2.3 Resuelve por el mtodo del punto fijo las ecuaciones de los problemas anteriores.

------------------------------------------------------------------------------------------2.1a) x = 1/(x+1)^2

function y=g(x)y=1/((x+1)^2);

>> puntofijo(1) 1 1.00000 0.25000 0.75000 2 0.25000 0.64000 0.39000 3 0.64000 0.37180 0.26820 4 0.37180 0.53139 0.15959 5 0.53139 0.42641 0.10499 6 0.42641 0.49149 0.06508 7 0.49149 0.44953 0.04195 8 0.44953 0.47593 0.02640 9 0.47593 0.45906 0.01687 10 0.45906 0.46974 0.01068 11 0.46974 0.46294 0.00680 12 0.46294 0.46725 0.00431 13 0.46725 0.46451 0.00274 14 0.46451 0.46625 0.00174 15 0.46625 0.46514 0.00111 16 0.46514 0.46584 0.00070 17 0.46584 0.46540 0.00045ans = 0.4654------------------------------------------------------------------------------------------2.1b) x = 4 + (x-1)/(x+1)

function y=g(x)y=4+(x-1)/(x+1);

>> puntofijo(1) 1 1.00000 4.00000 3.00000 2 4.00000 4.60000 0.60000 3 4.60000 4.64286 0.04286 4 4.64286 4.64557 0.00271 5 4.64557 4.64574 0.00017ans = 4.6457------------------------------------------------------------------------------------------2.1c) x = sin(x)

function y=g(x)y=sin(x);

>> puntofijo(1) 1 1.00000 0.84147 0.15853 2 0.84147 0.74562 0.09585 3 0.74562 0.67843 0.06719 4 0.67843 0.62757 0.05086 5 0.62757 0.58718 0.04039 6 0.58718 0.55402 0.03316 7 0.55402 0.52611 0.02791 8 0.52611 0.50217 0.02394 9 0.50217 0.48133 0.02084 10 0.48133 0.46296 0.01837 11 0.46296 0.44660 0.01636 12 0.44660 0.43190 0.01470 13 0.43190 0.41860 0.01330 14 0.41860 0.40648 0.01212 15 0.40648 0.39538 0.01110 16 0.39538 0.38516 0.01022 17 0.38516 0.37570 0.00945 18 0.37570 0.36693 0.00878 19 0.36693 0.35875 0.00818 20 0.35875 0.35110 0.00765 21 0.35110 0.34393 0.00717 22 0.34393 0.33719 0.00674 23 0.33719 0.33084 0.00635 24 0.33084 0.32484 0.00600 25 0.32484 0.31915 0.00568 26 0.31915 0.31376 0.00539 27 0.31376 0.30864 0.00512 28 0.30864 0.30376 0.00488 29 0.30376 0.29911 0.00465 30 0.29911 0.29467 0.00444 31 0.29467 0.29043 0.00425 32 0.29043 0.28636 0.00407 33 0.28636 0.28246 0.00390 34 0.28246 0.27872 0.00374 35 0.27872 0.27513 0.00359 36 0.27513 0.27167 0.00346 37 0.27167 0.26834 0.00333 38 0.26834 0.26513 0.00321 39 0.26513 0.26204 0.00310 40 0.26204 0.25905 0.00299 41 0.25905 0.25616 0.00289 42 0.25616 0.25337 0.00279 43 0.25337 0.25067 0.00270 44 0.25067 0.24805 0.00262 45 0.24805 0.24551 0.00254 46 0.24551 0.24305 0.00246 47 0.24305 0.24067 0.00239 48 0.24067 0.23835 0.00232 49 0.23835 0.23610 0.00225 50 0.23610 0.23391 0.00219no se pudo encontrar la raz>>------------------------------------------------------------------------------------------2.1d) tanx = ln(x)

function y=g(x)y=atan(log(x));

