Taller1_soluciones.ipynb

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      "provenance": [],
      "authorship_tag": "ABX9TyOk4hWB93m9avYnxtaKQ+gg",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Slrosales/Soluciones_Computacionales/blob/main/Taller1_soluciones.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Realizado por**\n",
        "*   Laura Gómez\n",
        "*   Felipe Bénitez\n",
        "\n"
      ],
      "metadata": {
        "id": "scmlCdIjGw7N"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Importaciones"
      ],
      "metadata": {
        "id": "AlfLPQUp1MaM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import warnings\n",
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import math as mt\n",
        "import matplotlib.pyplot as plt\n",
        "import sympy.plotting as pls\n",
        "import seaborn as sns\n",
        "import sympy as sp\n",
        "from IPython.display import display, Math\n",
        "from sympy.parsing.sympy_parser import parse_expr\n",
        "\n",
        "warnings.filterwarnings('ignore')\n",
        "sns.set_style('darkgrid')"
      ],
      "metadata": {
        "id": "_ceF_qwnPpeR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Punto 1"
      ],
      "metadata": {
        "id": "Hh-n4OB-1JYD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Halle el $P_3$ de la serie de Taylor dada la siguiente función:\n",
        "$f(x)=\\sqrt{x+1}$ con $x_0=0$ para $\\sqrt{0.5}, \\sqrt{0.75}, \\sqrt{1.25}, \\sqrt{1.5}$\n",
        "\n",
        "Halle el valor teorico y experimental, además el error absoluto y relativo"
      ],
      "metadata": {
        "id": "KaSItn3vCQxo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = sp.symbols('x')\n",
        "f = sp.sqrt(x+1)\n",
        "x0 = 0\n",
        "n = 0\n",
        "i = 1"
      ],
      "metadata": {
        "id": "EyWpgoSJuBGr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def taylor(y):\n",
        "  x = sp.symbols('x')\n",
        "  f = sp.sqrt(x+1)\n",
        "  x0 = 0\n",
        "  n = 0\n",
        "  i = 1\n",
        "\n",
        "  p = sp.series(expr=f, x=x, x0=x0, n=0).removeO()\n",
        "  p_eval = p.subs(x, np.sqrt(y)).evalf()\n",
        "  f_eval = f.subs(x,  np.sqrt(y)).evalf()\n",
        "  valor_teorico = f_eval\n",
        "\n",
        "  valor_experimental = p_eval\n",
        "\n",
        "  error_absoluto = abs(valor_teorico - valor_experimental)\n",
        "  error_relativo = error_absoluto / abs(valor_teorico)\n",
        "\n",
        "  print(f\"Iteración {0}:\")\n",
        "  print(f\"  Valor teórico: {valor_teorico}\")\n",
        "  print(f\"  Valor experimental: {valor_experimental}\")\n",
        "  print(f\"  Error absoluto: {error_absoluto}\")\n",
        "  print(f\"  Error relativo: {error_relativo}\\n\")\n",
        "\n",
        "\n",
        "\n",
        "  while n<=3:\n",
        "      p = sp.series(expr=f, x=x, x0=x0, n=i).removeO()\n",
        "      p_eval = p.subs(x, np.sqrt(y)).evalf()\n",
        "      display(Math(sp.latex(p)))\n",
        "      n += 1\n",
        "\n",
        "      valor_experimental = p_eval\n",
        "\n",
        "      error_absoluto = abs(valor_teorico - valor_experimental)\n",
        "      error_relativo = error_absoluto / abs(valor_teorico)\n",
        "\n",
        "      print(f\"Iteración {i}:\")\n",
        "      print(f\"  Valor teórico: {valor_teorico}\")\n",
        "      print(f\"  Valor experimental: {valor_experimental}\")\n",
        "      print(f\"  Error absoluto: {error_absoluto}\")\n",
        "      print(f\"  Error relativo: {error_relativo}\\n\")\n",
        "      i += 1"
      ],
      "metadata": {
        "id": "b6lYR0rGBAZd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "taylor(0.5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "id": "pQMwU6O9BMoe",
        "outputId": "128e0e1a-5b73-4b61-f735-cdb907ead150"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0:\n",
            "  Valor teórico: 1.30656296487638\n",
            "  Valor experimental: 0\n",
            "  Error absoluto: 1.30656296487638\n",
            "  Error relativo: 1.00000000000000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1:\n",
            "  Valor teórico: 1.30656296487638\n",
            "  Valor experimental: 1.00000000000000\n",
            "  Error absoluto: 0.306562964876377\n",
            "  Error relativo: 0.234633135269820\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 2:\n",
            "  Valor teórico: 1.30656296487638\n",
            "  Valor experimental: 1.35355339059327\n",
            "  Error absoluto: 0.0469904257168972\n",
            "  Error relativo: 0.0359649148032780\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 3:\n",
            "  Valor teórico: 1.30656296487638\n",
            "  Valor experimental: 1.29105339059327\n",
            "  Error absoluto: 0.0155095742831028\n",
            "  Error relativo: 0.0118705142423582\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x^{3}}{16} - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 4:\n",
            "  Valor teórico: 1.30656296487638\n",
            "  Valor experimental: 1.31315047750535\n",
            "  Error absoluto: 0.00658751262897672\n",
            "  Error relativo: 0.00504186388721038\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "taylor(0.75)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "id": "GrrH37igBR-2",
        "outputId": "9fb126bf-ae0b-4b87-dfa1-40d11410a71a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0:\n",
            "  Valor teórico: 1.36602540378444\n",
            "  Valor experimental: 0\n",
            "  Error absoluto: 1.36602540378444\n",
            "  Error relativo: 1.00000000000000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1:\n",
            "  Valor teórico: 1.36602540378444\n",
            "  Valor experimental: 1.00000000000000\n",
            "  Error absoluto: 0.366025403784439\n",
            "  Error relativo: 0.267949192431123\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 2:\n",
            "  Valor teórico: 1.36602540378444\n",
            "  Valor experimental: 1.43301270189222\n",
            "  Error absoluto: 0.0669872981077806\n",
            "  Error relativo: 0.0490381056766579\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 3:\n",
            "  Valor teórico: 1.36602540378444\n",
            "  Valor experimental: 1.33926270189222\n",
            "  Error absoluto: 0.0267627018922194\n",
            "  Error relativo: 0.0195916575329243\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x^{3}}{16} - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 4:\n",
            "  Valor teórico: 1.36602540378444\n",
            "  Valor experimental: 1.37985764269461\n",
