29
f(x) = e^(2x) Forward x y y' 0.5 2.718282 1 7.389056 9.341549 dy/dx di x=1 Backward x y y' 1 7.389056 25.39296 dy/dx di x=1 1.5 20.08554 Middle x y y' 0.5 2.718282 1 7.389056 17.36726 dy/dx di x=1 1.5 20.08554

Metode Numerik Matematika Teknik

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Metode Numerik Matematika Teknik

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Page 1: Metode Numerik Matematika Teknik

f(x) = e^(2x)

Forwardx y y'

0.5 2.71828181 7.3890561 9.3415485 dy/dx di x=1 Middle

xBackward 0x y y' 0.5

1 7.3890561 25.392962 dy/dx di x=1 11.5 20.085537 1.5

2Middlex y y'

0.5 2.71828181 7.3890561 17.367255 dy/dx di x=1

1.5 20.085537

Page 2: Metode Numerik Matematika Teknik

y y' y''1

2.7182818 6.38905617.3890561 17.367255 40.82003820.085537 47.209094

54.59815

Page 3: Metode Numerik Matematika Teknik

Metode Trapezoid Metode Simpson 1/6x y A x y A1 12 6.9375 1 12

1.5 15.75 8.9375 1.5 15.75 15.833332 20 11.1875 2 20

2.5 24.75 13.6875 2.5 24.75 24.833333 30 3 30

Hasil 40.75 Hasil 40.66667

∫(x²+5x+6) dx dengan 'range' x=1 sampai x=3 dan step=0,5

Page 4: Metode Numerik Matematika Teknik

i x1 f(x1) f'(x1) e1 i x21 -1 2 3 1 -42 -1.666667 0.4444444 1.6666667 2 -3.3333333 -1.933333 0.0711111 1.1333333 0.16 3 -3.0666674 -1.996078 0.0039369 1.0078431 0.0324544 4 -3.0039225 -1.999985 1.526E-05 1.0000305 0.001957 5 -3.0000156 -2 2.328E-10 1 7.629E-06 6 -37 -2 0 1 1.164E-10 7 -38 -2 0 1 0 8 -39 -2 0 1 0 9 -3

10 -2 0 1 0 10 -3

f(x)=x²+5x+6

Page 5: Metode Numerik Matematika Teknik

f(x2) f'(x2) e22 -3 x y

0.4444444 -1.666667 0.1666667 -20 3060.0711111 -1.133333 0.08 -19 2720.0039369 -1.007843 0.0204604 -18 2401.526E-05 -1.000031 0.0013004 -17 2102.328E-10 -1 5.086E-06 -16 182

0 -1 7.761E-11 -15 1560 -1 0 -14 1320 -1 0 -13 1100 -1 0 -12 90

Page 6: Metode Numerik Matematika Teknik

ẋ1 0 1 0 x1ẋ2 = 0 0 1 . x2 +ẋ3 -5 -7 -3 x3

t x1 x2 x3 ẋ1 ẋ2 ẋ30 1 0 0 0 0 -5

0.01 1 0 -0.05 0 -0.05 -4.840.02 1 -0.0005 -0.0984 -0.0005 -0.0984 -4.68130.03 0.999995 -0.001484 -0.145213 -0.001484 -0.145213 -4.5239480.04 0.9999802 -0.002936 -0.190452 -0.002936 -0.190452 -4.367990.05 0.9999508 -0.004841 -0.234132 -0.004841 -0.234132 -4.2134720.06 0.9999024 -0.007182 -0.276267 -0.007182 -0.276267 -4.0604370.07 0.9998306 -0.009945 -0.316871 -0.009945 -0.316871 -3.9089260.08 0.9997311 -0.013113 -0.355961 -0.013113 -0.355961 -3.758980.09 0.9996 -0.016673 -0.393551 -0.016673 -0.393551 -3.610638

0.1 0.9994333 -0.020608 -0.429657 -0.020608 -0.429657 -3.4639360.11 0.9992272 -0.024905 -0.464296 -0.024905 -0.464296 -3.3189120.12 0.9989781 -0.029548 -0.497485 -0.029548 -0.497485 -3.1755980.13 0.9986826 -0.034523 -0.529241 -0.034523 -0.529241 -3.0340290.14 0.9983374 -0.039815 -0.559582 -0.039815 -0.559582 -2.8942350.15 0.9979393 -0.045411 -0.588524 -0.045411 -0.588524 -2.7562470.16 0.9974852 -0.051296 -0.616086 -0.051296 -0.616086 -2.6200920.17 0.9969722 -0.057457 -0.642287 -0.057457 -0.642287 -2.4857980.18 0.9963976 -0.06388 -0.667145 -0.06388 -0.667145 -2.3533910.19 0.9957588 -0.070552 -0.690679 -0.070552 -0.690679 -2.222896