puntofijo(1) 1 1.00000 0.00000 1.00000 2 0.00000 -1.57080 1.57080 3 -1.57080 1.52119 3.10869 4 1.52119 0.42944 1.10155 5 0.42944 -0.70169 1.13295 6 -0.70169 -1.52816 0.83621 7 -1.52816 1.51198 3.04020 8 1.51198 0.43021 1.09320 9 0.43021 -0.70075 1.13313 10 -0.70075 -1.52841 0.83491 11 -1.52841 1.51177 3.04026 12 1.51177 0.43016 1.09305 13 0.43016 -0.70082 1.13315 14 -0.70082 -1.52843 0.83484 15 -1.52843 1.51177 3.04028 16 1.51177 0.43016 1.09305 17 0.43016 -0.70082 1.13315 18 -0.70082 -1.52843 0.83484 19 -1.52843 1.51177 3.04028 20 1.51177 0.43016 1.09305 21 0.43016 -0.70082 1.13315 22 -0.70082 -1.52843 0.83484 23 -1.52843 1.51177 3.04028 24 1.51177 0.43016 1.09305 25 0.43016 -0.70082 1.13315 26 -0.70082 -1.52843 0.83484 27 -1.52843 1.51177 3.04028 28 1.51177 0.43016 1.09305 29 0.43016 -0.70082 1.13315 30 -0.70082 -1.52843 0.83484 31 -1.52843 1.51177 3.04028 32 1.51177 0.43016 1.09305 33 0.43016 -0.70082 1.13315 34 -0.70082 -1.52843 0.83484 35 -1.52843 1.51177 3.04028 36 1.51177 0.43016 1.09305 37 0.43016 -0.70082 1.13315 38 -0.70082 -1.52843 0.83484 39 -1.52843 1.51177 3.04028 40 1.51177 0.43016 1.09305 41 0.43016 -0.70082 1.13315 42 -0.70082 -1.52843 0.83484 43 -1.52843 1.51177 3.04028 44 1.51177 0.43016 1.09305 45 0.43016 -0.70082 1.13315 46 -0.70082 -1.52843 0.83484 47 -1.52843 1.51177 3.04028 48 1.51177 0.43016 1.09305 49 0.43016 -0.70082 1.13315 50 -0.70082 -1.52843 0.83484no se pudo encontrar la raz>>------------------------------------------------------------------------------------------2.1

e) x = ((6-x-x^3)/4)^(1/2)

function y=g(x)y=((6-x-x^3)/4)^(1/2);

>> puntofijo(1) 1 1.00000 1.00000 0.00000ans = 1------------------------------------------------------------------------------------------2.1f) x = sec(x)/2

function y=g(x)y=sec(x)/2;

>> puntofijo(1) 1 1.00000 0.92541 0.07459 2 0.92541 0.83124 0.09416 3 0.83124 0.74189 0.08936 4 0.74189 0.67825 0.06364 5 0.67825 0.64212 0.03613 6 0.64212 0.62435 0.01776 7 0.62435 0.61626 0.00809 8 0.61626 0.61271 0.00355 9 0.61271 0.61118 0.00153 10 0.61118 0.61052 0.00066 11 0.61052 0.61024 0.00028ans = 0.6102------------------------------------------------------------------------------------------2.2a) 2x = 4x^2-1

function y=g(x)y=sqrt((2*x+1)/4);

>> puntofijo(1) 1 1.00000 0.86603 0.13397 2 0.86603 0.82645 0.03958 3 0.82645 0.81438 0.01206 4 0.81438 0.81067 0.00371 5 0.81067 0.80953 0.00115 6 0.80953 0.80918 0.00035ans = 0.8092------------------------------------------------------------------------------------------2.2b) x^3-10x-5 = 0

function y=g(x)y=sqrt((5/x)+10);

>> puntofijo(1) 1 1.00000 3.87298 2.87298 2 3.87298 3.36021 0.51278 3 3.36021 3.38940 0.02919 4 3.38940 3.38750 0.00189 5 3.38750 3.38763 0.00012ans = 3.3876------------------------------------------------------------------------------------------2.2c) senx + lnx = 0

function y=g(x)y=exp(-sin(x));

>> puntofijo(1) 1 1.00000 0.43108 0.56892 2 0.43108 0.65846 0.22739 3 0.65846 0.54232 0.11614 4 0.54232 0.59683 0.05451 5 0.59683 0.57005 0.02677 6 0.57005 0.58294 0.01288 7 0.58294 0.57667 0.00626 8 0.57667 0.57970 0.00303 9 0.57970 0.57823 0.00147 10 0.57823 0.57895 0.00071 11 0.57895 0.57860 0.00034ans = 0.5786------------------------------------------------------------------------------------------2.2d) exp(x) - tanx=0

function y=g(x)y=atan(exp(x));

>> puntofijo(1) 1 1.00000 1.21828 0.21828 2 1.21828 1.28325 0.06497 3 1.28325 1.30045 0.01719 4 1.30045 1.30484 0.00439 5 1.30484 1.30595 0.00111 6 1.30595 1.30623 0.00028ans = 1.3062------------------------------------------------------------------------------------------2.2

e) sqrt(x^3*sinx)-ln(cosx) = 3

function y=g(x)y=(3+log(cos(x)))/(sqrt(x*sin(x)))

