Metodo Biseccion
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Use el metodo de bisección para encontrar la raíz real de la siguiente funci funcion f(x) = (e^-x |Ea| = Aproximacion |Ea|<Error f(x1)f(xU)= -0.63212056 Tiene Raiz Termino X1 Xu f(x1) f(xu) Xr 1 0 1 1 -0.63212056 0.5 2 0.5 1 0.10653066 -0.63212056 0.75 3 0.5 0.75 0.10653066 -0.27763345 0.625 4 0.5 0.625 0.10653066 -0.08973857 0.5625 5 0.5625 0.625 0.007282825 -0.08973857 0.59375 6 0.5625 0.59375 0.007282825 -0.04149755 0.578125 7 0.5625 0.578125 0.007282825 -0.01717584 0.5703125 8 0.5625 0.5703125 0.007282825 -0.00496376 0.56640625 9 0.56640625 0.5703125 0.001155202 -0.00496376 0.568359375 10 0.56640625 0.56835938 0.001155202 -0.00190536 0.5673828125 es el valor de la ra Funcion f(x)x^3+2x^2+10x-20 f(x1)f(xU)= -112 Tiene Raiz Termino X1 Xu f(x1) f(xu) Xr 1 1 2 -7 16 1.5 2 1 1.5 -7 2.875 1.25 3 1.25 1.5 -2.421875 2.875 1.375 4 1.25 1.375 -2.421875 0.130859375 1.3125 5 1.3125 1.375 -1.16870117 0.130859375 1.34375 6 1.34375 1.375 -0.52481079 0.130859375 1.359375 7 1.359375 1.375 -0.19845963 0.130859375 1.3671875 8 1.3671875 1.375 -0.03417253 0.130859375 1.37109375 9 1.3671875 1.37109375 -0.03417253 0.048250139 1.369140625 10 1.3671875 1.36914063 -0.03417253 0.007015504 1.3681640625 es el valor de la ra funcion f(x) = xsinx-1 f(x1)f(xU)= -0.81859485 Tiene Raiz Termino X1 Xu f(x1) f(xu) Xr 1 0 2 -1 0.818594854 1 2 1 2 -0.15852902 0.818594854 1.5 3 1 1.5 -0.15852902 0.49624248 1.25 4 1 1.25 -0.15852902 0.186230774 1.125 5 1 1.125 -0.15852902 0.015051043 1.0625 6 1.0625 1.125 -0.07182663 0.015051043 1.09375 7 1.09375 1.125 -0.02836172 0.015051043 1.109375
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Transcript of Metodo Biseccion
Use el metodo de bisección para encontrar la raíz real de la siguiente función:
funcion f(x) = (e^-x)-x |Ea| = Aproximacion Actual- Aproximacion Anterior|Ea|<Error
f(x1)f(xU)= -0.632120559 Tiene RaizTermino X1 Xu f(x1) f(xu) Xr f(Xr)
1 0 1 1 -0.632120559 0.5 0.106530662 0.5 1 0.1065306597 -0.632120559 0.75 -0.277633453 0.5 0.75 0.1065306597 -0.277633447 0.625 -0.089738574 0.5 0.625 0.1065306597 -0.089738571 0.5625 0.007282825 0.5625 0.625 0.0072828247 -0.089738571 0.59375 -0.041497556 0.5625 0.59375 0.0072828247 -0.04149755 0.578125 -0.017175847 0.5625 0.578125 0.0072828247 -0.017175839 0.5703125 -0.004963768 0.5625 0.5703125 0.0072828247 -0.00496376 0.56640625 0.00115529 0.56640625 0.5703125 0.001155202 -0.00496376 0.568359375 -0.00190536
10 0.56640625 0.56835938 0.001155202 -0.00190536 0.5673828125 -0.00037535es el valor de la raiz
Funcion f(x)= x^3+2x^2+10x-20 x1=1f(x1)f(xU)= -112 Tiene Raiz xu=2
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 1 2 -7 16 1.5 2.8752 1 1.5 -7 2.875 1.25 -2.4218753 1.25 1.5 -2.421875 2.875 1.375 0.130859384 1.25 1.375 -2.421875 0.130859375 1.3125 -1.168701175 1.3125 1.375 -1.168701172 0.130859375 1.34375 -0.524810796 1.34375 1.375 -0.524810791 0.130859375 1.359375 -0.198459637 1.359375 1.375 -0.198459625 0.130859375 1.3671875 -0.034172538 1.3671875 1.375 -0.034172535 0.130859375 1.37109375 0.048250149 1.3671875 1.37109375 -0.034172535 0.048250139 1.369140625 0.0070155