0.2 0.9950533 -0.077458 -0.712908 -0.077458 -0.712908 -2.0943340.21 0.9942787 -0.084587 -0.733852 -0.084587 -0.733852 -1.9677270.22 0.9934328 -0.091926 -0.753529 -0.091926 -0.753529 -1.8430960.23 0.9925136 -0.099461 -0.77196 -0.099461 -0.77196 -1.720460.24 0.991519 -0.107181 -0.789164 -0.107181 -0.789164 -1.5998360.25 0.9904472 -0.115072 -0.805163 -0.115072 -0.805163 -1.481240.26 0.9892964 -0.123124 -0.819975 -0.123124 -0.819975 -1.3646880.27 0.9880652 -0.131324 -0.833622 -0.131324 -0.833622 -1.2501930.28 0.986752 -0.13966 -0.846124 -0.13966 -0.846124 -1.1377670.29 0.9853554 -0.148121 -0.857502 -0.148121 -0.857502 -1.027423

0.3 0.9838742 -0.156696 -0.867776 -0.156696 -0.867776 -0.9191690.31 0.9823072 -0.165374 -0.876968 -0.165374 -0.876968 -0.8130150.32 0.9806534 -0.174144 -0.885098 -0.174144 -0.885098 -0.7089680.33 0.978912 -0.182995 -0.892187 -0.182995 -0.892187 -0.6070350.34 0.9770821 -0.191917 -0.898258 -0.191917 -0.898258 -0.5072210.35 0.9751629 -0.200899 -0.90333 -0.200899 -0.90333 -0.409530.36 0.9731539 -0.209932 -0.907425 -0.209932 -0.907425 -0.3139660.37 0.9710546 -0.219007 -0.910565 -0.219007 -0.910565 -0.2205310.38 0.9688645 -0.228112 -0.91277 -0.228112 -0.91277 -0.1292250.39 0.9665834 -0.23724 -0.914063 -0.23724 -0.914063 -0.040049

0.4 0.964211 -0.246381 -0.914463 -0.246381 -0.914463 0.04699890.41 0.9617472 -0.255525 -0.913993 -0.255525 -0.913993 0.1319204

Page 7: Metode Numerik Matematika Teknik

0.42 0.9591919 -0.264665 -0.912674 -0.264665 -0.912674 0.21471860.43 0.9565453 -0.273792 -0.910527 -0.273792 -0.910527 0.29539740.44 0.9538074 -0.282897 -0.907573 -0.282897 -0.907573 0.3739620.45 0.9509784 -0.291973 -0.903833 -0.291973 -0.903833 0.45041810.46 0.9480587 -0.301011 -0.899329 -0.301011 -0.899329 0.52477250.47 0.9450485 -0.310005 -0.894081 -0.310005 -0.894081 0.59703290.48 0.9419485 -0.318945 -0.888111 -0.318945 -0.888111 0.66720780.49 0.938759 -0.327827 -0.881439 -0.327827 -0.881439 0.7353066

0.5 0.9354808 -0.336641 -0.874086 -0.336641 -0.874086 0.80133940.51 0.9321144 -0.345382 -0.866072 -0.345382 -0.866072 0.86531730.52 0.9286605 -0.354042 -0.857419 -0.354042 -0.857419 0.92725190.53 0.9251201 -0.362617 -0.848147 -0.362617 -0.848147 0.98715580.54 0.921494 -0.371098 -0.838275 -0.371098 -0.838275 1.04504220.55 0.917783 -0.379481 -0.827825 -0.379481 -0.827825 1.10092510.56 0.9139882 -0.387759 -0.816815 -0.387759 -0.816815 1.15481910.57 0.9101106 -0.395927 -0.805267 -0.395927 -0.805267 1.20673960.58 0.9061513 -0.40398 -0.7932 -0.40398 -0.7932 1.25670250.59 0.9021115 -0.411912 -0.780633 -0.411912 -0.780633 1.3047244

0.6 0.8979924 -0.419718 -0.767585 -0.419718 -0.767585 1.35082250.61 0.8937952 -0.427394 -0.754077 -0.427394 -0.754077 1.39501480.62 0.8895213 -0.434935 -0.740127 -0.434935 -0.740127 1.43731940.63 0.8851719 -0.442336 -0.725754 -0.442336 -0.725754 1.47775550.64 0.8807485 -0.449594 -0.710976 -0.449594 -0.710976 1.51634240.65 0.8762526 -0.456703 -0.695813 -0.456703 -0.695813 1.55310020.66 0.8716856 -0.463662 -0.680282 -0.463662 -0.680282 1.58804920.67 0.867049 -0.470464 -0.664401 -0.470464 -0.664401 1.62121060.68 0.8623443 -0.477108 -0.648189 -0.477108 -0.648189 1.65260560.69 0.8575732 -0.48359 -0.631663 -0.48359 -0.631663 1.6822561

0.7 0.8527373 -0.489907 -0.614841 -0.489907 -0.614841 1.71018440.71 0.8478383 -0.496055 -0.597739 -0.496055 -0.597739 1.7364130.72 0.8428777 -0.502033 -0.580375 -0.502033 -0.580375 1.76096510.73 0.8378574 -0.507837 -0.562765 -0.507837 -0.562765 1.7838640.74 0.832779 -0.513464 -0.544926 -0.513464 -0.544926 1.80513350.75 0.8276444 -0.518913 -0.526875 -0.518913 -0.526875 1.82479760.76 0.8224552 -0.524182 -0.508627 -0.524182 -0.508627 1.84288060.77 0.8172134 -0.529268 -0.490198 -0.529268 -0.490198 1.85940710.78 0.8119207 -0.53417 -0.471604 -0.53417 -0.471604 1.87440220.79 0.806579 -0.538886 -0.45286 -0.538886 -0.45286 1.887891