>> puntofijo(1) 1 1.00000 2.59929 1.59929 2 2.59929 2.45642 2.71615 3 2.45642 0.96722 3.49238 4 0.96722 2.32086 2.32740 5 2.32086 1.61596 2.42546 6 1.61596 1.57689 2.29219 7 1.57689 1.33048 2.71915 8 1.33048 1.32275 2.76599 9 1.32275 1.20275 2.89307 10 1.20275 1.19393 2.93180 11 1.19393 1.12213 2.99643 12 1.12213 1.11439 3.02280 13 1.11439 1.06649 3.06197 14 1.06649 1.06007 3.08050 15 1.06007 1.02597 3.10661 16 1.02597 1.02071 3.12013 17 1.02071 0.99539 3.13862 18 0.99539 0.99107 3.14879 19 0.99107 0.97171 3.16243 20 0.97171 0.96816 3.17027 21 0.96816 0.95304 3.18063 22 0.95304 0.95011 3.18678 23 0.95011 0.93810 3.19482 24 0.93810 0.93567 3.19972 25 0.93567 0.92601 3.20608 26 0.92601 0.92399 3.21002 27 0.92399 0.91615 3.21511 28 0.91615 0.91446 3.21831 29 0.91446 0.90804 3.22243 30 0.90804 0.90663 3.22505 31 0.90663 0.90135 3.22841 32 0.90135 0.90016 3.23057 33 0.90016 0.89579 3.23332 34 0.89579 0.89479 3.23512 35 0.89479 0.89116 3.23739 36 0.89116 0.89032 3.23888 37 0.89032 0.88728 3.24076 38 0.88728 0.88658 3.24201 39 0.88658 0.88404 3.24358 40 0.88404 0.88345 3.24462 41 0.88345 0.88132 3.24593 42 0.88132 0.88082 3.24680 43 0.88082 0.87903 3.24790 44 0.87903 0.87860 3.24863 45 0.87860 0.87709 3.24955 46 0.87709 0.87674 3.25017 47 0.87674 0.87547 3.25095 48 0.87547 0.87516 3.25147 49 0.87516 0.87409 3.25212 50 0.87409 0.87383 3.25256no se pudo encontrar la raz>>------------------------------------------------------------------------------------------function y=g(x)y=acos(exp(x*sqrt(x*sin(x)-3)));

>> puntofijo(1) 1 1.00000 1.49892 1.01120 2 1.49892 2.01378 1.67649 3 2.01378 1.49951 1.50664 4 1.49951 1.85993 1.46207 5 1.85993 1.66804 1.56585 6 1.66804 1.90849 1.74397 7 1.90849 1.55552 2.07484 8 1.55552 2.61664 2.20451 9 2.61664 2.27405 2.52127 10 2.27405 0.00047 16.82685 11 0.00047 1.57080 13.48865 12 1.57080 1.78881 0.89160 13 1.78881 1.79508 1.89375 14 1.79508 2.02431 2.38130 15 2.02431 2.48385 4.39046 16 2.48385 0.60056 13.24320 17 0.60056 1.57080 16.16306 18 1.57080 1.78881 0.89160 19 1.78881 1.79508 1.89375 20 1.79508 2.02431 2.38130 21 2.02431 2.48385 4.39046 22 2.48385 0.60056 13.24320 23 0.60056 1.57080 16.16306 24 1.57080 1.78881 0.89160 25 1.78881 1.79508 1.89375 26 1.79508 2.02431 2.38130 27 2.02431 2.48385 4.39046 28 2.48385 0.60056 13.24320 29 0.60056 1.57080 16.16306 30 1.57080 1.78881 0.89160 31 1.78881 1.79508 1.89375 32 1.79508 2.02431 2.38130 33 2.02431 2.48385 4.39046 34 2.48385 0.60056 13.24320 35 0.60056 1.57080 16.16306 36 1.57080 1.78881 0.89160 37 1.78881 1.79508 1.89375 38 1.79508 2.02431 2.38130 39 2.02431 2.48385 4.39046 40 2.48385 0.60056 13.24320 41 0.60056 1.57080 16.16306 42 1.57080 1.78881 0.89160 43 1.78881 1.79508 1.89375 44 1.79508 2.02431 2.38130 45 2.02431 2.48385 4.39046 46 2.48385 0.60056 13.24320 47 0.60056 1.57080 16.16306 48 1.57080 1.78881 0.89160 49 1.78881 1.79508 1.89375 50 1.79508 2.02431 2.38130no se pudo encontrar la raz>>------------------------------------------------------------------------------------------2.8 Resuelva las siguientes ecuaciones por medio del mtodo de Newton-Rapson------------------------------------------------------------------------------------------2.8a) log(x)-x+2=0

function x=f(x)x=log(x)-x+2;

function x=df(x)x=(1/x)-1;