            "  Error absoluto: 0.0138322389101762\n",
            "  Error relativo: 0.0101259016646801\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "taylor(1.25)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "id": "zgdksY5qBV3F",
        "outputId": "7a4dd7f7-6ba8-4aa6-feb1-bd81f76d43b3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0:\n",
            "  Valor teórico: 1.45534669022535\n",
            "  Valor experimental: 0\n",
            "  Error absoluto: 1.45534669022535\n",
            "  Error relativo: 1.00000000000000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1:\n",
            "  Valor teórico: 1.45534669022535\n",
            "  Valor experimental: 1.00000000000000\n",
            "  Error absoluto: 0.455346690225355\n",
            "  Error relativo: 0.312878500554975\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 2:\n",
            "  Valor teórico: 1.45534669022535\n",
            "  Valor experimental: 1.55901699437495\n",
            "  Error absoluto: 0.103670304149593\n",
            "  Error relativo: 0.0712340948351898\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 3:\n",
            "  Valor teórico: 1.45534669022535\n",
            "  Valor experimental: 1.40276699437495\n",
            "  Error absoluto: 0.0525796958504074\n",
            "  Error relativo: 0.0361286394530953\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x^{3}}{16} - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 4:\n",
            "  Valor teórico: 1.45534669022535\n",
            "  Valor experimental: 1.49011339974603\n",
            "  Error absoluto: 0.0347667095206781\n",
            "  Error relativo: 0.0238889535766179\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "taylor(1.5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 662
        },
        "id": "NXaXZey_BZss",
        "outputId": "4cd6bd76-9a31-413e-d7d7-d4d774b7023b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0:\n",
            "  Valor teórico: 1.49155786726214\n",
            "  Valor experimental: 0\n",
            "  Error absoluto: 1.49155786726214\n",
            "  Error relativo: 1.00000000000000\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1:\n",
            "  Valor teórico: 1.49155786726214\n",
            "  Valor experimental: 1.00000000000000\n",
            "  Error absoluto: 0.491557867262142\n",
            "  Error relativo: 0.329560037898114\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 2:\n",
            "  Valor teórico: 1.49155786726214\n",
            "  Valor experimental: 1.61237243569579\n",
            "  Error absoluto: 0.120814568433653\n",
            "  Error relativo: 0.0809989146820139\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 3:\n",
            "  Valor teórico: 1.49155786726214\n",
            "  Valor experimental: 1.42487243569579\n",
            "  Error absoluto: 0.0666854315663472\n",
            "  Error relativo: 0.0447085782120897\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.Math object>"
            ],
            "text/latex": "$\\displaystyle \\frac{x^{3}}{16} - \\frac{x^{2}}{8} + \\frac{x}{2} + 1$"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 4:\n",
            "  Valor teórico: 1.49155786726214\n",
            "  Valor experimental: 1.53969226738876\n",
            "  Error absoluto: 0.0481344001266142\n",
            "  Error relativo: 0.0322712253966842\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Punto 2"
      ],
      "metadata": {
        "id": "87Nv_O7i1gsb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Mediante el método de bisección, halle la solución con $10^{-2}$ para $f(x)=x^4-2x^3-4x^2+4x+4$ dado los siguientes intervalos\n",
        "\n",
        "\\[-2, -1\\], \\[0, 2\\], \\[2, 3\\] y \\[-1, 0\\]"
      ],
      "metadata": {
        "id": "1SvsWrnwDV5O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def graficar(f, x_i, x_f, lista_puntos=None, num=1000):\n",
        "    \"\"\"\n",
        "    Gráfica de funciones algebraicas\n",
        "    :param f: función, previamente definida\n",
        "    :param x_i: límite inferior del intervalo\n",
        "    :param x_f: límite superior del intervalo\n",
        "    :param lista_puntos: lista de puntos a marcar en el gráfico (opcional)\n",
        "    :param num: división del intervalo\n",
        "    :return: gráfica de la función\n",
        "    \"\"\"\n",
        "    plt.style.use('seaborn')\n",
        "    x = np.linspace(x_i, x_f, num)\n",
        "    fig, ax = plt.subplots(figsize=(15, 5))\n",
        "    ax.plot(x, f(x))\n",
        "\n",
        "    if lista_puntos is not None:\n",
        "        for punto in lista_puntos:\n",
        "            plt.plot(punto[0], punto[1], 'ro')\n",
        "\n",
        "    xmin, xmax = ax.get_xlim()\n",
        "    ymin, ymax = ax.get_ylim()\n",
        "    ax.annotate(\"\", xy=(xmax, 0), xytext=(xmin, 0), arrowprops=dict(color='gray', width=1.5, headwidth=8, headlength=10))\n",
        "    ax.annotate(\"\", xy=(0, ymax), xytext=(0, ymin), arrowprops=dict(color='gray', width=1.5, headwidth=8, headlength=10))\n",
        "\n",
        "    plt.show()\n"
      ],
      "metadata": {
        "id": "oq7GhwwM2vh0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def metodo_biseccion(f, a, b, tol=1e-6, n=500):\n",
        "    \"\"\"\n",
        "    Método de bisección\n",
        "    :param f: Funcion a la que se le intenta encontrar una solucion para la ecuacion f(x)=0, previamente definida\n",
        "    :param a: límite inferior\n",
        "    :param b: límite superior\n",
        "    :param tol: toleracia, criterio de parada\n",
        "    :param n: número máximo de iteraciones, criterio de parada\n",
        "    :return: lista de puntos hallados por iteración\n",
        "    \"\"\"\n",
        "    puntos = []\n",
        "\n",
        "    if f(a) * f(b) >= 0:  # el intervalo escogido no sirve\n",
        "        print(\"Error: f(a) y f(b) deben tener signos opuestos.\")\n",
        "        return None\n",
        "\n",
        "    k = 0\n",
        "    while k <= n and (b-a)/2>tol:\n",
        "        c = (a + b) / 2  # punto medio\n",
        "        fc = f(c)\n",
        "\n",
        "        # Valor teórico (aproximado) y experimental\n",
        "        valor_teorico = c\n",
        "        valor_experimental = (a + b) / 2\n",
        "\n",
        "        # Cálculo del error absoluto y relativo\n",
        "        error_absoluto = abs(valor_teorico - valor_experimental)\n",
        "        error_relativo = error_absoluto / abs(valor_teorico)\n",
        "\n",
        "        # Valor de cada variable por iteración\n",
        "        print('Iteración {:<2}: a_{:<2}={:.7f}, b_{:<2}={:.7f}, c_{:<2}={:.7f}, '\n",