0.8 0.8011902 -0.543415 -0.433981 -0.543415 -0.433981 1.89989880.81 0.795756 -0.547755 -0.414982 -0.547755 -0.414982 1.91045130.82 0.7902785 -0.551905 -0.395878 -0.551905 -0.395878 1.91957430.83 0.7847594 -0.555864 -0.376682 -0.555864 -0.376682 1.92729370.84 0.7792008 -0.55963 -0.357409 -0.55963 -0.357409 1.93363580.85 0.7736045 -0.563204 -0.338073 -0.563204 -0.338073 1.93862690.86 0.7679724 -0.566585 -0.318687 -0.566585 -0.318687 1.94229340.87 0.7623066 -0.569772 -0.299264 -0.569772 -0.299264 1.94466190.88 0.7566089 -0.572765 -0.279817 -0.572765 -0.279817 1.94575910.89 0.7508812 -0.575563 -0.260359 -0.575563 -0.260359 1.9456118

Page 8: Metode Numerik Matematika Teknik

0.9 0.7451256 -0.578166 -0.240903 -0.578166 -0.240903 1.94424670.91 0.7393439 -0.580575 -0.221461 -0.580575 -0.221461 1.94169080.92 0.7335382 -0.58279 -0.202044 -0.58279 -0.202044 1.93797110.93 0.7277103 -0.58481 -0.182664 -0.58481 -0.182664 1.93311460.94 0.7218622 -0.586637 -0.163333 -0.586637 -0.163333 1.92714820.95 0.7159958 -0.58827 -0.144062 -0.58827 -0.144062 1.92009890.96 0.7101131 -0.589711 -0.124861 -0.589711 -0.124861 1.91199380.97 0.704216 -0.59096 -0.105741 -0.59096 -0.105741 1.90285970.98 0.6983064 -0.592017 -0.086712 -0.592017 -0.086712 1.89272380.99 0.6923862 -0.592884 -0.067785 -0.592884 -0.067785 1.8816127

1 0.6864574 -0.593562 -0.048969 -0.593562 -0.048969 1.8695535

Page 9: Metode Numerik Matematika Teknik

00t

0 0.2 0.4 0.6 0.8 1 1.2

-1.5

-1

-0.5

0

0.5

1

1.5

x1x2x3

Page 10: Metode Numerik Matematika Teknik

0 0.2 0.4 0.6 0.8 1 1.2

-1.5

-1

-0.5

0

0.5

1

1.5

x1x2x3

Page 11: Metode Numerik Matematika Teknik

0 0.2 0.4 0.6 0.8 1 1.2

-1.5

-1

-0.5

0

0.5

1

1.5

x1x2x3

Page 12: Metode Numerik Matematika Teknik

R(x1)^4 (x1^2)(x2^2) (x2)^4 (x1)^3 x1(x2)^2 (x1)^2 (x2)^2

1 -6 1 6 -18 26 -26

f1=

f'11 f'12f2 f'21 f'22

i x1 x2 F G F'10 1 1 95 110 721 -0.217508 1.0764526 31.588138 31.815268 16.8153822 -1.449855 1.3281588 20.128244 -5.445046 -42.644783 -0.952046 1.282051 19.610888 7.377384 -17.765874 1.0294506 0.7299528 120.74651 85.827921 87.7221085 -0.268812 0.8242675 40.191715 24.644599 21.9061926 -1.67802 1.1036844 26.62545 -9.497953 -57.554437 -1.212438 1.0961352 24.743773 0.9888497 -28.322078 -0.162802 0.8815157 40.728648 29.828511 25.0479019 -1.43201 1.1154073 24.992048 -4.057123 -41.2258

10 -0.781196 1.0333277 26.926817 11.765054 -5.73933511 -15.62911 5.0634313 12085.649 -51605 -11690.5712 -12.39393 2.8707904 9758.1133 -14611.44 -7136.40913 -10.15156 1.3348629 5801.3188 -3670.724 -4481.53814 -8.615984 0.4513025 3207.6012 -730.4047 -2943.07615 -7.491144 0.0904782 1804.4407 -91.81387 -2024.4816 -6.598027 0.0018019 1065.1496 -1.193671 -1446.0517 -5.861434 -0.000536 660.73647 0.2392134 -1064.30618 -5.240619 0.0005609 428.70105 -0.172674 -802.227619 -4.706231 -0.00269 289.51868 0.5836883 -615.669520 -4.23599 -0.017044 202.58106 2.6472993 -478.297721 -3.81256 -0.045428 146.23284 5.099912 -373.867422 -3.42188 -0.087469 108.46988 7.1185221 -292.03223 -3.051546 -0.140376 82.425961 8.2269219 -225.976724 -2.688764 -0.19936 64.085613 8.2235517 -171.001925 -2.316817 -0.257209 51.094197 7.0434571 -123.569426 -1.906382 -0.301964 42.214194 4.6139382 -80.4005727 -1.381915 -0.307787 37.713456 0.6420583 -36.5499628 -0.321106 -0.168973 52.127777 -5.219803 28.76615229 -2.087691 -0.355489 44.861936 7.183408 -98.0651430 -1.633999 -0.391884 38.29464 3.2437294 -56.1717731 -0.941836 -0.331164 38.949235 -3.114544 -7.051854