>> newton(1) 1 1.00000 -Inf Inf Inf 2 -Inf NaN NaN NaN 3 NaN NaN NaN NaN 4 NaN NaN NaN NaN 5 NaN NaN NaN NaN 6 NaN NaN NaN NaN 7 NaN NaN NaN NaN 8 NaN NaN NaN NaN 9 NaN NaN NaN NaN 10 NaN NaN NaN NaN 11 NaN NaN NaN NaN 12 NaN NaN NaN NaN 13 NaN NaN NaN NaN 14 NaN NaN NaN NaN 15 NaN NaN NaN NaN 16 NaN NaN NaN NaN 17 NaN NaN NaN NaN 18 NaN NaN NaN NaN 19 NaN NaN NaN NaN 20 NaN NaN NaN NaN 21 NaN NaN NaN NaN 22 NaN NaN NaN NaN 23 NaN NaN NaN NaN 24 NaN NaN NaN NaN 25 NaN NaN NaN NaN 26 NaN NaN NaN NaN 27 NaN NaN NaN NaN 28 NaN NaN NaN NaN 29 NaN NaN NaN NaN 30 NaN NaN NaN NaN 31 NaN NaN NaN NaN 32 NaN NaN NaN NaN 33 NaN NaN NaN NaN 34 NaN NaN NaN NaN 35 NaN NaN NaN NaN 36 NaN NaN NaN NaN 37 NaN NaN NaN NaN 38 NaN NaN NaN NaN 39 NaN NaN NaN NaN 40 NaN NaN NaN NaN 41 NaN NaN NaN NaN 42 NaN NaN NaN NaN 43 NaN NaN NaN NaN 44 NaN NaN NaN NaN 45 NaN NaN NaN NaN 46 NaN NaN NaN NaN 47 NaN NaN NaN NaN 48 NaN NaN NaN NaN 49 NaN NaN NaN NaN 50 NaN NaN NaN NaNNo se encontro la raiz en 50 iteraciones>>------------------------------------------------------------------------------------------2.8b) x*exp(x)-2=0

function x=f(x)x=x*exp(x)-2;function x=df(x)x=exp(x);

>> newton(1) 1 1.00000 0.73576 0.26424 0.46442 2 0.73576 0.95828 0.22252 0.49845 3 0.95828 0.76710 0.19118 0.34804 4 0.76710 0.92871 0.16161 0.35081 5 0.92871 0.79012 0.13859 0.25883 6 0.79012 0.90758 0.11746 0.24926 7 0.90758 0.80700 0.10058 0.19137 8 0.80700 0.89239 0.08539 0.17828 9 0.89239 0.81935 0.07304 0.14087 10 0.81935 0.88143 0.06208 0.12810 11 0.88143 0.82838 0.05306 0.10335 12 0.82838 0.87352 0.04514 0.09235 13 0.87352 0.83496 0.03855 0.07564 14 0.83496 0.86778 0.03282 0.06673 15 0.86778 0.83976 0.02802 0.05526 16 0.83976 0.86362 0.02386 0.04829 17 0.86362 0.84326 0.02036 0.04031 18 0.84326 0.86061 0.01735 0.03500 19 0.86061 0.84581 0.01480 0.02938 20 0.84581 0.85842 0.01261 0.02538 21 0.85842 0.84766 0.01076 0.02140 22 0.84766 0.85683 0.00917 0.01842 23 0.85683 0.84901 0.00782 0.01558 24 0.84901 0.85568 0.00667 0.01337 25 0.85568 0.84999 0.00568 0.01134 26 0.84999 0.85484 0.00485 0.00971 27 0.85484 0.85071 0.00413 0.00825 28 0.85071 0.85423 0.00352 0.00706 29 0.85423 0.85122 0.00300 0.00600 30 0.85122 0.85378 0.00256 0.00513 31 0.85378 0.85160 0.00218 0.00436 32 0.85160 0.85346 0.00186 0.00373 33 0.85346 0.85188 0.00159 0.00317 34 0.85188 0.85323 0.00135 0.00271 35 0.85323 0.85207 0.00115 0.00231 36 0.85207 0.85306 0.00098 0.00197ans = 0.8531------------------------------------------------------------------------------------------2.8c) x-2*cos(x)=0

function x=f(x)x=x-2*cos(x);function x=df(x)x=1+2*sin(x);

>> newton(1) 1 1.00000 1.03004 0.03004 0.00048ans = 1.0300------------------------------------------------------------------------------------------2.8d) x^3-5*x = -1

function x=f(x)x=x^3-5*x+1;function x=df(x)x=3*x^2-8;

>> newton(1) 1 1.00000 0.40000 0.60000 0.93600 2 0.40000 0.27553 0.12447 0.35674 3 0.27553 0.22963 0.04590 0.13605 4 0.22963 0.21228 0.01735 0.05185 5 0.21228 0.20569 0.00659 0.01975 6 0.20569 0.20318 0.00251 0.00752 7 0.20318 0.20223 0.00095 0.00286ans = 0.2022

------------------------------------------------------------------------------------------2.17Resuelva por el mtodo de la secante, posicin falsa o biseccin las siguientes ecuaciones.a) x*log(x)-10 = 0function y=f(x)y=x*log(x)-10;