        "              'Valor teórico={:.7f}, Valor experimental={:.7f}, Error absoluto={:.7f}, Error relativo={:.7f}'.format(\n",
        "              k, k-1, a, k-1, b, k, c, valor_teorico, valor_experimental, error_absoluto, error_relativo))\n",
        "\n",
        "        puntos.append((c, fc))\n",
        "\n",
        "        if fc * f(a)< 0:\n",
        "            b = c\n",
        "        else:\n",
        "            a = c\n",
        "\n",
        "        k += 1\n",
        "\n",
        "    print(\"Resultado final: raíz = {:.7f}, valor teórico = {:.7f}, valor experimental = {:.7f}, \"\n",
        "          \"error absoluto = {:.7f}, error relativo = {:.7f}\".format(c, valor_teorico, valor_experimental, error_absoluto, error_relativo))\n",
        "\n",
        "    return puntos\n"
      ],
      "metadata": {
        "id": "qxG1CoGPdW20"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: x**4-2*x**3-4*x**2+4*x+4"
      ],
      "metadata": {
        "id": "5v14Ovtbdxty"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = metodo_biseccion(f, -2, -1, tol=1e-2)\n",
        "graficar(f, -2, -1, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 586
        },
        "id": "sp1nSI5yeWEJ",
        "outputId": "345bf70a-a982-4228-90a0-1ada87dea338"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=-2.0000000, b_-1=-1.0000000, c_0 =-1.5000000, Valor teórico=-1.5000000, Valor experimental=-1.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =-1.5000000, b_0 =-1.0000000, c_1 =-1.2500000, Valor teórico=-1.2500000, Valor experimental=-1.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =-1.5000000, b_1 =-1.2500000, c_2 =-1.3750000, Valor teórico=-1.3750000, Valor experimental=-1.3750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =-1.5000000, b_2 =-1.3750000, c_3 =-1.4375000, Valor teórico=-1.4375000, Valor experimental=-1.4375000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =-1.4375000, b_3 =-1.3750000, c_4 =-1.4062500, Valor teórico=-1.4062500, Valor experimental=-1.4062500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =-1.4375000, b_4 =-1.4062500, c_5 =-1.4218750, Valor teórico=-1.4218750, Valor experimental=-1.4218750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = -1.4218750, valor teórico = -1.4218750, valor experimental = -1.4218750, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = metodo_biseccion(f, 0, 2, tol=1e-2)\n",
        "graficar(f, 0, 2, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 604
        },
        "id": "m1996GqPw79A",
        "outputId": "3bd8f51e-4473-4b27-ea8f-22702c1b7ae2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=0.0000000, b_-1=2.0000000, c_0 =1.0000000, Valor teórico=1.0000000, Valor experimental=1.0000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =1.0000000, b_0 =2.0000000, c_1 =1.5000000, Valor teórico=1.5000000, Valor experimental=1.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =1.0000000, b_1 =1.5000000, c_2 =1.2500000, Valor teórico=1.2500000, Valor experimental=1.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =1.2500000, b_2 =1.5000000, c_3 =1.3750000, Valor teórico=1.3750000, Valor experimental=1.3750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =1.3750000, b_3 =1.5000000, c_4 =1.4375000, Valor teórico=1.4375000, Valor experimental=1.4375000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =1.3750000, b_4 =1.4375000, c_5 =1.4062500, Valor teórico=1.4062500, Valor experimental=1.4062500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =1.4062500, b_5 =1.4375000, c_6 =1.4218750, Valor teórico=1.4218750, Valor experimental=1.4218750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 1.4218750, valor teórico = 1.4218750, valor experimental = 1.4218750, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = metodo_biseccion(f, 2, 3, tol=1e-2)\n",
        "graficar(f, 2, 3, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 586
        },
        "id": "Ovr9zqJew__X",
        "outputId": "5c398a42-48d9-4677-a884-25eafd1b14ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=2.0000000, b_-1=3.0000000, c_0 =2.5000000, Valor teórico=2.5000000, Valor experimental=2.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =2.5000000, b_0 =3.0000000, c_1 =2.7500000, Valor teórico=2.7500000, Valor experimental=2.7500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =2.5000000, b_1 =2.7500000, c_2 =2.6250000, Valor teórico=2.6250000, Valor experimental=2.6250000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =2.6250000, b_2 =2.7500000, c_3 =2.6875000, Valor teórico=2.6875000, Valor experimental=2.6875000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =2.6875000, b_3 =2.7500000, c_4 =2.7187500, Valor teórico=2.7187500, Valor experimental=2.7187500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =2.7187500, b_4 =2.7500000, c_5 =2.7343750, Valor teórico=2.7343750, Valor experimental=2.7343750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 2.7343750, valor teórico = 2.7343750, valor experimental = 2.7343750, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = metodo_biseccion(f, -1, 0, tol=1e-2)\n",
        "graficar(f, -1, 0, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 586
        },
        "id": "Bs5KQymfxD-o",
        "outputId": "1b74bc1b-797a-4eeb-ba1a-285b1a98e3e9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=-1.0000000, b_-1=0.0000000, c_0 =-0.5000000, Valor teórico=-0.5000000, Valor experimental=-0.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =-1.0000000, b_0 =-0.5000000, c_1 =-0.7500000, Valor teórico=-0.7500000, Valor experimental=-0.7500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =-0.7500000, b_1 =-0.5000000, c_2 =-0.6250000, Valor teórico=-0.6250000, Valor experimental=-0.6250000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =-0.7500000, b_2 =-0.6250000, c_3 =-0.6875000, Valor teórico=-0.6875000, Valor experimental=-0.6875000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =-0.7500000, b_3 =-0.6875000, c_4 =-0.7187500, Valor teórico=-0.7187500, Valor experimental=-0.7187500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =-0.7500000, b_4 =-0.7187500, c_5 =-0.7343750, Valor teórico=-0.7343750, Valor experimental=-0.7343750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = -0.7343750, valor teórico = -0.7343750, valor experimental = -0.7343750, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Punto 3"
      ],
      "metadata": {
        "id": "_3pHBhnL19Lk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Halle la solución para cada función en el intervalo dado con el método de bisección"
      ],
      "metadata": {
        "id": "ACOYTSM5Eibm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "a"
      ],
      "metadata": {