f(x)=(x^4)+6x³+26x²+46x+65

Page 13: Metode Numerik Matematika Teknik

32 7.1663448 1.6138472 5376.1928 4397.6275 1619.945233 3.9760976 1.7546872 703.05101 1265.6936 301.8691334 1.9418079 1.89078 24.499462 368.53926 28.60568635 0.6796657 1.8506258 -18.33504 112.98754 -6.98095336 -0.165672 1.7522728 -3.687298 37.626398 -11.7971537 -0.926913 1.840901 3.1054769 4.2552039 -28.6906938 -0.748329 1.7696447 2.9812118 10.750094 -22.8369339 -0.281081 1.5439664 8.6313306 32.568845 -3.5734340 -1.351945 1.7863183 8.7224245 -5.67224 -39.8544541 -1.136151 1.7917846 6.7915648 -0.687389 -32.9638142 -0.903707 1.7564366 5.2746526 5.9665923 -26.0202143 -0.553705 1.6275288 6.2502476 19.563755 -13.5508344 -6.454417 3.7336575 -1059.57 -1265.888 -536.394345 -2.894063 0.7188629 62.134112 -34.36664 -192.804646 -2.600913 0.8876869 46.47694 -30.52762 -149.215547 -2.319587 1.0269425 35.937306 -24.88736 -114.168348 -2.031909 1.1313876 29.053756 -18.30158 -85.0450749 -1.710069 1.1952953 24.72025 -10.86318 -59.3252750 -1.29632 1.2026629 22.466456 -1.265943 -33.6574751 -0.535457 1.0701176 27.589284 19.566891 4.287563652 -2.628817 1.6208553 16.484779 -43.94384 -127.778953 -2.571278 1.8100419 7.5524192 -41.01661 -113.588854 -2.577193 1.9870713 -0.705605 -39.57553 -105.445255 -2.659006 2.159414 -10.42425 -40.13184 -102.61456 -2.845045 2.3380333 -25.86048 -44.3044 -105.82657 -3.205118 2.5488337 -59.69718 -59.00145 -119.439358 -3.949618 2.8870401 -172.2307 -125.2027 -160.817359 -6.407638 4.1005794 -1412.344 -1108.831 -349.283560 -2.90022 1.4940619 25.48619 -57.49787 -164.882461 -2.835175 1.7435683 10.174794 -55.20888 -143.880462 -2.863231 1.9816718 -4.641836 -55.0919 -132.538863 -3.012239 2.2229827 -24.46685 -59.4588 -130.288264 -3.353952 2.4990681 -64.49866 -76.28078 -140.377165 -4.125909 2.9244515 -201.4143 -155.7067 -179.996466 -7.250469 4.6031089 -2444.978 -1942.547 -393.499467 -4.234607 2.2623686 -65.04943 -224.3756 -309.978968 -5.352436 3.5821424 -674.0253 -473.8353 -252.483669 1.339057 -0.765314 155.534 -115.4545 105.2808770 0.0194248 -0.947028 43.073749 -39.36421 30.65756171 -0.61215 -1.456786 13.2867 -18.1499 -9.35998472 -0.648767 -1.817035 -0.084755 -13.6391 -22.553573 -0.814961 -1.91544 -0.757428 -6.432974 -28.7032174 -0.897594 -1.968264 -0.884326 -3.148343 -31.5726775 -0.946991 -1.99302 -0.698606 -1.425423 -33.0000476 -0.975685 -2.002768 -0.462921 -0.545052 -33.687777 -0.99115 -2.005133 -0.266412 -0.129984 -33.9848878 -0.998503 -2.004448 -0.130683 0.0355826 -34.0832679 -1.001288 -2.002954 -0.050127 0.0781704 -34.09138

Page 14: Metode Numerik Matematika Teknik

80 -1.001822 -2.001619 -0.009643 0.0695585 -34.0679281 -1.001473 -2.000719 0.0063214 0.0468029 -34.0407982 -1.000936 -2.000219 0.0097027 0.0259474 -34.0202383 -1.000492 -1.999994 0.0080066 0.0117004 -34.0077384 -1.000206 -1.999923 0.0051479 0.0037047 -34.0014485 -1.000054 -1.999922 0.0027369 4.352E-05 -33.9989986 -0.999989 -1.999944 0.0011665 -0.001156 -33.9984887 -0.999971 -1.999967 0.0003214 -0.001212 -33.9987688 -0.999974 -1.999984 -4.505E-05 -0.000881 -33.999289 -0.999982 -1.999994 -0.000151 -0.00052 -33.9995890 -0.99999 -1.999999 -0.000142 -0.000253 -33.9998291 -0.999995 -2.000001 -9.788E-05 -9.365E-05 -33.9999592 -0.999998 -2.000001 -5.549E-05 -1.504E-05 -34.0000193 -1 -2.000001 -2.577E-05 1.478E-05 -34.0000294 -1 -2.000001 -8.711E-06 2.018E-05 -34.0000295 -1 -2 -6.731E-07 1.612E-05 -34.0000296 -1 -2 2.126E-06 1.016E-05 -34.0000197 -1 -2 2.42E-06 5.3E-06 -3498 -1 -2 1.819E-06 2.199E-06 -3499 -1 -2 1.1E-06 5.601E-07 -34