>> reglafalsa(1,2) 1 1.00000 2.00000 -10.00000 -8.61371 8.21348 7.29574 1.00000 7.29574 2 1.00000 8.21348 -10.00000 7.29574 5.17067 -1.50459 7.21348 1.50459 3 5.17067 8.21348 -1.50459 7.29574 5.69089 -0.10429 3.04281 0.10429 4 5.69089 8.21348 -0.10429 7.29574 5.72645 -0.00681 2.52258 0.00681 5 5.72645 8.21348 -0.00681 7.29574 5.72876 -0.00044 2.48703 0.00044

ans =

5.7288------------------------------------------------------------------------------------------>> secante(1,2) 1 2 3 4ans = 5.7292------------------------------------------------------------------------------------------b) sin(x)-csc(x)+1= 0function y=f(x)y=sin(x)-csc(x)+1;

>> reglafalsa(1,2) 1 1.00000 2.00000 0.65308 0.80955 -3.17377 -30.04887 1.00000 30.04887 2 1.00000 -3.17377 0.65308 -30.04887 0.91122 0.52483 4.17377 0.52483 3 0.91122 -3.17377 0.52483 -30.04887 0.84109 0.40376 4.08499 0.40376 4 0.84109 -3.17377 0.40376 -30.04887 0.78786 0.29811 4.01487 0.29811 5 0.78786 -3.17377 0.29811 -30.04887 0.74895 0.21215 3.96163 0.21215 6 0.74895 -3.17377 0.21215 -30.04887 0.72145 0.14640 3.92272 0.14640 7 0.72145 -3.17377 0.14640 -30.04887 0.70256 0.09860 3.89522 0.09860 8 0.70256 -3.17377 0.09860 -30.04887 0.68988 0.06522 3.87633 0.06522 9 0.68988 -3.17377 0.06522 -30.04887 0.68151 0.04259 3.86365 0.04259 10 0.68151 -3.17377 0.04259 -30.04887 0.67606 0.02757 3.85529 0.02757 11 0.67606 -3.17377 0.02757 -30.04887 0.67253 0.01774 3.84983 0.01774 12 0.67253 -3.17377 0.01774 -30.04887 0.67026 0.01137 3.84630 0.01137 13 0.67026 -3.17377 0.01137 -30.04887 0.66880 0.00727 3.84403 0.00727 14 0.66880 -3.17377 0.00727 -30.04887 0.66787 0.00464 3.84258 0.00464 15 0.66787 -3.17377 0.00464 -30.04887 0.66728 0.00296 3.84165 0.00296 16 0.66728 -3.17377 0.00296 -30.04887 0.66690 0.00189 3.84105 0.00189 17 0.66690 -3.17377 0.00189 -30.04887 0.66666 0.00120 3.84068 0.00120 18 0.66666 -3.17377 0.00120 -30.04887 0.66651 0.00077 3.84043 0.00077

ans =

0.6665

------------------------------------------------------------------------------------------

c) exp(x)+2^-x+2*cos(x)-6= 0function y=f(x)y=exp(x)+2^-x+2*cos(x)-6;

>> reglafalsa(1,2) 1 1.00000 2.00000 -1.70111 0.80676 1.67831 -0.54567 1.00000 0.54567 2 1.67831 2.00000 -0.54567 0.80676 1.80810 -0.08574 0.32169 0.08574 3 1.80810 2.00000 -0.08574 0.80676 1.82654 -0.01165 0.19190 0.01165 4 1.82654 2.00000 -0.01165 0.80676 1.82901 -0.00155 0.17346 0.00155 5 1.82901 2.00000 -0.00155 0.80676 1.82933 -0.00021 0.17099 0.00021

ans =

1.8293

>> biseccion(1,2) 0 1.00000 2.00000 1.50000 1 1.50000 2.00000 1.75000 2 1.75000 2.00000 1.87500 3 1.75000 1.87500 1.81250 4 1.81250 1.87500 1.84375 5 1.81250 1.84375 1.82813 6 1.82813 1.84375 1.83594 7 1.82813 1.83594 1.83203 8 1.82813 1.83203 1.83008 9 1.82813 1.83008 1.82910

ans =

1.8291------------------------------------------------------------------------------------------

d) exp(x)+x^3+2*x^2+10*x-20 = 0

function y=f(x)y=exp(x)+x^3+2*x^2+10*x-20;

