Metode Tabulasi
mencari akar persamaan
b. y = f(x) = 2 – 3x + sin x = 0
tentukan x1=0 dan x2=1
f(x1)=f(0)=2-3(0)+sin(0)=2
f(x2)=f(1)=2-3(1)+sin(1)=-0.98254
f(x1).f(x2)=2(-0.98254)<0
membuat tabel fungsi disekitar 0 dan 1
| | | |
| METODE TABULASI | | |
| | | |
| x | f(x) | AE |
| 0.0 | 2 | 1.4912736 |
| 0.1 | 1.7017453 | 1.1930189 |
| 0.2 | 1.4034907 | 0.8947642 |
| 0.3 | 1.105236 | 0.5965096 |
| 0.4 | 0.8069813 | 0.2982549 |
| 0.5 | 0.5087265 | 1.329E-07 |
| 0.6 | 0.2104718 | 0.2982546 |
| 0.7 | -0.087783 | 0.5965094 |
| 0.8 | -0.3860378 | 0.8947642 |
| 0.9 | -0.6842927 | 1.1930191 |
| 1.0 | -0.9825476 | 1.491274 |
| x | 0.5087264 | |
| | | |
| x | f(x) | AE |
| 0.60 | 0.2104718 | 0.1491274 |
| 0.61 | 0.1806463 | 0.1193019 |
| 0.62 | 0.1508208 | 0.0894764 |
| 0.63 | 0.1209954 | 0.059651 |
| 0.64 | 0.0911699 | 0.0298255 |
| 0.65 | 0.0613444 | 1.728E-09 |
| 0.66 | 0.0315189 | 0.0298255 |
| 0.67 | 0.0016934 | 0.059651 |
| 0.68 | -0.028132 | 0.0894764 |
| 0.69 | -0.0579575 | 0.1193019 |
| 0.70 | -0.087783 | 0.1491274 |
| x | 0.0613444 | |
| | | |
| x | f(x) | AE |
| 0.670 | 0.0016934 | 0.0115259 |
| 0.671 | -0.0012891 | 0.0145084 |
| 0.672 | -0.0042717 | 0.017491 |
| 0.673 | -0.0072542 | 0.0204735 |
| 0.674 | -0.0102368 | 0.0234561 |
| 0.675 | -0.0132193 | 0.0264386 |
| 0.676 | -0.0162018 | 0.0294211 |
| 0.677 | -0.0191844 | 0.0324037 |
| 0.678 | -0.0221669 | 0.0353862 |
| 0.679 | -0.0251495 | 0.0383688 |
| 0.680 | -0.028132 | 0.0413513 |
| x | -0.0132193 | |
| | | |
| x | f(x) | AE |
| 0.6700 | 0.0016934 | 0.0016404 |
| 0.6701 | 0.0013952 | 0.0013421 |
| 0.6702 | 0.0010969 | 0.0010439 |
| 0.6703 | 0.0007987 | 0.0007456 |
| 0.6704 | 0.0005004 | 0.0004474 |
| 0.6705 | 0.0002022 | 0.0001491 |
| 0.6706 | -9.609E-05 | 0.0001491 |
| 0.6707 | -0.0003943 | 0.0004474 |
| 0.6708 | -0.0006926 | 0.0007456 |
| 0.6709 | -0.0009909 | 0.0010439 |
| 0.6710 | -0.0012891 | 0.0013421 |
| x | 5.304E-05 | |
| | | |
| x | f(x) | AE |
| 0.67050 | 0.0002022 | 0.000164 |
| 0.67051 | 0.0001723 | 0.0001342 |
| 0.67052 | 0.0001425 | 0.0001044 |
| 0.67053 | 0.0001127 | 7.456E-05 |
| 0.67054 | 8.286E-05 | 4.474E-05 |
| 0.67055 | 5.304E-05 | 1.491E-05 |
| 0.67056 | 2.321E-05 | 1.491E-05 |
| 0.67057 | -6.613E-06 | 4.474E-05 |
| 0.67058 | -3.644E-05 | 7.456E-05 |
| 0.67059 | -6.626E-05 | 0.0001044 |
| 0.67060 | -9.609E-05 | 0.0001342 |
| x | 3.813E-05 | |
| | | |
| x | f(x) | AE |
| 0.670560 | 2.321E-05 | 1.64E-05 |
| 0.670561 | 2.023E-05 | 1.342E-05 |
| 0.670562 | 1.725E-05 | 1.044E-05 |
| 0.670563 | 1.427E-05 | 7.456E-06 |
| 0.670564 | 1.128E-05 | 4.474E-06 |
| 0.670565 | 8.3E-06 | 1.491E-06 |
| 0.670566 | 5.317E-06 | 1.491E-06 |
| 0.670567 | 2.335E-06 | 4.474E-06 |
| 0.670568 | -6.477E-07 | 7.456E-06 |
| 0.670569 | -3.63E-06 | 1.044E-05 |
| 0.670570 | -6.613E-06 | 1.342E-05 |
| x | 6.809E-06 | |
| | | |
| x | f(x) | AE |
| 0.6705670 | 2.335E-06 | 1.64E-06 |
| 0.6705671 | 2.037E-06 | 1.342E-06 |
| 0.6705672 | 1.738E-06 | 1.044E-06 |
| 0.6705673 | 1.44E-06 | 7.456E-07 |
| 0.6705674 | 1.142E-06 | 4.474E-07 |
| 0.6705675 | 8.436E-07 | 1.491E-07 |
| 0.6705676 | 5.453E-07 | 1.491E-07 |
| 0.6705677 | 2.47E-07 | 4.474E-07 |
| 0.6705678 | -5.121E-08 | 7.456E-07 |
| 0.6705679 | -3.495E-07 | 1.044E-06 |
| 0.6705680 | -6.477E-07 | 1.342E-06 |
| x | 6.944E-07 | |
| | | |
jadi y = f(x) = 2 – 3x + sinx = 0
akan menghasilkan
x = 0.6705677
dengan error sebesar 4.474 x 10-7