100 -1 -2 5.499E-07 -1.323E-07 -34101 -1 -2 2.133E-07 -3.186E-07 -34102 -1 -2 4.272E-08 -2.872E-07 -34103 -1 -2 -2.485E-08 -1.943E-07 -34104 -1 -2 -3.96E-08 -1.082E-07 -34105 -1 -2 -3.297E-08 -4.913E-08 -34106 -1 -2 -2.132E-08 -1.583E-08 -34107 -1 -2 -1.14E-08 -4.772E-10 -34108 -1 -2 -4.905E-09 4.636E-09 -34109 -1 -2 -1.385E-09 4.958E-09 -34110 -1 -2 1.545E-10 3.634E-09 -34111 -1 -2 6.09E-10 2.158E-09 -34112 -1 -2 5.809E-10 1.058E-09 -34113 -1 -2 4.044E-10 3.965E-10 -34114 -1 -2 2.307E-10 6.8E-11 -34115 -1 -2 1.079E-10 -5.809E-11 -34116 -1 -2 3.706E-11 -8.221E-11 -34117 -1 -2 3.411E-12 -6.632E-11 -34118 -1 -2 -8.498E-12 -4.209E-11 -34119 -1 -2 -9.891E-12 -2.208E-11 -34120 -1 -2 -7.503E-12 -9.251E-12 -34121 -1 -2 -4.547E-12 -2.416E-12 -34122 -1 -2 -2.274E-12 4.974E-13 -34123 -1 -2 -8.811E-13 1.265E-12 -34124 -1 -2 0 1.165E-12 -34125 -1 -2 0 7.248E-13 -34126 -1 -2 0 4.263E-13 -34127 -1 -2 0 0 -34

Page 15: Metode Numerik Matematika Teknik

128 -1 -2 0 0 -34129 -1 -2 0 0 -34130 -1 -2 0 0 -34131 -1 -2 0 0 -34132 -1 -2 0 0 -34133 -1 -2 0 0 -34134 -1 -2 0 0 -34135 -1 -2 0 0 -34136 -1 -2 0 0 -34137 -1 -2 0 0 -34138 -1 -2 0 0 -34139 -1 -2 0 0 -34140 -1 -2 0 0 -34141 -1 -2 0 0 -34142 -1 -2 0 0 -34143 -1 -2 0 0 -34144 -1 -2 0 0 -34145 -1 -2 0 0 -34146 -1 -2 0 0 -34147 -1 -2 0 0 -34148 -1 -2 0 0 -34149 -1 -2 0 0 -34150 -1 -2 0 0 -34151 -1 -2 0 0 -34152 -1 -2 0 0 -34153 -1 -2 0 0 -34154 -1 -2 0 0 -34155 -1 -2 0 0 -34156 -1 -2 0 0 -34157 -1 -2 0 0 -34158 -1 -2 0 0 -34159 -1 -2 0 0 -34160 -1 -2 0 0 -34161 -1 -2 0 0 -34162 -1 -2 0 0 -34163 -1 -2 0 0 -34164 -1 -2 0 0 -34165 -1 -2 0 0 -34

Page 16: Metode Numerik Matematika Teknik

R Ix1 + (x1^3)x2 (x2^3)x1 (x1^2)x2 (x2)^3 x1.x2 x2

46 4 -4 18 -6 52 4665

65 Re Im Rel. Err.x1-a1 46 -2 3 1E-24x2-a2 26 -2 -3 1E-24

6 -1 2 1E-241 -1 -2 1E-24

0.0546875

F'2 G'1 G'2 i x1 x2 F G-96 96 90 0 -2 2.99 -0.236012 -0.358202

-43.16837 43.168375 84.952888 1 -2.006018 2.9907405 -0.434906 -0.192447-23.87253 23.872527 139.64937 2 -2.018192 2.9904429 -0.887494 0.0743321-28.24156 28.241563 114.72223 3 -2.044075 2.9882294 -1.921755 0.5594204-72.73696 72.736961 91.224056 4 -2.10072 2.982336 -4.370774 1.4520596-33.35993 33.359929 80.047013 5 -2.22784 2.969914 -10.63703 2.7947839-22.63416 22.634159 137.77778 6 -2.521084 2.9506548 -28.95532 2.2844991