>> reglafalsa(1,2) 1 1.00000 2.00000 -4.28172 23.38906 1.15474 -1.07284 1.00000 1.07284 2 1.15474 2.00000 -1.07284 23.38906 1.19181 -0.25520 0.84526 0.25520 3 1.19181 2.00000 -0.25520 23.38906 1.20053 -0.05994 0.80819 0.05994 4 1.20053 2.00000 -0.05994 23.38906 1.20258 -0.01404 0.79947 0.01404 5 1.20258 2.00000 -0.01404 23.38906 1.20305 -0.00328 0.79742 0.00328 6 1.20305 2.00000 -0.00328 23.38906 1.20317 -0.00077 0.79695 0.00077

ans =

1.2032

>> biseccion(1,2) 0 1.00000 2.00000 1.50000 1 1.00000 1.50000 1.25000 2 1.00000 1.25000 1.12500 3 1.12500 1.25000 1.18750 4 1.18750 1.25000 1.21875 5 1.18750 1.21875 1.20313 6 1.20313 1.21875 1.21094 7 1.20313 1.21094 1.20703 8 1.20313 1.20703 1.20508 9 1.20313 1.20508 1.20410

ans =

1.2041

------------------------------------------------------------------------------------------

2.19Encuentre una aproximacin a mediante el mtodo de la biseccin.El clculo deber ser correcto en cuatro dgitos significativos.Sugerencia: considere

function y=f(x)y=x^3-2;

>> biseccion(1,2) 0 1.00000 2.00000 1.50000 1 1.00000 1.50000 1.25000 2 1.25000 1.50000 1.37500 3 1.25000 1.37500 1.31250 4 1.25000 1.31250 1.28125 5 1.25000 1.28125 1.26563 6 1.25000 1.26563 1.25781 7 1.25781 1.26563 1.26172 8 1.25781 1.26172 1.25977 9 1.25977 1.26172 1.26074

ans =

1.2607

------------------------------------------------------------------------------------------

function y=f(x)y=x^2-3;

>> biseccion(1,2) 0 1.00000 2.00000 1.50000 1 1.50000 2.00000 1.75000 2 1.50000 1.75000 1.62500 3 1.62500 1.75000 1.68750 4 1.68750 1.75000 1.71875 5 1.71875 1.75000 1.73438 6 1.71875 1.73438 1.72656 7 1.72656 1.73438 1.73047 8 1.73047 1.73438 1.73242 9 1.73047 1.73242 1.73145ans = 1.7314------------------------------------------------------------------------------------------2.21Aplique el mtodo de biseccin y de posicin falsa a la ecuacin

(7*x-3)/(x-0.45)^2 =0

Use los intervalos (0.4,0.5) y (0.39,0.53)

function y=f(x)y=(7*x-3)/(x-0.45)^2;

>> biseccion(0.4,0.5) 0 0.40000 0.50000 0.45000 1 0.40000 0.45000 0.42500 2 0.42500 0.45000 0.43750 3 0.42500 0.43750 0.43125 4 0.42500 0.43125 0.42813 5 0.42813 0.43125 0.42969 6 0.42813 0.42969 0.42891

ans =

0.4289

------------------------------------------------------------------------------------------

>> reglafalsa(0.4,0.5) 1 0.40000 0.50000 -80.00000 200.00000 0.42857 0.00000 0.10000 0.00000

ans =

0.4286

------------------------------------------------------------------------------------------

>> biseccion(0.39,0.53) 0 0.39000 0.53000 0.46000 1 0.39000 0.46000 0.42500 2 0.42500 0.46000 0.44250 3 0.42500 0.44250 0.43375 4 0.42500 0.43375 0.42938 5 0.42500 0.42938 0.42719 6 0.42719 0.42938 0.42828 7 0.42828 0.42938 0.42883

ans =

0.4288

------------------------------------------------------------------------------------------

