Nama : Beny Cuknolan NainggolanNIM : 071652Jurusan / kelas : Teknik Sipil / B

1. x5-3x3+2x2+3x-40.3681

Metode Grafik

Y= x5-3x3+2x2+3x-40.3681

y

-50

0

50

100

150

200

0 1 2 3 4

y

metode Bisection

f=

2. x5-3x3+2x2+3x-40.3681

[0.21,3] e=0.01

r xa xp xb fxa fxp fxbselang baru lebar

0 0.21 1.605 3 -39.6773 -32.154 148.6319 [c,b] 1.395

1 1.605 2.3025 3 -32.154 5.236251 148.6319 [a,c] 0.6975

2 1.605 1.95375 2.3025 -32.154 -20.7786 5.236251 [c,b] 0.34875

3 1.95375 2.128125 2.3025 -20.7786 -10.19 5.236251 [c,b] 0.174375

4 2.128125 2.2153125 2.3025 -10.19 -3.16763 5.236251 [c,b] 0.087187

5 2.215313 2.25890625 2.3025 -3.16763 0.850057 5.236251 [a,c] 0.043594

6 2.215313 2.237109375 2.258906 -3.16763 -1.20336 0.850057 [c,b] 0.021797

7 2.237109 2.248007813 2.258906 -1.20336 -0.18798 0.850057 [c,b] 0.010898

8 2.248008 2.253457031 2.258906 -0.18798 0.328182 0.850057 [a,c] 0.005449

9 2.248008 2.250732422 2.253457 -0.18798 0.069389 0.328182 [a,c] 0.002725

Beny C N 1

x y0.21 -39.67732.25 0

3 148.6319

metode Regula Falsi

f=

3. x5-3x3+2x2+3x-40.3681

[0.21,2.5] e=0.01

r a0 c0 b0 fa0 fc0 fb0selang baru lebar

0 0.21 1.506339113 2.5 -39.6773 -33.8093 30.41315 [c,b] 0.993661

1 1.506339 2.02944252 2.5 -33.8093 -16.6923 30.41315 [c,b] 0.470557

2 2.029443 2.196189592 2.5 -16.6923 -4.81978 30.41315 [c,b] 0.30381

3 2.19619 2.237750138 2.5 -4.81978 -1.14429 30.41315 [c,b] 0.26225

4 2.23775 2.247259429 2.5 -1.14429 -0.25843 30.41315 [c,b] 0.252741

5 2.247259 2.249388927 2.5 -0.25843 -0.0577 30.41315 [c,b] 0.250611

6 2.249389 2.249863461 2.5 -0.0577 -0.01285 30.41315 [c,b] 0.250137

7 2.249863 2.249969089 2.5 -0.01285 -0.00286 30.41315 [c,b] 0.250031

8 2.249969 2.249992595 2.5 -0.00286 -0.00064 30.41315 [c,b] 0.250007

9 2.249993 2.249997826 2.5 -0.00064 -0.00014 30.41315 [c,b] 0.250002

10 2.249998 2.24999899 2.5 -0.00014 -3.2E-05 30.41315 [c,b] 0.250001

11 2.249999 2.249999249 2.5 -3.2E-05 -7E-06 30.41315 [c,b] 0.250001

12 2.249999 2.249999306 2.5 -7E-06 -1.6E-06 30.41315 [c,b] 0.250001

13 2.249999 2.249999319 2.5 -1.6E-06 -3.5E-07 30.41315 [c,b] 0.250001

14 2.249999 2.249999322 2.5 -3.5E-07 -7.7E-08 30.41315 [c,b] 0.250001

15 2.249999 2.249999322 2.5 -7.7E-08 -1.7E-08 30.41315 [c,b] 0.250001

16 2.249999 2.249999323 2.5 -1.7E-08 -3.8E-09 30.41315 [c,b] 0.250001

17 2.249999 2.249999323 2.5 -3.8E-09 -8.5E-10 30.41315 [c,b] 0.250001

18 2.249999 2.249999323 2.5 -8.5E-10 -1.9E-10 30.41315 [c,b] 0.250001

19 2.249999 2.249999323 2.5 -1.9E-10 -4.2E-11 30.41315 [c,b] 0.250001

20 2.249999 2.249999323 2.5 -4.2E-11 -9.4E-12 30.41315 [c,b] 0.250001

21 2.249999 2.249999323 2.5 -9.4E-12 -2.1E-12 30.41315 [c,b] 0.250001

22 2.249999 2.249999323 2.5 -2.1E-12 -5.1E-13 30.41315 [c,b] 0.250001

23 2.249999 2.249999323 2.5 -5.1E-13 -1.3E-13 30.41315 [c,b] 0.250001

24 2.249999 2.249999323 2.5 -1.3E-13 0 30.41315 [a,c] 0.250001

25 2.249999 2.249999323 2.249999 -1.3E-13 0 0 [a,c] 0

Beny C N 2

Metode Newton Raphson

f= 4. x5-3x3+2x2+3x-40.3681 [0.21] e=0.01

r xn fxn f'xn xn+1 dho0 0.21 -39.67727459 3.452824 11.70125 -1 11.70125 214824.4156 92552.03 9.380133 11.491252 9.380133 70305.85845 37957.1 7.527887 -2.321123 7.527887 22990.70493 15580.02 6.052234 -1.852254 6.052234 7506.395936 6406.157 4.880487 -1.475655 4.880487 2442.117958 2644.909 3.957159 -1.171756 3.957159 787.2504169 1103.935 3.244028 -0.923337 3.244028 247.2652291 475.0056 2.723475 -0.713138 2.723475 71.87070757 222.2211 2.400056 -0.520559 2.400056 16.51318804 126.6612 2.269683 -0.32342

10 2.269683 1.899121815 98.40328 2.250383 -0.1303711 2.250383 0.036338726 94.6554 2.249999 -0.019312 2.249999 1.41035E-05 94.58193 2.249999 -0.0003813 2.249999 2.13873E-12 94.5819 2.249999 -1.5E-07