-23.223 23.222996 118.18387 7 -3.20383 2.9594262 -92.7765 -22.76069-38.21275 38.212752 79.829474 8 -4.79846 3.2829354 -411.9445 -291.5559-22.39619 22.396193 128.15164 9 236.86036 -141.1075 -3.16E+09 -4.97E+09-27.82657 27.826565 99.600733 10 177.28055 -106.5411 -1.03E+09 -1.57E+09-11737.17 11737.166 -6217.72 11 132.59734 -80.61047 -3.35E+08 -4.97E+08-4065.519 4065.5192 -3577.672 12 99.086894 -61.15488 -1.11E+08 -1.57E+08-1222.824 1222.8241 -2029.267 13 73.95623 -46.55319 -36877498 -49637330-285.1474 285.14739 -1135.343 14 55.110411 -35.58897 -12455703 -15669512-41.23028 41.230281 -620.1255 15 40.977773 -27.34921 -4269524 -4937844-0.607033 0.6070328 -319.2479 16 30.378732 -21.14854 -1487376 -15511830.1358729 -0.135873 -141.1238 17 22.42722 -16.47257 -527008.8 -484581.3-0.108194 0.1081938 -35.33256 18 16.456638 -12.93576 -189874.6 -149857.10.3990667 -0.399067 27.589531 19 11.964367 -10.25025 -69456.01 -45477.371.9571331 -1.957133 64.072429 20 8.570498 -8.202886 -25715.51 -13300.94.0506419 -4.050642 83.664488 21 5.987651 -6.638078 -9585.891 -3595.346.0610072 -6.061007 92.124004 22 3.9994846 -5.444532 -3566.428 -793.35937.5534337 -7.553434 93.018978 23 2.4462368 -4.544558 -1304.612 -61.191698.3330355 -8.333036 88.577212 24 1.217145 -3.885102 -456.95 81.1231088.4214515 -8.421452 80.147758 25 0.2521653 -3.428254 -146.9219 75.5962848.0373782 -8.037378 68.446394 26 -0.449978 -3.133968 -42.21888 48.1718817.6295562 -7.629556 53.679118 27 -0.87227 -2.936979 -12.55701 29.2996967.0230642 -7.023064 38.533027 28 -1.093848 -2.773947 -5.220133 19.637362

10.18088 -10.18088 70.461532 29 -1.221311 -2.620791 -2.984742 14.6841619.6408 -9.6408 56.477329 30 -1.296786 -2.467315 -1.730181 11.928134

9.3719105 -9.37191 40.670038 31 -1.325261 -2.308469 -0.369188 10.007076

f(x)=(x^4)+6x³+26x²+46x+65

Page 17: Metode Numerik Matematika Teknik

-1478.039 1478.0393 2255.6323 32 -1.300297 -2.153112 1.2476257 7.9208201-653.6842 653.6842 470.92412 33 -1.226051 -2.030219 2.497277 5.2494854-289.0101 289.01009 93.823361 34 -1.129927 -1.966358 2.6338319 2.4954819

-126.42 126.42003 62.223991 35 -1.048431 -1.953828 1.829397 0.4646278-59.7233 59.723297 88.430041 36 -1.001764 -1.964394 0.8935575 -0.511075

-28.32315 28.323154 130.70062 37 -0.985285 -1.978465 0.2914673 -0.700944-34.07193 34.071926 118.17764 38 -0.984485 -1.989157 0.0148406 -0.550649-51.40454 51.404543 92.751174 39 -0.988818 -1.995661 -0.074666 -0.340036-22.32775 22.327747 156.23486 40 -0.993434 -1.998985 -0.080965 -0.174462-24.63107 24.631068 142.52392 41 -0.996797 -2.000347 -0.059719 -0.071424-29.73033 29.730333 127.00762 42 -0.998797 -2.000688 -0.035799 -0.017855-40.93282 40.932816 105.39195 43 -0.999788 -2.000601 -0.017812 0.00454-984.9173 984.91729 743.25669 44 -1.00017 -2.0004 -0.006871 0.010475-33.25021 33.250211 145.82844 45 -1.000245 -2.000219 -0.001347 0.0093827-32.30485 32.30485 153.95718 46 -1.000199 -2.000098 0.0008327 0.006327