>> reglafalsa(0.39,0.53) 1 0.39000 0.53000 -75.00000 110.93750 0.4464710058.33333 0.1400010058.33333 2 0.39000 0.44647 -75.0000010058.33333 0.39042 -75.23178 0.05647 75.23178 3 0.39042 0.44647 -75.2317810058.33333 0.39083 -75.46164 0.05605 75.46164 4 0.39083 0.44647 -75.4616410058.33333 0.39125 -75.68948 0.05564 75.68948 5 0.39125 0.44647 -75.6894810058.33333 0.39166 -75.91519 0.05522 75.91519 6 0.39166 0.44647 -75.9151910058.33333 0.39207 -76.13866 0.05481 76.13866 7 0.39207 0.44647 -76.1386610058.33333 0.39248 -76.35978 0.05440 76.35978 8 0.39248 0.44647 -76.3597810058.33333 0.39289 -76.57844 0.05399 76.57844 9 0.39289 0.44647 -76.5784410058.33333 0.39329 -76.79452 0.05358 76.79452 10 0.39329 0.44647 -76.7945210058.33333 0.39369 -77.00790 0.05318 77.00790 11 0.39369 0.44647 -77.0079010058.33333 0.39410 -77.21845 0.05278 77.21845 12 0.39410 0.44647 -77.2184510058.33333 0.39449 -77.42605 0.05237 77.42605 13 0.39449 0.44647 -77.4260510058.33333 0.39489 -77.63057 0.05198 77.63057 14 0.39489 0.44647 -77.6305710058.33333 0.39529 -77.83188 0.05158 77.83188 15 0.39529 0.44647 -77.8318810058.33333 0.39568 -78.02985 0.05118 78.02985 16 0.39568 0.44647 -78.0298510058.33333 0.39607 -78.22433 0.05079 78.22433 17 0.39607 0.44647 -78.2243310058.33333 0.39646 -78.41520 0.05040 78.41520 18 0.39646 0.44647 -78.4152010058.33333 0.39685 -78.60230 0.05001 78.60230 19 0.39685 0.44647 -78.6023010058.33333 0.39723 -78.78550 0.04962 78.78550 20 0.39723 0.44647 -78.7855010058.33333 0.39761 -78.96464 0.04924 78.96464 21 0.39761 0.44647 -78.9646410058.33333 0.39799 -79.13958 0.04886 79.13958 22 0.39799 0.44647 -79.1395810058.33333 0.39837 -79.31016 0.04848 79.31016 23 0.39837 0.44647 -79.3101610058.33333 0.39875 -79.47623 0.04810 79.47623 24 0.39875 0.44647 -79.4762310058.33333 0.39912 -79.63763 0.04772 79.63763 25 0.39912 0.44647 -79.6376310058.33333 0.39950 -79.79419 0.04735 79.79419 26 0.39950 0.44647 -79.7941910058.33333 0.39987 -79.94577 0.04698 79.94577 27 0.39987 0.44647 -79.9457710058.33333 0.40023 -80.09219 0.04661 80.09219 28 0.40023 0.44647 -80.0921910058.33333 0.40060 -80.23328 0.04624 80.23328 29 0.40060 0.44647 -80.2332810058.33333 0.40096 -80.36887 0.04587 80.36887 30 0.40096 0.44647 -80.3688710058.33333 0.40132 -80.49880 0.04551 80.49880 31 0.40132 0.44647 -80.4988010058.33333 0.40168 -80.62289 0.04515 80.62289 32 0.40168 0.44647 -80.6228910058.33333 0.40204 -80.74097 0.04479 80.74097 33 0.40204 0.44647 -80.7409710058.33333 0.40239 -80.85285 0.04443 80.85285 34 0.40239 0.44647 -80.8528510058.33333 0.40274 -80.95835 0.04408 80.95835 35 0.40274 0.44647 -80.9583510058.33333 0.40309 -81.05731 0.04373 81.05731 36 0.40309 0.44647 -81.0573110058.33333 0.40344 -81.14953 0.04338 81.14953 37 0.40344 0.44647 -81.1495310058.33333 0.40378 -81.23484 0.04303 81.23484 38 0.40378 0.44647 -81.2348410058.33333 0.40412 -81.31304 0.04269 81.31304 39 0.40412 0.44647 -81.3130410058.33333 0.40446 -81.38395 0.04235 81.38395 40 0.40446 0.44647 -81.3839510058.33333 0.40480 -81.44740 0.04201 81.44740 41 0.40480 0.44647 -81.4474010058.33333 0.40514 -81.50318 0.04167 81.50318 42 0.40514 0.44647 -81.5031810058.33333 0.40547 -81.55111 0.04134 81.55111 43 0.40547 0.44647 -81.5511110058.33333 0.40580 -81.59102 0.04100 81.59102 44 0.40580 0.44647 -81.5910210058.33333 0.40612 -81.62270 0.04067 81.62270 45 0.40612 0.44647 -81.6227010058.33333 0.40645 -81.64597 0.04035 81.64597 46 0.40645 0.44647 -81.6459710058.33333 0.40677 -81.66065 0.04002 81.66065 47 0.40677 0.44647 -81.6606510058.33333 0.40709 -81.66655 0.03970 81.66655 48 0.40709 0.44647 -81.6665510058.33333 0.40741 -81.66349 0.03938 81.66349 49 0.40741 0.44647 -81.6634910058.33333 0.40772 -81.65127 0.03906 81.65127 50 0.40772 0.44647 -81.6512710058.33333 0.40804 -81.62973 0.03875 81.62973No se puede hallar la raiz>>

------------------------------------------------------------------------------------------2.50Para determinar la constante de nacimientos de una poblacin se necesita calcular x en la siguiente ecuacin

function y=f(x)y=10^6*exp(x)+((0.435*10^6)/x)*(exp(x)-1)-1.546*10^6;