        "id": "n8VQDeOW3FvQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: x-2**(-x)\n",
        "x = metodo_biseccion(f, 0, 1, tol=1e-5)\n",
        "graficar(f, 0, 1, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 760
        },
        "id": "C39DB21_0Yyh",
        "outputId": "33b32ba2-f409-479b-c5d4-a7e458b7302b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=0.0000000, b_-1=1.0000000, c_0 =0.5000000, Valor teórico=0.5000000, Valor experimental=0.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =0.5000000, b_0 =1.0000000, c_1 =0.7500000, Valor teórico=0.7500000, Valor experimental=0.7500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =0.5000000, b_1 =0.7500000, c_2 =0.6250000, Valor teórico=0.6250000, Valor experimental=0.6250000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =0.6250000, b_2 =0.7500000, c_3 =0.6875000, Valor teórico=0.6875000, Valor experimental=0.6875000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =0.6250000, b_3 =0.6875000, c_4 =0.6562500, Valor teórico=0.6562500, Valor experimental=0.6562500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =0.6250000, b_4 =0.6562500, c_5 =0.6406250, Valor teórico=0.6406250, Valor experimental=0.6406250, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =0.6406250, b_5 =0.6562500, c_6 =0.6484375, Valor teórico=0.6484375, Valor experimental=0.6484375, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =0.6406250, b_6 =0.6484375, c_7 =0.6445312, Valor teórico=0.6445312, Valor experimental=0.6445312, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =0.6406250, b_7 =0.6445312, c_8 =0.6425781, Valor teórico=0.6425781, Valor experimental=0.6425781, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =0.6406250, b_8 =0.6425781, c_9 =0.6416016, Valor teórico=0.6416016, Valor experimental=0.6416016, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =0.6406250, b_9 =0.6416016, c_10=0.6411133, Valor teórico=0.6411133, Valor experimental=0.6411133, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=0.6411133, b_10=0.6416016, c_11=0.6413574, Valor teórico=0.6413574, Valor experimental=0.6413574, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=0.6411133, b_11=0.6413574, c_12=0.6412354, Valor teórico=0.6412354, Valor experimental=0.6412354, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 13: a_12=0.6411133, b_12=0.6412354, c_13=0.6411743, Valor teórico=0.6411743, Valor experimental=0.6411743, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 14: a_13=0.6411743, b_13=0.6412354, c_14=0.6412048, Valor teórico=0.6412048, Valor experimental=0.6412048, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 15: a_14=0.6411743, b_14=0.6412048, c_15=0.6411896, Valor teórico=0.6411896, Valor experimental=0.6411896, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 0.6411896, valor teórico = 0.6411896, valor experimental = 0.6411896, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "b"
      ],
      "metadata": {
        "id": "w77pd4Vk3G1a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: np.exp(x)-x**2+3*x-2\n",
        "x = metodo_biseccion(f, 0, 1, tol=1e-5)\n",
        "graficar(f, 0, 1, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 760
        },
        "id": "gqv5N79F0w6w",
        "outputId": "b3eac26d-9829-42b6-bd1d-b7e60c36e9a0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=0.0000000, b_-1=1.0000000, c_0 =0.5000000, Valor teórico=0.5000000, Valor experimental=0.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =0.0000000, b_0 =0.5000000, c_1 =0.2500000, Valor teórico=0.2500000, Valor experimental=0.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =0.2500000, b_1 =0.5000000, c_2 =0.3750000, Valor teórico=0.3750000, Valor experimental=0.3750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =0.2500000, b_2 =0.3750000, c_3 =0.3125000, Valor teórico=0.3125000, Valor experimental=0.3125000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =0.2500000, b_3 =0.3125000, c_4 =0.2812500, Valor teórico=0.2812500, Valor experimental=0.2812500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =0.2500000, b_4 =0.2812500, c_5 =0.2656250, Valor teórico=0.2656250, Valor experimental=0.2656250, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =0.2500000, b_5 =0.2656250, c_6 =0.2578125, Valor teórico=0.2578125, Valor experimental=0.2578125, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =0.2500000, b_6 =0.2578125, c_7 =0.2539062, Valor teórico=0.2539062, Valor experimental=0.2539062, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =0.2539062, b_7 =0.2578125, c_8 =0.2558594, Valor teórico=0.2558594, Valor experimental=0.2558594, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =0.2558594, b_8 =0.2578125, c_9 =0.2568359, Valor teórico=0.2568359, Valor experimental=0.2568359, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =0.2568359, b_9 =0.2578125, c_10=0.2573242, Valor teórico=0.2573242, Valor experimental=0.2573242, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=0.2573242, b_10=0.2578125, c_11=0.2575684, Valor teórico=0.2575684, Valor experimental=0.2575684, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=0.2573242, b_11=0.2575684, c_12=0.2574463, Valor teórico=0.2574463, Valor experimental=0.2574463, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 13: a_12=0.2574463, b_12=0.2575684, c_13=0.2575073, Valor teórico=0.2575073, Valor experimental=0.2575073, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 14: a_13=0.2575073, b_13=0.2575684, c_14=0.2575378, Valor teórico=0.2575378, Valor experimental=0.2575378, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 15: a_14=0.2575073, b_14=0.2575378, c_15=0.2575226, Valor teórico=0.2575226, Valor experimental=0.2575226, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 0.2575226, valor teórico = 0.2575226, valor experimental = 0.2575226, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "c"
      ],
      "metadata": {
        "id": "D0m3zCl43H9I"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: 2*x*np.cos(2*x)-(x+1)**2\n",
        "x = metodo_biseccion(f, -3, -2, tol=1e-5)\n",
        "graficar(f, -3, -2, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 760
        },
        "id": "amtnJnRP1C8Y",