-29.6193 29.619304 156.69985 47 -1.000126 -2.00003 0.0012997 0.0035139-26.33301 26.333013 153.76209 48 -1.000067 -2 0.0010767 0.0015897-23.68433 23.684328 144.39172 49 -1.000028 -1.99999 0.0006942 0.0005079-23.70717 23.707171 126.53769 50 -1.000007 -1.99999 0.0003702 1.096E-05-33.79807 33.79807 92.938304 51 -0.999999 -1.999992 0.0001585 -0.000153-48.27238 48.272379 217.5962 52 -0.999996 -1.999996 4.427E-05 -0.000162-46.45766 46.457663 233.24623 53 -0.999996 -1.999998 -5.523E-06 -0.000119-45.96163 45.961626 251.45122 54 -0.999998 -1.999999 -2.01E-05 -7.02E-05-48.51612 48.516124 275.20944 55 -0.999999 -2 -1.9E-05 -3.428E-05-58.08643 58.086426 309.39102 56 -0.999999 -2 -1.318E-05 -1.278E-05-86.41288 86.412877 364.67618 57 -1 -2 -7.498E-06 -2.126E-06-183.8107 183.81067 475.47958 58 -1 -2 -3.496E-06 1.939E-06-1011.859 1011.8589 936.18479 59 -1 -2 -1.192E-06 2.698E-06-59.16261 59.16261 215.02318 60 -1 -2 -1.01E-07 2.166E-06-59.68615 59.68615 238.90212 61 -1 -2 2.81E-07 1.37E-06-62.60633 62.606333 266.96172 62 -1 -2 3.24E-07 7.173E-07-72.63775 72.637754 305.26793 63 -1 -2 2.446E-07 2.991E-07-103.1222 103.12224 366.46183 64 -1 -2 1.484E-07 7.738E-08-215.0499 215.04993 493.0387 65 -1 -2 7.448E-08 -1.676E-08-1551.525 1551.5253 1169.1341 66 -1 -2 2.906E-08 -4.245E-08-213.2592 213.25919 350.63803 67 -1 -2 5.966E-09 -3.854E-08-543.6552 543.65524 727.7888 68 -1 -2 -3.237E-09 -2.617E-0891.363251 -91.36325 28.128917 69 -1 -2 -5.287E-09 -1.462E-0846.514564 -46.51456 -19.59117 70 -1 -2 -4.428E-09 -6.668E-0937.833355 -37.83335 -46.53596 71 -1 -2 -2.874E-09 -2.169E-0937.228678 -37.22868 -75.72726 72 -1 -2 -1.543E-09 -8.546E-1130.562185 -30.56219 -73.97325 73 -1 -2 -6.665E-10 6.142E-10

27.27712 -27.27712 -72.74537 74 -1 -2 -1.906E-10 6.641E-1025.473394 -25.47339 -71.25129 75 -1 -2 1.856E-11 4.889E-1024.543037 -24.54304 -69.96068 76 -1 -2 8.1E-11 2.913E-1024.111531 -24.11153 -69.02918 77 -1 -2 7.788E-11 1.433E-1023.946629 -23.94663 -68.44624 78 -1 -2 5.446E-11 5.409E-1123.909808 -23.90981 -68.13164 79 -1 -2 3.116E-11 9.564E-12

Page 18: Metode Numerik Matematika Teknik

23.92388 -23.92388 -67.99173 80 -1 -2 1.465E-11 -7.603E-1223.950308 -23.95031 -67.94853 81 -1 -2 5.073E-12 -1.098E-1123.973179 -23.97318 -67.94929 82 -1 -2 4.974E-13 -8.95E-1223.988326 -23.98833 -67.96415 83 -1 -2 -1.123E-12 -5.656E-1223.996605 -23.99661 -67.9793 84 -1 -2 -1.336E-12 -2.98E-1224.000269 -24.00027 -67.99018 85 -1 -2 -9.948E-13 -1.251E-12

24.00138 -24.00138 -67.99654 86 -1 -2 -6.253E-13 024.001342 -24.00134 -67.9996 87 -1 -2 -2.7E-13 024.000943 -24.00094 -68.0007 88 -1 -2 0 024.000542 -24.00054 -68.00086 89 -1 -2 0 024.000256 -24.00026 -68.00066 90 -1 -2 0 0

24.00009 -24.00009 -68.00041 91 -1 -2 0 024.00001 -24.00001 -68.00021 92 -1 -2 0 0

23.999981 -23.99998 -68.00008 93 -1 -2 0 023.999977 -23.99998 -68.00002 94 -1 -2 0 023.999983 -23.99998 -67.99999 95 -1 -2 0 023.999989 -23.99999 -67.99999 96 -1 -2 0 023.999995 -23.99999 -67.99999 97 -1 -2 0 0

24 -24 -67.99999 98 -1 -2 0 024 -24 -68 99 -1 -2 0 024 -24 -68 100 -1 -2 0 024 -24 -68 101 -1 -2 0 024 -24 -68 102 -1 -2 0 024 -24 -68 103 -1 -2 0 024 -24 -68 104 -1 -2 0 024 -24 -68 105 -1 -2 0 024 -24 -68 106 -1 -2 0 024 -24 -68 107 -1 -2 0 024 -24 -68 108 -1 -2 0 024 -24 -68 109 -1 -2 0 024 -24 -68 110 -1 -2 0 024 -24 -68 111 -1 -2 0 024 -24 -68 112 -1 -2 0 024 -24 -68 113 -1 -2 0 024 -24 -68 114 -1 -2 0 024 -24 -68 115 -1 -2 0 024 -24 -68 116 -1 -2 0 024 -24 -68 117 -1 -2 0 024 -24 -68 118 -1 -2 0 024 -24 -68 119 -1 -2 0 024 -24 -68 120 -1 -2 0 024 -24 -68 121 -1 -2 0 024 -24 -68 122 -1 -2 0 024 -24 -68 123 -1 -2 0 024 -24 -68 124 -1 -2 0 024 -24 -68 125 -1 -2 0 024 -24 -68 126 -1 -2 0 024 -24 -68 127 -1 -2 0 0