>> secante(1,2) 1 2 3 4 5 6ans =

0.0875

------------------------------------------------------------------------------------------>> reglafalsa(1,2) 1 1.00000 2.000001919734.423847232675.80045 0.63867956835.24966 1.00000956835.24966 2 0.63867 2.00000956835.249667232675.80045 0.43112536802.25760 1.36133536802.25760 3 0.43112 2.00000536802.257607232675.80045 0.30534319804.72355 1.56888319804.72355 4 0.30534 2.00000319804.723557232675.80045 0.22694197070.13086 1.69466197070.13086 5 0.22694 2.00000197070.130867232675.80045 0.17728123901.42892 1.77306123901.42892 6 0.17728 2.00000123901.428927232675.80045 0.1455178866.41142 1.8227278866.41142 7 0.14551 2.0000078866.411427232675.80045 0.1250650590.76636 1.8544950590.76636 8 0.12506 2.0000050590.766367232675.80045 0.1118632612.81063 1.8749432612.81063 9 0.11186 2.0000032612.810637232675.80045 0.1033021089.93074 1.8881421089.93074 10 0.10330 2.0000021089.930747232675.80045 0.0977613666.10022 1.8967013666.10022 11 0.09776 2.0000013666.100227232675.80045 0.094168867.15900 1.902248867.15900 12 0.09416 2.000008867.159007232675.80045 0.091825758.29518 1.905845758.29518 13 0.09182 2.000005758.295187232675.80045 0.090303741.47695 1.908183741.47695 14 0.09030 2.000003741.476957232675.80045 0.089312431.91212 1.909702431.91212 15 0.08931 2.000002431.912127232675.80045 0.088661581.07987 1.910691581.07987 16 0.08866 2.000001581.079877232675.80045 0.088251028.07659 1.911341028.07659 17 0.08825 2.000001028.076597232675.80045 0.08797 668.55919 1.91175 668.55919 18 0.08797 2.00000 668.559197232675.80045 0.08780 434.79250 1.91203 434.79250 19 0.08780 2.00000 434.792507232675.80045 0.08768 282.77583 1.91220 282.77583 20 0.08768 2.00000 282.775837232675.80045 0.08761 183.91378 1.91232 183.91378 21 0.08761 2.00000 183.913787232675.80045 0.08756 119.61728 1.91239 119.61728 22 0.08756 2.00000 119.617287232675.80045 0.08753 77.79981 1.91244 77.79981 23 0.08753 2.00000 77.799817232675.80045 0.08751 50.60185 1.91247 50.60185 24 0.08751 2.00000 50.601857232675.80045 0.08749 32.91215 1.91249 32.91215 25 0.08749 2.00000 32.912157232675.80045 0.08749 21.40660 1.91251 21.40660 26 0.08749 2.00000 21.406607232675.80045 0.08748 13.92322 1.91251 13.92322 27 0.08748 2.00000 13.923227232675.80045 0.08748 9.05592 1.91252 9.05592 28 0.08748 2.00000 9.055927232675.80045 0.08747 5.89014 1.91252 5.89014 29 0.08747 2.00000 5.890147232675.80045 0.08747 3.83106 1.91253 3.83106 30 0.08747 2.00000 3.831067232675.80045 0.08747 2.49180 1.91253 2.49180 31 0.08747 2.00000 2.491807232675.80045 0.08747 1.62071 1.91253 1.62071 32 0.08747 2.00000 1.620717232675.80045 0.08747 1.05414 1.91253 1.05414 33 0.08747 2.00000 1.054147232675.80045 0.08747 0.68564 1.91253 0.68564 34 0.08747 2.00000 0.685647232675.80045 0.08747 0.44595 1.91253 0.44595 35 0.08747 2.00000 0.445957232675.80045 0.08747 0.29006 1.91253 0.29006 36 0.08747 2.00000 0.290067232675.80045 0.08747 0.18866 1.91253 0.18866 37 0.08747 2.00000 0.188667232675.80045 0.08747 0.12271 1.91253 0.12271 38 0.08747 2.00000 0.122717232675.80045 0.08747 0.07981 1.91253 0.07981 39 0.08747 2.00000 0.079817232675.80045 0.08747 0.05191 1.91253 0.05191 40 0.08747 2.00000 0.051917232675.80045 0.08747 0.03376 1.91253 0.03376 41 0.08747 2.00000 0.033767232675.80045 0.08747 0.02196 1.91253 0.02196 42 0.08747 2.00000 0.021967232675.80045 0.08747 0.01428 1.91253 0.01428 43 0.08747 2.00000 0.014287232675.80045 0.08747 0.00929 1.91253 0.00929 44 0.08747 2.00000 0.009297232675.80045 0.08747 0.00604 1.91253 0.00604 45 0.08747 2.00000 0.006047232675.80045 0.08747 0.00393 1.91253 0.00393 46 0.08747 2.00000 0.003937232675.80045 0.08747 0.00256 1.91253 0.00256 47 0.08747 2.00000 0.002567232675.80045 0.08747 0.00166 1.91253 0.00166 48 0.08747 2.00000 0.001667232675.80045 0.08747 0.00108 1.91253 0.00108 49 0.08747 2.00000 0.001087232675.80045 0.08747 0.00070 1.91253 0.00070

ans =

0.0875