        "outputId": "e8a66f35-761e-40e2-ac85-cebbc1c98b19"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=-3.0000000, b_-1=-2.0000000, c_0 =-2.5000000, Valor teórico=-2.5000000, Valor experimental=-2.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =-2.5000000, b_0 =-2.0000000, c_1 =-2.2500000, Valor teórico=-2.2500000, Valor experimental=-2.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =-2.2500000, b_1 =-2.0000000, c_2 =-2.1250000, Valor teórico=-2.1250000, Valor experimental=-2.1250000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =-2.2500000, b_2 =-2.1250000, c_3 =-2.1875000, Valor teórico=-2.1875000, Valor experimental=-2.1875000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =-2.2500000, b_3 =-2.1875000, c_4 =-2.2187500, Valor teórico=-2.2187500, Valor experimental=-2.2187500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =-2.2187500, b_4 =-2.1875000, c_5 =-2.2031250, Valor teórico=-2.2031250, Valor experimental=-2.2031250, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =-2.2031250, b_5 =-2.1875000, c_6 =-2.1953125, Valor teórico=-2.1953125, Valor experimental=-2.1953125, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =-2.1953125, b_6 =-2.1875000, c_7 =-2.1914062, Valor teórico=-2.1914062, Valor experimental=-2.1914062, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =-2.1914062, b_7 =-2.1875000, c_8 =-2.1894531, Valor teórico=-2.1894531, Valor experimental=-2.1894531, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =-2.1914062, b_8 =-2.1894531, c_9 =-2.1904297, Valor teórico=-2.1904297, Valor experimental=-2.1904297, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =-2.1914062, b_9 =-2.1904297, c_10=-2.1909180, Valor teórico=-2.1909180, Valor experimental=-2.1909180, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=-2.1914062, b_10=-2.1909180, c_11=-2.1911621, Valor teórico=-2.1911621, Valor experimental=-2.1911621, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=-2.1914062, b_11=-2.1911621, c_12=-2.1912842, Valor teórico=-2.1912842, Valor experimental=-2.1912842, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 13: a_12=-2.1914062, b_12=-2.1912842, c_13=-2.1913452, Valor teórico=-2.1913452, Valor experimental=-2.1913452, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 14: a_13=-2.1913452, b_13=-2.1912842, c_14=-2.1913147, Valor teórico=-2.1913147, Valor experimental=-2.1913147, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 15: a_14=-2.1913147, b_14=-2.1912842, c_15=-2.1912994, Valor teórico=-2.1912994, Valor experimental=-2.1912994, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = -2.1912994, valor teórico = -2.1912994, valor experimental = -2.1912994, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: 2*x*np.cos(2*x)-(x+1)**2\n",
        "x = metodo_biseccion(f, -1, 0, tol=1e-5)\n",
        "graficar(f, -1, 0, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 760
        },
        "id": "a9S3BNT-1xOw",
        "outputId": "1e286f77-2f8a-404b-ea6b-03f8ff4e5739"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=-1.0000000, b_-1=0.0000000, c_0 =-0.5000000, Valor teórico=-0.5000000, Valor experimental=-0.5000000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =-1.0000000, b_0 =-0.5000000, c_1 =-0.7500000, Valor teórico=-0.7500000, Valor experimental=-0.7500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =-1.0000000, b_1 =-0.7500000, c_2 =-0.8750000, Valor teórico=-0.8750000, Valor experimental=-0.8750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =-0.8750000, b_2 =-0.7500000, c_3 =-0.8125000, Valor teórico=-0.8125000, Valor experimental=-0.8125000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =-0.8125000, b_3 =-0.7500000, c_4 =-0.7812500, Valor teórico=-0.7812500, Valor experimental=-0.7812500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =-0.8125000, b_4 =-0.7812500, c_5 =-0.7968750, Valor teórico=-0.7968750, Valor experimental=-0.7968750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =-0.8125000, b_5 =-0.7968750, c_6 =-0.8046875, Valor teórico=-0.8046875, Valor experimental=-0.8046875, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =-0.8046875, b_6 =-0.7968750, c_7 =-0.8007812, Valor teórico=-0.8007812, Valor experimental=-0.8007812, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =-0.8007812, b_7 =-0.7968750, c_8 =-0.7988281, Valor teórico=-0.7988281, Valor experimental=-0.7988281, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =-0.7988281, b_8 =-0.7968750, c_9 =-0.7978516, Valor teórico=-0.7978516, Valor experimental=-0.7978516, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =-0.7988281, b_9 =-0.7978516, c_10=-0.7983398, Valor teórico=-0.7983398, Valor experimental=-0.7983398, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=-0.7983398, b_10=-0.7978516, c_11=-0.7980957, Valor teórico=-0.7980957, Valor experimental=-0.7980957, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=-0.7983398, b_11=-0.7980957, c_12=-0.7982178, Valor teórico=-0.7982178, Valor experimental=-0.7982178, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 13: a_12=-0.7982178, b_12=-0.7980957, c_13=-0.7981567, Valor teórico=-0.7981567, Valor experimental=-0.7981567, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 14: a_13=-0.7982178, b_13=-0.7981567, c_14=-0.7981873, Valor teórico=-0.7981873, Valor experimental=-0.7981873, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 15: a_14=-0.7981873, b_14=-0.7981567, c_15=-0.7981720, Valor teórico=-0.7981720, Valor experimental=-0.7981720, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = -0.7981720, valor teórico = -0.7981720, valor experimental = -0.7981720, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "d"
      ],
      "metadata": {
        "id": "ndargs1V3KZi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: x*np.cos(x)-2*x**2+3*x-1\n",
        "x = metodo_biseccion(f, 0.2, 0.3, tol=1e-5)\n",
        "graficar(f, 0.2, 0.3, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 708
        },
        "id": "QIK9mKOu2aB3",
        "outputId": "4e2a50b7-0f81-4f66-9109-b7e1cbb17fb7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=0.2000000, b_-1=0.3000000, c_0 =0.2500000, Valor teórico=0.2500000, Valor experimental=0.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =0.2500000, b_0 =0.3000000, c_1 =0.2750000, Valor teórico=0.2750000, Valor experimental=0.2750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =0.2750000, b_1 =0.3000000, c_2 =0.2875000, Valor teórico=0.2875000, Valor experimental=0.2875000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =0.2875000, b_2 =0.3000000, c_3 =0.2937500, Valor teórico=0.2937500, Valor experimental=0.2937500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =0.2937500, b_3 =0.3000000, c_4 =0.2968750, Valor teórico=0.2968750, Valor experimental=0.2968750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =0.2968750, b_4 =0.3000000, c_5 =0.2984375, Valor teórico=0.2984375, Valor experimental=0.2984375, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =0.2968750, b_5 =0.2984375, c_6 =0.2976563, Valor teórico=0.2976563, Valor experimental=0.2976563, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =0.2968750, b_6 =0.2976563, c_7 =0.2972656, Valor teórico=0.2972656, Valor experimental=0.2972656, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =0.2972656, b_7 =0.2976563, c_8 =0.2974609, Valor teórico=0.2974609, Valor experimental=0.2974609, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =0.2974609, b_8 =0.2976563, c_9 =0.2975586, Valor teórico=0.2975586, Valor experimental=0.2975586, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =0.2974609, b_9 =0.2975586, c_10=0.2975098, Valor teórico=0.2975098, Valor experimental=0.2975098, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=0.2975098, b_10=0.2975586, c_11=0.2975342, Valor teórico=0.2975342, Valor experimental=0.2975342, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=0.2975098, b_11=0.2975342, c_12=0.2975220, Valor teórico=0.2975220, Valor experimental=0.2975220, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 0.2975220, valor teórico = 0.2975220, valor experimental = 0.2975220, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: x*np.cos(x)-2*x**2+3*x-1\n",