10 1.3671875 1.36914063 -0.034172535 0.007015504 1.3681640625 -0.01358434es el valor de la raiz
funcion f(x) = xsinx-1 x1=0f(x1)f(xU)= -0.818594854 Tiene Raiz xu=2
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 0 2 -1 0.818594854 1 -0.158529022 1 2 -0.158529015 0.818594854 1.5 0.496242483 1 1.5 -0.158529015 0.49624248 1.25 0.186230774 1 1.25 -0.158529015 0.186230774 1.125 0.015051045 1 1.125 -0.158529015 0.015051043 1.0625 -0.071826636 1.0625 1.125 -0.071826631 0.015051043 1.09375 -0.028361727 1.09375 1.125 -0.028361723 0.015051043 1.109375 -0.00664277
8 1.109375 1.125 -0.006642775 0.015051043 1.1171875 0.004208039 1.109375 1.1171875 -0.006642775 0.004208034 1.11328125 -0.00121649
10 1.11328125 1.1171875 -0.00121649 0.004208034 1.115234375 0.00149611 1.11328125 1.11523438 -0.00121649 0.001496004 1.1142578125 0.00013981
funcion f(x) = x^4+3x^3-2 x1=0f(x1)f(xU)= -4 Tiene Raiz x2=1
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 0 1 -2 2 0.5 -1.56252 0.5 1 -1.5625 2 0.75 -0.417968753 0.75 1 -0.41796875 2 0.875 0.595947274 0.75 0.875 -0.41796875 0.595947266 0.8125 0.044937135 0.75 0.8125 -0.41796875 0.044937134 0.78125 -0.19695956 0.78125 0.8125 -0.196959496 0.044937134 0.796875 -0.078692387 0.796875 0.8125 -0.078692377 0.044937134 0.8046875 -0.017556788 0.8046875 0.8125 -0.017556783 0.044937134 0.80859375 0.013519279 0.8046875 0.80859375 -0.017556783 0.013519272 0.806640625 -0.00206134
10 0.80664063 0.80859375 -0.002061342 0.013519272 0.8076171875 0.0057183
funcion f(x) = arctan (x) +x -1 x1=0f(x1)f(xU)= -0.785398163 Tiene Raiz x2=1
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 0 1 -1 0.785398163 0.5 -0.036352392 0.5 1 -0.036352391 0.785398163 0.75 0.393501113 0.5 0.75 -0.036352391 0.393501109 0.625 0.183599324 0.5 0.625 -0.036352391 0.183599315 0.5625 0.074889465 0.5 0.5625 -0.036352391 0.07488946 0.53125 0.019583956 0.5 0.53125 -0.036352391 0.019583951 0.515625 -0.008305677 0.515625 0.53125 -0.00830567 0.019583951 0.5234375 0.005658828 0.515625 0.5234375 -0.00830567 0.005658824 0.51953125 -0.001318519 0.51953125 0.5234375 -0.001318507 0.005658824 0.521484375 0.00217139
10 0.51953125 0.52148438 -0.001318507 0.002171388 0.5205078125 0.00042675
funcion f(x) = e^-x-ln(x) x1=1f(x1)f(xU)= -0.067077279 Tiene Raiz x2=1.5
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 1 1.5 0.3678794412 -0.182334948 1.25 0.063361252 1.25 1.5 0.0633612455 -0.182334948 1.375 -0.065614143 1.25 1.375 0.0633612455 -0.065614135 1.3125 -0.002787374 1.25 1.3125 0.0633612455 -0.002787367 1.28125 0.029853815 1.28125 1.3125 0.029853807 -0.002787367 1.296875 0.013427266 1.296875 1.3125 0.0134272626 -0.002787367 1.3046875 0.005293747 1.3046875 1.3125 0.0052937412 -0.002787367 1.30859375 0.001246678 1.30859375 1.3125 0.0012466704 -0.002787367 1.310546875 -0.000771979 1.30859375 1.31054688 0.0012466704 -0.000771973 1.3095703125 0.00023694