Page 19: Metode Numerik Matematika Teknik

24 -24 -68 128 -1 -2 0 024 -24 -68 129 -1 -2 0 024 -24 -68 130 -1 -2 0 024 -24 -68 131 -1 -2 0 024 -24 -68 132 -1 -2 0 024 -24 -68 133 -1 -2 0 024 -24 -68 134 -1 -2 0 024 -24 -68 135 -1 -2 0 024 -24 -68 136 -1 -2 0 024 -24 -68 137 -1 -2 0 024 -24 -68 138 -1 -2 0 024 -24 -68 139 -1 -2 0 024 -24 -68 140 -1 -2 0 024 -24 -68 141 -1 -2 0 024 -24 -68 142 -1 -2 0 024 -24 -68 143 -1 -2 0 024 -24 -68 144 -1 -2 0 024 -24 -68 145 -1 -2 0 024 -24 -68 146 -1 -2 0 024 -24 -68 147 -1 -2 0 024 -24 -68 148 -1 -2 0 024 -24 -68 149 -1 -2 0 024 -24 -68 150 -1 -2 0 024 -24 -68 151 -1 -2 0 024 -24 -68 152 -1 -2 0 024 -24 -68 153 -1 -2 0 024 -24 -68 154 -1 -2 0 024 -24 -68 155 -1 -2 0 024 -24 -68 156 -1 -2 0 024 -24 -68 157 -1 -2 0 024 -24 -68 158 -1 -2 0 024 -24 -68 159 -1 -2 0 024 -24 -68 160 -1 -2 0 024 -24 -68 161 -1 -2 0 024 -24 -68 162 -1 -2 0 024 -24 -68 163 -1 -2 0 024 -24 -68 164 -1 -2 0 024 -24 -68 165 -1 -2 0 0

Page 20: Metode Numerik Matematika Teknik

F'1 F'2 G'1 G'2-36.3594 23.203596 -23.2036 295.1206

-36.28955 23.045031 -23.04503 295.9759-36.21844 22.574025 -22.57402 297.54634-36.15455 21.413184 -21.41318 300.73369-36.20355 18.630475 -18.63047 307.54977-37.03919 11.655562 -11.65556 322.58289-42.51189 -7.925132 7.9251322 356.42404-73.07248 -73.4045 73.4045 432.17832-218.8658 -369.1574 369.15744 615.82057-3786337 84970368 -84970368 -2796141-2056224 36029084 -36029084 -1505272-1124175 15301317 -15301317 -818784.3

-617618.5 6511649 -6511649 -449223.3-340431.4 2778290 -2778290 -248246.4-187988.1 1189226 -1189226 -138035.7-103857.2 511031.39 -511031.4 -77184.99-57329.37 220600.4 -220600.4 -43397.18-31576.53 95701.674 -95701.67 -24545.68

-17328.1 41717.241 -41717.24 -13981.73-9457.273 18247.491 -18247.49 -8035.804-5121.608 7980.0118 -7980.012 -4671.662-2743.203 3461.9083 -3461.908 -2754.406-1446.376 1466.5405 -1466.541 -1649.539-746.2619 587.43586 -587.4359 -1002.07-375.6477 206.75909 -206.7591 -614.2986-187.9401 50.838608 -50.83861 -378.1773

-101.52 -3.31092 3.3109195 -237.4428-66.98913 -14.02358 14.023579 -160.6586

-53.6183 -10.53993 10.539929 -119.4464-47.76527 -4.041737 4.041737 -93.68941-45.00099 2.8250241 -2.825024 -75.59876-43.39816 9.349969 -9.349969 -62.91122

Page 21: Metode Numerik Matematika Teknik

-41.5191 14.931839 -14.93184 -55.43155-38.67657 19.111312 -19.11131 -53.4357-35.69761 21.978358 -21.97836 -56.2108-33.81425 23.792157 -23.79216 -61.10919-33.18431 24.640368 -24.64037 -65.17754-33.23796 24.774106 -24.77411 -67.40919-33.48707 24.590115 -24.59011 -68.28422-33.71624 24.357104 -24.3571 -68.47239-33.87079 24.17881 -24.17881 -68.39507-33.95726 24.070192 -24.07019 -68.25704-33.99733 24.01514 -24.01514 -68.13897-34.01104 23.993056 -23.99306 -68.06093-34.01231 23.987922 -23.98792 -68.01814-34.00918 23.989738 -23.98974 -67.99904-34.00552 23.993282 -23.99328 -67.99313-34.00274 23.996366 -23.99637 -67.99319-34.00105 23.998412 -23.99841 -67.99517

-34.0002 23.999533 -23.99953 -67.9972-33.99987 24.000031 -24.00003 -67.99867

-33.9998 24.000183 -24.00018 -67.99953-33.99983 24.00018 -24.00018 -67.99994-33.99989 24.000127 -24.00013 -68.00009-33.99994 24.000073 -24.00007 -68.00011-33.99998 24.000035 -24.00003 -68.00009-33.99999 24.000012 -24.00001 -68.00006

-34 24 -24 -68.00003-34 24 -24 -68.00001-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68

Page 22: Metode Numerik Matematika Teknik

-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68

Page 23: Metode Numerik Matematika Teknik

-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68-34 24 -24 -68