        "x = metodo_biseccion(f, 1.2, 1.3, tol=1e-5)\n",
        "graficar(f, 1.2, 1.3, x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 708
        },
        "id": "2aUs17RQ29JQ",
        "outputId": "56e4e4dc-4cd5-4dae-bbc5-f456659c08b5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 0 : a_-1=1.2000000, b_-1=1.3000000, c_0 =1.2500000, Valor teórico=1.2500000, Valor experimental=1.2500000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 1 : a_0 =1.2500000, b_0 =1.3000000, c_1 =1.2750000, Valor teórico=1.2750000, Valor experimental=1.2750000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 2 : a_1 =1.2500000, b_1 =1.2750000, c_2 =1.2625000, Valor teórico=1.2625000, Valor experimental=1.2625000, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 3 : a_2 =1.2500000, b_2 =1.2625000, c_3 =1.2562500, Valor teórico=1.2562500, Valor experimental=1.2562500, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 4 : a_3 =1.2562500, b_3 =1.2625000, c_4 =1.2593750, Valor teórico=1.2593750, Valor experimental=1.2593750, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 5 : a_4 =1.2562500, b_4 =1.2593750, c_5 =1.2578125, Valor teórico=1.2578125, Valor experimental=1.2578125, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 6 : a_5 =1.2562500, b_5 =1.2578125, c_6 =1.2570313, Valor teórico=1.2570313, Valor experimental=1.2570313, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 7 : a_6 =1.2562500, b_6 =1.2570313, c_7 =1.2566406, Valor teórico=1.2566406, Valor experimental=1.2566406, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 8 : a_7 =1.2562500, b_7 =1.2566406, c_8 =1.2564453, Valor teórico=1.2564453, Valor experimental=1.2564453, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 9 : a_8 =1.2564453, b_8 =1.2566406, c_9 =1.2565430, Valor teórico=1.2565430, Valor experimental=1.2565430, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 10: a_9 =1.2565430, b_9 =1.2566406, c_10=1.2565918, Valor teórico=1.2565918, Valor experimental=1.2565918, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 11: a_10=1.2565918, b_10=1.2566406, c_11=1.2566162, Valor teórico=1.2566162, Valor experimental=1.2566162, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Iteración 12: a_11=1.2566162, b_11=1.2566406, c_12=1.2566284, Valor teórico=1.2566284, Valor experimental=1.2566284, Error absoluto=0.0000000, Error relativo=0.0000000\n",
            "Resultado final: raíz = 1.2566284, valor teórico = 1.2566284, valor experimental = 1.2566284, error absoluto = 0.0000000, error relativo = 0.0000000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Punto 4"
      ],
      "metadata": {
        "id": "y_VBr9zz2Jxs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Los siguientes métodos estan propuestos para computar $21^{1/3}$. haga un ranking basado en su velocidad de convergencia asumiendo que $p_0=1$"
      ],
      "metadata": {
        "id": "DEWh1wLXEwWN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$P_n=\\frac{20P_{n-1}+21/P^2_{n-1}}{21}$"
      ],
      "metadata": {
        "id": "x0gfL2U5Fqyl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def metodo_a(z0=1, tol=1e-6, n=500):\n",
        "\n",
        "    z1 = (20*z0+(21/(z0**2)))/(21)\n",
        "    k = 0\n",
        "    while abs(z0 - z1) > tol and k <= n:\n",
        "        e_abs = abs(z1 - z0)\n",
        "        e_rel = e_abs / abs(z1) if z1 != 0 else e_abs\n",
        "        print('Iteración {:<2}: p_{:<2}={:.7f}, Error absoluto={:.7f}, Error relativo={:.7f}'.format(k+1, k, z1, e_abs, e_rel))\n",
        "        z0 = z1\n",
        "        z1 = (20*z0+(21/(z0**2)))/(21)\n",
        "        k += 1\n",
        "\n",
        "    print(\"Resultado final: zn = {:.7f}, k = {}\".format(z1, k))"
      ],
      "metadata": {
        "id": "l0gFOgAi4wxI"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$P_n=P_{n-1}-\\frac{P_{n-1}^3-21}{3P^2_{n-1}}$"
      ],
      "metadata": {
        "id": "q1NFBDbOF7Kc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def metodo_b(z0=1, tol=1e-6, n=50):\n",
        "\n",
        "    z1 = z0-((z0**3-21)/(3*z0**2))\n",
        "    k = 0\n",
        "    while abs(z0 - z1) > tol and k <= n:\n",
        "        e_abs = abs(z1 - z0)\n",
        "        e_rel = e_abs / abs(z1) if z1 != 0 else e_abs\n",
        "        print('Iteración {:<2}: p_{:<2}={:.7f}, Error absoluto={:.7f}, Error relativo={:.7f}'.format(k+1, k, z1, e_abs, e_rel))\n",
        "        z0 = z1\n",
        "        z1 = z0-((z0**3-21)/(3*z0**2))\n",
        "        k += 1\n",
        "\n",
        "    print(\"Resultado final: zn = {:.7f}, k = {}\".format(z1, k))"
      ],
      "metadata": {
        "id": "qGBp7GKX4xh_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$P_n=P_{n-1}-\\frac{P^4_{n-1}-21P_{n-1}}{P_{n-1}^2-21}$"
      ],
      "metadata": {
        "id": "_sVfUhxrGLqT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def metodo_c(z0=1, tol=1e-6, n=50):\n",
        "\n",
        "    z1 = z0-(((z0**4)-(21*z0))/((z0**2)-(21)))\n",
        "    k = 0\n",
        "    while abs(z0 - z1) > tol and k <= n:\n",
        "        e_abs = abs(z1 - z0)\n",
        "        e_rel = e_abs / abs(z1) if z1 != 0 else e_abs\n",
        "        print('Iteración {:<2}: p_{:<2}={:.7f}, Error absoluto={:.7f}, Error relativo={:.7f}'.format(k+1, k, z1, e_abs, e_rel))\n",
        "        z0 = z1\n",
        "        z1 = z0-(((z0**4)-(21*z0))/((z0**2)-(21)))\n",
        "        k += 1\n",
        "\n",
        "    print(\"Resultado final: zn = {:.7f}, k = {}\".format(z1, k))"
      ],
      "metadata": {
        "id": "NPk-LJAi4yUf"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$P_n = \\left(\\frac{21}{P_{n-1}} \\right)$"
      ],
      "metadata": {
        "id": "yG7aL_zRGjQE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def metodo_d(z0=1, tol=1e-6, n=50):\n",
        "\n",
        "    z1 = (21/(z0))**(1/2)\n",
        "    k = 0\n",
