/n+ ela al/+ !etn apn+ an #eant /perle akar ar/
letak paa enekat/ t/t/k 0+5 /ana akar at peraaan aala perptnan
n pal/n banak a/t 49 /tera/ an an pal/n e/k/t /tera/na aala etea eba/ a /ntervalna+ e/na ?/ka ?arak /ntervalna kp ?a akan eeeerlkan akt an kp banak ?/ka k/ta ener?akanna eara anal.
tn apn+ an #eant alatna aala 0 an pre berent/ paa f(x : 0 eana n/la/ alat terebt : 4.7E-16 @ T: 5.10
-16.
kar peraaan /keta/ baa ete !etn apn pal/n efekt/f+ karena /tera
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f(x
antara
etnrlkan
nkan
/ an
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