2. 6e(-2x)+3x3-4x2-2x-10,8013

Metoda Grafis

Y=6e(-2x)+3x3-4x2-2x-10,8013

Beny C N 3

x Y0.21 -7.427642.29 0

7 808.1987

y

-200

0

200

400

600

800

1000

0 2 4 6 8

y

Metode Bisection

f= 6e(-2x)+3x3-4x2-2x-10,8013 [0.21,3] e=0.01

r xa xp xb fa fxp fbselang baru lebar

0 0.21 1.605 3 -7.42764 -11.6697 28.21357 [c,b] 1.395

1 1.605 2.3025 3 -11.6697 0.06784 28.21357 [a,c] 0.6975

2 1.605 1.95375 2.3025 -11.6697 -7.48361 0.06784 [c,b] 0.34875

3 1.95375 2.128125 2.3025 -7.48361 -4.17386 0.06784 [c,b] 0.174375

4 2.128125 2.2153125 2.3025 -4.17386 -2.17525 0.06784 [c,b] 0.087187

5 2.215313 2.25890625 2.3025 -2.17525 -1.08499 0.06784 [c,b] 0.043594

6 2.258906 2.280703125 2.3025 -1.08499 -0.51649 0.06784 [c,b] 0.021797

7 2.280703 2.291601563 2.3025 -0.51649 -0.22631 0.06784 [c,b] 0.010898

Metode Regula Falsi

f=

6e(-2x)+3x3-4x2-2x-10,8013 [0.21,3] e=0.01

r a0 c0 b0 fa0 fc0 fb0selang baru lebar

0 0.21 0.791577547 3 -7.42944 -12.1727 28.21177 [c,b] 2.208422

1 0.791578 1.457240228 3 -12.1727 -12.6028 28.21177 [c,b] 1.54276

2 1.45724 1.933617001 3 -12.6028 -7.81168 28.21177 [c,b] 1.066383

3 1.933617 2.164862006 3 -7.81168 -3.3626 28.21177 [c,b] 0.835138

4 2.164862 2.253802368 3 -3.3626 -1.21764 28.21177 [c,b] 0.746198

5 2.253802 2.284676315 3 -1.21764 -0.41296 28.21177 [c,b] 0.715324

6 2.284676 2.294996036 3 -0.41296 -0.13692 28.21177 [c,b] 0.705004

7 2.294996 2.298401161 3 -0.13692 -0.04506 28.21177 [c,b] 0.701599

8 2.298401 2.299519911 3 -0.04506 -0.01479 28.21177 [c,b] 0.70048

9 2.29952 2.299886955 3 -0.01479 -0.00485 28.21177 [c,b] 0.700113

10 2.299887 2.300007321 3 -0.00485 -0.00159 28.21177 [c,b] 0.699993

11 2.300007 2.300046786 3 -0.00159 -0.00052 28.21177 [c,b] 0.699953

12 2.300047 2.300059726 3 -0.00052 -0.00017 28.21177 [c,b] 0.69994

13 2.30006 2.300063968 3 -0.00017 -5.6E-05 28.21177 [c,b] 0.699936

14 2.300064 2.300065359 3 -5.6E-05 -1.8E-05 28.21177 [c,b] 0.699935

15 2.300065 2.300065815 3 -1.8E-05 -6E-06 28.21177 [c,b] 0.699934

16 2.300066 2.300065964 3 -6E-06 -2E-06 28.21177 [c,b] 0.699934

17 2.300066 2.300066013 3 -2E-06 -6.5E-07 28.21177 [c,b] 0.699934

18 2.300066 2.30006603 3 -6.5E-07 -2.1E-07 28.21177 [c,b] 0.699934

19 2.300066 2.300066035 3 -2.1E-07 -7E-08 28.21177 [c,b] 0.699934

20 2.300066 2.300066037 3 -7E-08 -2.3E-08 28.21177 [c,b] 0.699934

21 2.300066 2.300066037 3 -2.3E-08 -7.5E-09 28.21177 [c,b] 0.699934

22 2.300066 2.300066037 3 -7.5E-09 -2.5E-09 28.21177 [c,b] 0.699934

23 2.300066 2.300066037 3 -2.5E-09 -8E-10 28.21177 [c,b] 0.699934

Beny C N 4

24 2.300066 2.300066037 3 -8E-10 -2.6E-10 28.21177 [c,b] 0.699934