        "    while abs(z0 - z1) > tol and k <= n:\n",
        "        e_abs = abs(z1 - z0)\n",
        "        e_rel = e_abs / abs(z1) if z1 != 0 else e_abs\n",
        "        print('Iteración {:<2}: p_{:<2}={:.7f}, Error absoluto={:.7f}, Error relativo={:.7f}'.format(k+1, k, z1, e_abs, e_rel))\n",
        "        z0 = z1\n",
        "        z1 = (21/(z0))**(1/2)\n",
        "        k += 1\n",
        "\n",
        "    print(\"Resultado final: zn = {:.7f}, k = {}\".format(z1, k))"
      ],
      "metadata": {
        "id": "BkgXRXw7n4Zg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "metodo_a()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XG_lOKeQ5lt_",
        "outputId": "181511ce-4c22-4905-9e85-568d22ce9667"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1 : p_0 =1.9523810, Error absoluto=0.9523810, Error relativo=0.4878049\n",
            "Iteración 2 : p_1 =2.1217543, Error absoluto=0.1693733, Error relativo=0.0798270\n",
            "Iteración 3 : p_2 =2.2428497, Error absoluto=0.1210954, Error relativo=0.0539918\n",
            "Iteración 4 : p_3 =2.3348397, Error absoluto=0.0919900, Error relativo=0.0393988\n",
            "Iteración 5 : p_4 =2.4070934, Error absoluto=0.0722537, Error relativo=0.0300170\n",
            "Iteración 6 : p_5 =2.4650593, Error absoluto=0.0579659, Error relativo=0.0235150\n",
            "Iteración 7 : p_6 =2.5122435, Error absoluto=0.0471842, Error relativo=0.0187817\n",
            "Iteración 8 : p_7 =2.5510571, Error absoluto=0.0388136, Error relativo=0.0152147\n",
            "Iteración 9 : p_8 =2.5832378, Error absoluto=0.0321807, Error relativo=0.0124575\n",
            "Iteración 10: p_9 =2.6100814, Error absoluto=0.0268437, Error relativo=0.0102846\n",
            "Iteración 11: p_10=2.6325803, Error absoluto=0.0224989, Error relativo=0.0085463\n",
            "Iteración 12: p_11=2.6515095, Error absoluto=0.0189292, Error relativo=0.0071390\n",
            "Iteración 13: p_12=2.6674845, Error absoluto=0.0159750, Error relativo=0.0059888\n",
            "Iteración 14: p_13=2.6810002, Error absoluto=0.0135157, Error relativo=0.0050413\n",
            "Iteración 15: p_14=2.6924589, Error absoluto=0.0114587, Error relativo=0.0042558\n",
            "Iteración 16: p_15=2.7021902, Error absoluto=0.0097314, Error relativo=0.0036013\n",
            "Iteración 17: p_16=2.7104665, Error absoluto=0.0082762, Error relativo=0.0030534\n",
            "Iteración 18: p_17=2.7175135, Error absoluto=0.0070470, Error relativo=0.0025932\n",
            "Iteración 19: p_18=2.7235199, Error absoluto=0.0060064, Error relativo=0.0022054\n",
            "Iteración 20: p_19=2.7286437, Error absoluto=0.0051238, Error relativo=0.0018778\n",
            "Iteración 21: p_20=2.7330177, Error absoluto=0.0043740, Error relativo=0.0016004\n",
            "Iteración 22: p_21=2.7367538, Error absoluto=0.0037361, Error relativo=0.0013652\n",
            "Iteración 23: p_22=2.7399467, Error absoluto=0.0031929, Error relativo=0.0011653\n",
            "Iteración 24: p_23=2.7426766, Error absoluto=0.0027299, Error relativo=0.0009953\n",
            "Iteración 25: p_24=2.7450115, Error absoluto=0.0023349, Error relativo=0.0008506\n",
            "Iteración 26: p_25=2.7470091, Error absoluto=0.0019976, Error relativo=0.0007272\n",
            "Iteración 27: p_26=2.7487186, Error absoluto=0.0017096, Error relativo=0.0006219\n",
            "Iteración 28: p_27=2.7501820, Error absoluto=0.0014634, Error relativo=0.0005321\n",
            "Iteración 29: p_28=2.7514348, Error absoluto=0.0012529, Error relativo=0.0004553\n",
            "Iteración 30: p_29=2.7525077, Error absoluto=0.0010728, Error relativo=0.0003898\n",
            "Iteración 31: p_30=2.7534264, Error absoluto=0.0009188, Error relativo=0.0003337\n",
            "Iteración 32: p_31=2.7542134, Error absoluto=0.0007870, Error relativo=0.0002857\n",
            "Iteración 33: p_32=2.7548875, Error absoluto=0.0006741, Error relativo=0.0002447\n",
            "Iteración 34: p_33=2.7554650, Error absoluto=0.0005775, Error relativo=0.0002096\n",
            "Iteración 35: p_34=2.7559598, Error absoluto=0.0004948, Error relativo=0.0001795\n",
            "Iteración 36: p_35=2.7563838, Error absoluto=0.0004239, Error relativo=0.0001538\n",
            "Iteración 37: p_36=2.7567470, Error absoluto=0.0003633, Error relativo=0.0001318\n",
            "Iteración 38: p_37=2.7570583, Error absoluto=0.0003113, Error relativo=0.0001129\n",
            "Iteración 39: p_38=2.7573250, Error absoluto=0.0002667, Error relativo=0.0000967\n",
            "Iteración 40: p_39=2.7575536, Error absoluto=0.0002286, Error relativo=0.0000829\n",
            "Iteración 41: p_40=2.7577495, Error absoluto=0.0001959, Error relativo=0.0000710\n",
            "Iteración 42: p_41=2.7579174, Error absoluto=0.0001679, Error relativo=0.0000609\n",
            "Iteración 43: p_42=2.7580613, Error absoluto=0.0001439, Error relativo=0.0000522\n",
            "Iteración 44: p_43=2.7581846, Error absoluto=0.0001233, Error relativo=0.0000447\n",
            "Iteración 45: p_44=2.7582903, Error absoluto=0.0001057, Error relativo=0.0000383\n",
            "Iteración 46: p_45=2.7583808, Error absoluto=0.0000906, Error relativo=0.0000328\n",
            "Iteración 47: p_46=2.7584585, Error absoluto=0.0000776, Error relativo=0.0000281\n",
            "Iteración 48: p_47=2.7585250, Error absoluto=0.0000665, Error relativo=0.0000241\n",
            "Iteración 49: p_48=2.7585820, Error absoluto=0.0000570, Error relativo=0.0000207\n",
            "Iteración 50: p_49=2.7586309, Error absoluto=0.0000489, Error relativo=0.0000177\n",
            "Iteración 51: p_50=2.7586728, Error absoluto=0.0000419, Error relativo=0.0000152\n",
            "Iteración 52: p_51=2.7587087, Error absoluto=0.0000359, Error relativo=0.0000130\n",
            "Iteración 53: p_52=2.7587395, Error absoluto=0.0000308, Error relativo=0.0000112\n",
            "Iteración 54: p_53=2.7587659, Error absoluto=0.0000264, Error relativo=0.0000096\n",
            "Iteración 55: p_54=2.7587885, Error absoluto=0.0000226, Error relativo=0.0000082\n",
            "Iteración 56: p_55=2.7588079, Error absoluto=0.0000194, Error relativo=0.0000070\n",
            "Iteración 57: p_56=2.7588245, Error absoluto=0.0000166, Error relativo=0.0000060\n",
            "Iteración 58: p_57=2.7588387, Error absoluto=0.0000142, Error relativo=0.0000052\n",
            "Iteración 59: p_58=2.7588509, Error absoluto=0.0000122, Error relativo=0.0000044\n",
            "Iteración 60: p_59=2.7588614, Error absoluto=0.0000105, Error relativo=0.0000038\n",
            "Iteración 61: p_60=2.7588704, Error absoluto=0.0000090, Error relativo=0.0000033\n",
            "Iteración 62: p_61=2.7588781, Error absoluto=0.0000077, Error relativo=0.0000028\n",