f(x)= sen (sqrt (x))-x x1=0.5f(x1)f(xU)= -0.023721797 Tiene Raiz x2=1
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 0.5 1 0.1496369391 -0.158529015 0.75 0.011759982 0.75 1 0.0117599814 -0.158529015 0.875 -0.070154943 0.75 0.875 0.0117599814 -0.070154944 0.8125 -0.028311164 0.75 0.8125 0.0117599814 -0.028311163 0.78125 -0.008042585 0.75 0.78125 0.0117599814 -0.008042578 0.765625 0.00191856 0.765625 0.78125 0.0019185022 -0.008042578 0.7734375 -0.003047297 0.765625 0.7734375 0.0019185022 -0.003047287 0.76953125 -0.000560688 0.765625 0.76953125 0.0019185022 -0.00056068 0.767578125 0.000679849 0.76757813 0.76953125 0.0006798423 -0.00056068 0.7685546875 5.98135E-05
f(x)=cos(x)-lnx x1=0.5f(x1)f(xU)= -0.599354115 Tiene Raiz x2=1
1 1 2 0.5403023059 -1.109294017 1.5 -0.334727912 1 1.5 0.5403023059 -0.334727906 1.25 0.092178813 1.25 1.5 0.0921788111 -0.334727906 1.375 -0.123906024 1.25 1.375 0.0921788111 -0.123906023 1.3125 -0.016499955 1.25 1.3125 0.0921788111 -0.016499949 1.28125 0.03768136 1.28125 1.3125 0.0376813022 -0.016499949 1.296875 0.010551117 1.296875 1.3125 0.0105511125 -0.016499949 1.3046875 -0.002984328 1.296875 1.3046875 0.0105511125 -0.002984321 1.30078125 0.003780929 1.30078125 1.3046875 0.0037809217 -0.002984321 1.302734375 0.00039768
10 1.30273438 1.3046875 0.0003976816 -0.002984321 1.3037109375 -0.00129347
f(x)=3x+sen(x)-e^x x1=0f(x1)f(xU)= -1.123189156 Tiene Raiz x2=1
Termino X1 Xu f(x1) f(xu) Xr f(Xr)1 0 1 -1 1.123189156 0.5 0.330704272 0 0.5 -1 0.330704268 0.25 -0.286621463 0.25 0.5 -0.286621457 0.330704268 0.375 0.036281114 0.25 0.375 -0.286621457 0.036281114 0.3125 -0.121899435 0.3125 0.375 -0.121899427 0.036281114 0.34375 -0.041955976 0.34375 0.375 -0.041955966 0.036281114 0.359375 -0.002619637 0.359375 0.375 -0.002619635 0.036281114 0.3671875 0.016885758 0.359375 0.3671875 -0.002619635 0.016885753 0.36328125 0.007146749 0.359375 0.36328125 -0.002619635 0.007146742 0.361328125 0.00226697
10 0.359375 0.36132813 -0.002619635 0.002266965 0.3603515625 -0.00017548
f(x)=e^-x+4x^3-5 x1=1f(x1)f(xU)= -17.1528033 Tiene Raiz x2=2
Termino X1 Xu f(x1) f(xu) Xr f(Xr)
1 1 2 -0.632120559 27.13533528 1.5 8.723130162 1 1.5 -0.632120559 8.72313016 1.25 3.09900483 1 1.25 -0.632120559 3.099004797 1.125 1.019964974 1 1.125 -0.632120559 1.019964967 1.0625 0.143442325 1 1.0625 -0.632120559 0.143442315 1.03125 -0.25659826 1.03125 1.0625 -0.256598199 0.143442315 1.046875 -0.059687817 1.046875 1.0625 -0.05968781 0.143442315 1.0546875 0.041094158 1.046875 1.0546875 -0.05968781 0.041094147 1.05078125 -0.00949199 1.05078125 1.0546875 -0.009491903 0.041094147 1.052734375 0.01575227
10 1.05078125 1.05273438 -0.009491903 0.015752266 1.0517578125 0.00311798
Use el metodo de bisección para encontrar la raíz real de la siguiente función:
|Ea| = Aproximacion Actual- Aproximacion Anterior x1 =0Error = 0.001 xu=1
f(x1)f(Xr) |Ea| Observacion0.10653066 No aplica