25 2.300066 2.300066037 3 -2.6E-10 -8.6E-11 28.21177 [c,b] 0.699934

26 2.300066 2.300066037 3 -8.6E-11 -2.8E-11 28.21177 [c,b] 0.699934

27 2.300066 2.300066037 3 -2.8E-11 -9.3E-12 28.21177 [c,b] 0.699934

28 2.300066 2.300066037 3 -9.3E-12 -3.1E-12 28.21177 [c,b] 0.699934

29 2.300066 2.300066037 3 -3.1E-12 -9.9E-13 28.21177 [c,b] 0.699934

30 2.300066 2.300066037 3 -9.9E-13 -3.4E-13 28.21177 [c,b] 0.699934

31 2.300066 2.300066037 3 -3.4E-13 -1E-13 28.21177 [c,b] 0.699934

32 2.300066 2.300066037 3 -1E-13 -3.2E-14 28.21177 [c,b] 0.699934

33 2.300066 2.300066037 3 -3.2E-14 0 28.21177 [a,c] 0.699934

34 2.300066 2.300066037 2.300066 -3.2E-14 0 0 [a,c] 0

Metode Newton Raphson

f= 6e(-2x)+3x3-4x2-2x-10,8013 [2] e=0.01

r Xn fxn f'xn xn+1 dho

0 2 -6.693206167 17.78021 2.376441 -

1 2.376441 2.168551043 29.71221 2.303456 0.376441

2 2.303456 0.092035845 27.20575 2.300073 -0.07299

3 2.300073 0.000192735 27.09184 2.300066 -0.00338

4 2.300066 8.51337E-10 27.0916 2.300066 -7.1E-06

5 2.300066 0 27.0916 2.300066 -3.1E-11

6 2.300066 0 27.0916 2.300066 0

3. 5lnx+3x2+4x+28,9446

Metoda Grafis

Y=5lnx+3x2+4x+28,9446

Beny C N 5

x Y0.21 21.849062.29 0

6 -46.096

y

-50

-40

-30

-20

-10

0

10

20

30

0 2 4 6 8y

Metode Bisection

f=5lnx+3x2+4x+28,9446

[0.21,5] e=0.01

r xa Cx xb fxa fxc fxbselang baru lebar

0 0.21 2.605 5 21.84906 23.79369 -18.0082 [c,b] 2.395

1 2.605 3.8025 5 23.79369 7.455875 -18.0082 [c,b] 1.1975

2 3.8025 4.40125 5 7.455875 -4.15396 -18.0082 [a,c] 0.59875

3 3.8025 4.101875 4.40125 7.455875 1.933185 -4.15396 [c,b] 0.299375

4 4.101875 4.2515625 4.40125 1.933185 -1.04007 -4.15396 [a,c] 0.149688

5 4.101875 4.17671875 4.251563 1.933185 0.464166 -1.04007 [c,b] 0.074844

6 4.176719 4.214140625 4.251563 0.464166 -0.28355 -1.04007 [a,c] 0.037422

7 4.176719 4.195429688 4.214141 0.464166 0.091407 -0.28355 [c,b] 0.018711

Metode Regula Falsi

f=5lnx+3x2+4x+28,9446

[0.21,4] e=0.01

r a0 c0 b0 fa0 fc0 fb0selang baru lebar

0 0.21 4.817354964 4 21.84906 -13.5456 3.876072 [c,b] 0.8173551 4.817355 4.181849934 4 -13.5456 0.362162 3.876072 [a,c] 0.181852 4.817355 4.198398671 4.18185 -13.5456 0.032056 0.362162 [a,c] 0.016549

Metode Newton Raphson

Beny C N 6

f=5lnx+3x2+4x+28,9446

[4] e=0.01

r xn fxn f'xn xn+1 dho0 3.5 12.45841484 -15.5714 4.300082 -1 4.300082 -2.034010702 -20.6377 4.201524 0.8000822 4.201524 -0.030474721 -20.0191 4.200001 -0.098563 4.200001 -7.28029E-06 -20.0095 4.200001 -0.001524 4.200001 -4.08562E-13 -20.0095 4.200001 -3.6E-075 4.200001 0 -20.0095 4.200001 -2E-146 4.200001 0 -20.0095 4.200001 0

Beny C N 7