            "Iteración 63: p_62=2.7588847, Error absoluto=0.0000066, Error relativo=0.0000024\n",
            "Iteración 64: p_63=2.7588903, Error absoluto=0.0000056, Error relativo=0.0000020\n",
            "Iteración 65: p_64=2.7588951, Error absoluto=0.0000048, Error relativo=0.0000018\n",
            "Iteración 66: p_65=2.7588993, Error absoluto=0.0000041, Error relativo=0.0000015\n",
            "Iteración 67: p_66=2.7589028, Error absoluto=0.0000036, Error relativo=0.0000013\n",
            "Iteración 68: p_67=2.7589059, Error absoluto=0.0000030, Error relativo=0.0000011\n",
            "Iteración 69: p_68=2.7589085, Error absoluto=0.0000026, Error relativo=0.0000009\n",
            "Iteración 70: p_69=2.7589107, Error absoluto=0.0000022, Error relativo=0.0000008\n",
            "Iteración 71: p_70=2.7589127, Error absoluto=0.0000019, Error relativo=0.0000007\n",
            "Iteración 72: p_71=2.7589143, Error absoluto=0.0000016, Error relativo=0.0000006\n",
            "Iteración 73: p_72=2.7589157, Error absoluto=0.0000014, Error relativo=0.0000005\n",
            "Iteración 74: p_73=2.7589169, Error absoluto=0.0000012, Error relativo=0.0000004\n",
            "Iteración 75: p_74=2.7589180, Error absoluto=0.0000010, Error relativo=0.0000004\n",
            "Resultado final: zn = 2.7589188, k = 75\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "metodo_b()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uFckoOmh6mhu",
        "outputId": "942d4815-da41-4194-8b54-a78e6afb2a6c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1 : p_0 =7.6666667, Error absoluto=6.6666667, Error relativo=0.8695652\n",
            "Iteración 2 : p_1 =5.2302037, Error absoluto=2.4364629, Error relativo=0.4658447\n",
            "Iteración 3 : p_2 =3.7426969, Error absoluto=1.4875068, Error relativo=0.3974425\n",
            "Iteración 4 : p_3 =2.9948536, Error absoluto=0.7478434, Error relativo=0.2497095\n",
            "Iteración 5 : p_4 =2.7770222, Error absoluto=0.2178313, Error relativo=0.0784406\n",
            "Iteración 6 : p_5 =2.7590419, Error absoluto=0.0179804, Error relativo=0.0065169\n",
            "Iteración 7 : p_6 =2.7589242, Error absoluto=0.0001177, Error relativo=0.0000427\n",
            "Resultado final: zn = 2.7589242, k = 7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "metodo_c()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7u0BRHEY-BV1",
        "outputId": "925c60a5-77aa-4900-c87f-276b45c3a45d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1 : p_0 =0.0000000, Error absoluto=1.0000000, Error relativo=1.0000000\n",
            "Resultado final: zn = 0.0000000, k = 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "metodo_c(z0=2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GeKiQSCA68FH",
        "outputId": "1b2285da-bd30-41d8-b8c7-1ee4a1315243"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1 : p_0 =0.4705882, Error absoluto=1.5294118, Error relativo=3.2500000\n",
            "Iteración 2 : p_1 =-0.0026552, Error absoluto=0.4732435, Error relativo=178.2309028\n",
            "Iteración 3 : p_2 =0.0000000, Error absoluto=0.0026552, Error relativo=2970738.6127563\n",
            "Resultado final: zn = 0.0000000, k = 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "metodo_d()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d1rEwOJQ4oaX",
        "outputId": "bdf10d9d-7841-4d75-a3d3-96df7d6d7230"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteración 1 : p_0 =4.5825757, Error absoluto=3.5825757, Error relativo=0.7817821\n",
            "Iteración 2 : p_1 =2.1406951, Error absoluto=2.4418806, Error relativo=1.1406951\n",
            "Iteración 3 : p_2 =3.1320756, Error absoluto=0.9913805, Error relativo=0.3165251\n",
            "Iteración 4 : p_3 =2.5893665, Error absoluto=0.5427091, Error relativo=0.2095914\n",
            "Iteración 5 : p_4 =2.8478223, Error absoluto=0.2584557, Error relativo=0.0907556\n",
            "Iteración 6 : p_5 =2.7155213, Error absoluto=0.1323010, Error relativo=0.0487203\n",
            "Iteración 7 : p_6 =2.7808851, Error absoluto=0.0653638, Error relativo=0.0235047\n",
            "Iteración 8 : p_7 =2.7480088, Error absoluto=0.0328763, Error relativo=0.0119637\n",
            "Iteración 9 : p_8 =2.7643981, Error absoluto=0.0163893, Error relativo=0.0059287\n",
            "Iteración 10: p_9 =2.7561913, Error absoluto=0.0082068, Error relativo=0.0029776\n",
            "Iteración 11: p_10=2.7602916, Error absoluto=0.0041004, Error relativo=0.0014855\n",
            "Iteración 12: p_11=2.7582407, Error absoluto=0.0020509, Error relativo=0.0007436\n",
            "Iteración 13: p_12=2.7592660, Error absoluto=0.0010253, Error relativo=0.0003716\n",
            "Iteración 14: p_13=2.7587533, Error absoluto=0.0005127, Error relativo=0.0001858\n",
            "Iteración 15: p_14=2.7590096, Error absoluto=0.0002563, Error relativo=0.0000929\n",
            "Iteración 16: p_15=2.7588815, Error absoluto=0.0001282, Error relativo=0.0000465\n",
            "Iteración 17: p_16=2.7589455, Error absoluto=0.0000641, Error relativo=0.0000232\n",
            "Iteración 18: p_17=2.7589135, Error absoluto=0.0000320, Error relativo=0.0000116\n",
            "Iteración 19: p_18=2.7589295, Error absoluto=0.0000160, Error relativo=0.0000058\n",
            "Iteración 20: p_19=2.7589215, Error absoluto=0.0000080, Error relativo=0.0000029\n",
            "Iteración 21: p_20=2.7589255, Error absoluto=0.0000040, Error relativo=0.0000015\n",
            "Iteración 22: p_21=2.7589235, Error absoluto=0.0000020, Error relativo=0.0000007\n",
            "Iteración 23: p_22=2.7589245, Error absoluto=0.0000010, Error relativo=0.0000004\n",
            "Resultado final: zn = 2.7589240, k = 23\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Resultados obtenidos**\n",
        "\n",
        "| Método | Cant. Iteración |\n",
        "|--------|-----------------|\n",
        "|   a    |       75        |\n",
        "|   b    |        7        |\n",
        "|   c    |      Error      |\n",
        "|   d    |       23        |\n",
        "\n",
        "\n",
        "**Ranking por Velocidad de convergencia**\n",
        "1.   b\n",
        "2.   d\n",
        "3.   a\n",
        "4.   c (descalificado)\n",
        "\n",
        "De acuerdo con la cantidad de iteraciones que le tomó a cada método llegar al valor teórico $21^{1/3}$, quien converge más rápido es **b** dado que es un método de grado tres, se podría decir, que entonces **c** debería ser el más rápido, pero dado el valor inicial **z0=1**, este converge hacia 0, no hacia el objetivo, por lo tanto es descalificado. en cuanto a los demás, **a** converge linealmente y **d** en $1/2$\n"
      ],
      "metadata": {
        "id": "UQixhGOi7Zj-"
      }
    }
  ]
}