-0.02957647 0.25 Continuar-0.00955991 0.125 Continuar0.00077584 0.0625 Continuar
-0.00030222 0.03125 Continuar-0.00012509 0.015625 Continuar
-3.615E-05 0.0078125 Continuar8.41313E-06 0.00390625 Continuar-2.2011E-06 0.001953125 Continuar
-4.336E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion-20.125 no aplica
16.953125 0.25 Continuar-0.31692505 0.125 Continuar2.83044815 0.0625 Continuar0.61334699 0.03125 Continuar0.10415375 0.015625 Continuar0.00678187 0.0078125 Continuar
-0.00164883 0.00390625 Continuar-0.00023974 0.001953125 Continuar0.00046421 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion0.15852902 no aplica
-0.07866883 0.5 Continuar-0.02952298 0.25 Continuar-0.00238603 0.125 Continuar0.01138661 0.0625 Continuar0.00203713 0.03125 Continuar
0.0001884 0.015625 Continuar
-2.7953E-05 0.0078125 Continuar8.08087E-06 0.00390625 Continuar-1.8199E-06 0.001953125 Continuar-1.7008E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion3.125 no aplica
0.65307617 0.25 Continuar-0.24908733 0.125 Continuar-0.01878232 0.0625 Continuar0.08232291 0.03125 Continuar0.01549921 0.015625 Continuar0.00138158 0.0078125 Continuar
-0.00023735 0.00390625 Continuar3.61905E-05 0.001953125 Continuar-1.1787E-05 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion0.03635239
-0.01430471 0.25 Continuar-0.00667427 0.125 Continuar-0.00272241 0.0625 Continuar-0.00071192 0.03125 Continuar0.00030193 0.015625 Continuar
-4.7E-05 0.0078125 Continuar1.09511E-05 0.00390625 Continuar
-2.863E-06 0.001953125 Continuar-5.6267E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion0.0233093
-0.00415739 0.125 Continuar-0.00017661 0.0625 Continuar0.00189157 0.03125 Continuar0.00040085 0.015625 Continuar
7.10805E-05 0.0078125 Continuar6.59955E-06 0.00390625 Continuar
-9.624E-07 0.001953125 Continuar2.95388E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion0.00175973
-0.00082502 0.125 Continuar-0.00033294 0.0625 Continuar-9.4581E-05 0.03125 Continuar2.25616E-05 0.015625 Continuar-5.8462E-06 0.0078125 Continuar-1.0757E-06 0.00390625 Continuar1.30428E-06 0.001953125 Continuar4.06638E-08 0.0009765625 Fin
-0.180854260.04980442 0.25 Continuar
-0.01142151 0.125 Continuar-0.00152095 0.0625 Continuar0.00347342 0.03125 Continuar0.00039758 0.015625 Continuar-3.1488E-05 0.0078125 Continuar3.98929E-05 0.00390625 Continuar
1.5036E-06 0.001953125 Continuar-5.1439E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion-0.330704270.28662146 0.25 Continuar
-0.01039895 0.125 Continuar0.03493899 0.0625 Continuar0.00511441 0.03125 Continuar0.00010991 0.015625 Continuar-4.4235E-05 0.0078125 Continuar-1.8722E-05 0.00390625 Continuar-5.9386E-06 0.001953125 Continuar4.59701E-07 0.0009765625 Fin
f(x1)f(Xr) |Ea| Observacion
-5.51406991-1.95894464 0.25 Continuar-0.64474083 0.125 Continuar-0.09067284 0.0625 Continuar
0.162201 0.03125 Continuar0.01531578 0.015625 Continuar
-0.00245282 0.0078125 Continuar0.00056655 0.00390625 Continuar
-0.00014952 0.001953125 Continuar-2.9596E-05 0.0009765625 Fin
