akar kelompok 9 kelas vib

7/24/2019 Akar Kelompok 9 Kelas VIB

1/13

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


2/13


3/13

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


4/13

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


5/13

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


6/13

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$%


7/13

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


8/13

4.90E-015 !E"T

0 !E"T

0 !E"T

0 #T$%


9/13

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)( +=


10/13

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*


11/13

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.


12/13

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


13/13

f(x

antara

etnrlkan

nkan

/ an

akar kelompok 9 kelas vib

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