sanchezcarlosjr/2-2-fixed-point-iteration-illustration.ipynb

## 2-2-fixed-point-iteration-illustration.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "2.2 Fixed-point iteration Illustration.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPTMGCZEx406wXn8pGpIDj9",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/sanchezcarlosjr/c814b73dfcf4e415315fc170578d4807/2-2-fixed-point-iteration-illustration.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2 Solutions of Equations in One Variable\n",
        "##  2.2 Fixed-point iteration\n",
        "### Illustration\n",
        "By [Carlos Eduardo Sanchez Torres](https://twitter.com/CharllierJr)\n",
        "\n",
        "[Numerical analysis](https://www.notion.so/sanchezcarlosjr/Numerical-analysis-f774bbfddd834cf1beffda5e9e935ff8)\n",
        "\n",
        "Burden, Richard L., and J. Douglas Faires. Numerical Analysis. 7th ed. Belmont, CA: Brooks Cole, 2000. ISBN: 0534382169. Page 61."
      ],
      "metadata": {
        "id": "aDI5jvlKM5Ci"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 73,
      "metadata": {
        "id": "5Kijoy9MMD20",
        "outputId": "72402734-5125-45eb-bcbd-35243b59f106",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in sqrt\n",
            "  \n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9e/bU8fHxOiIiQu/evVtrrXVKSoru1q1bleIqeh07BQVap6drffKk1ocPax0drfWZM1rfvFml6xW3f/9+PXbsWK218/vUunru1R1qw3dPCCFE7QVEayc5TW0YvqLemD59OtHR0fTs2ZMNGzYQEBBAYGCgbX/xt/xGjhzJ119/za1bt5g4cSJvvvkmwcHBLFy4kMWLFwOwf/9+xo4dW6W4rNcpLvzee9n7739DUBALPvmEZ9auNYa8sA5/kZZWoVH7y1LafUL13KsQQghRpzjL0GrzUltbxDIyMmzry5cv1/Pnz9daa11QUKBffPFFvXfvXrv6R44c0dOmTSv1nL/5zW/0iRMnqhSXs+t8+eWXetiwYXrz5s16zJgxOj8/X+u8PK2TkrSOjTVayY4d0/rKFa0tlirFUB7Vca/uUBu+e0IIIWovSmkRq6mR9e8Iq1atYtu2bXh6evKrX/2KlStXAs7f8uvbty/h4eFYLBaHY3zl5uYyYcIEunbtWqW4nF3HWad52rc3OvFfvw6XLxvDXiQlGSP2t2ljDJFRzarrXoUQQoi6ROlqfPRUU/r376+jo+2nrUxISCjXwKGi0LFjx5g0aRI+Pj58++23jitpDRkZRkKWllY4CXnbttCgQc0GXEvJd08IIURplFJHtNb9He2TPmJ3qOTkZKZOncqOHTto0qQJe/bscVxRKWjWDLp0MaZRatXKGP7i2DFj5P6bN2s2cCGEEKIekUTsDlRWp3mnGjY0xiPr2dMYvT89HRISXNKxXwghhLgTSB+xO1CjRo3sHkWGhYU5fzTpiJeXMZ9l+/ZG69iVK3DypJGotW1rtJqZJMcXQgghyiKJmKg8s9loGfP1hWvXjH5k584ZHfvbtjX6kpUy0bgQQghxp5NETFSdtQO/j4/xiPLSJbhwAZKTjbcsfX3B09PdUQohhBC1jiRiovooBS1aGEtmppGQJScbLWXypqUQQghRgiRiwjWaNIGgIMjKMhKyq1eNpVUr43Fmw4bujlAIIYRwO0nEhGs1bAidO8NddxktYykpkJpqtJq1bw+NG7s7QiGEEMJtJBETNaNBA+jY0Ui+rlwxlhs3jDHK2rc3WtCUcneUQgghRI2SREzULE9P8PMzHk9evWq0kp04YSRi7dpB8+aSkAkhhLhjSCIm3KPo0BcpKUY/slOnoFEjo7xlS0nIhBBC1Hsy6uYdYMaMGfj6+tKjRw93h1KSyWQkYz16GKP2FxTAmTNw/LiRoMlo/UIIIeoxScTuAI899pjzuSRrC+tYZN27Q2Cg0Rp27hzExRmPMAsK3B2hEEIIUe0kEbsDhIWF0apVK3eHUT5KGUNchIQYw1+YzXD+vJGQXbkiCZkQQoh6RfqIiVojISGBNWvWkJKSwn333cfs2bONzvvp6ZCczJlvvmHpe++RlpfHJzt22KZPev/997l06RInT54kPT2dmTNnMnLkSDffjRBCCFE2aRFzo6ysLIYNG4bFYnG4Pzc3l7CwMPLz82ssBmf9yfbs2UO3bt0ICgpi2bJlLoklODiY9evX89FHH3Hw4EHj/ocNI79xY+jWjcB772XDsmXGILHHjhkd/C0WoqOj+eMf/8g777zD+vXr+fDDD10SnxBCCFHdJBFzo40bNzJx4kTMTibG9vLy4r777nNpYlE8Bkf9ySwWC3PmzGH37t3Ex8ezdetW4uPjXRJPZGQkY8eOZcyYMfb3r5Qx5li3btC0qfF2ZWIied9/j0dODur2I8slS5YwZ84cl8QmhBBCVDdJxKpZQkICYWFh9OrVizfeeIOgoCCndbds2cL48eNt2+Hh4ezduxeABQsW8MwzzzBhwgS2bNnisniLx+CoP9mhQ4cICgoiMDAQLy8vpkyZwo4dOyp9TUf3aTVu3Dh2795tu2eH9+/hAV27wj33cCA+niF3340+epR5c+YweuRI+vbtW+nYhBBCiJokfcSqUX5+PlOnTmXDhg306dOH2bNnOx0yIjc3lzNnzhAQEGArW7x4MYsWLeLKlSvExMQQGRkJwOHDh0scP3ToUDIyMkqUr1ixgoiICLuyhx56iKioKFJSUvD392fx4sXMnDnTYQyOXLx4kQ4dOti2/f39+e6770o9pjTO7jMqKort27eTk5PDmDFjAOjRo4ft/lNTU5k/fz4xMTG89tprvPzyy+z98UfmP/ssa//yF/Z98QVply9zKjaWWS+8YOtDJoQQQtRW9TIRe+45iI2t3nOGhsLq1aXX2b59O71796ZPnz4AhISE4Ovr67BuSkoKLVq0sCsLCwtDa83KlSuJioqyPS708vIiIyODpk2b2uoeOHCg3LFv3bq13DFURUREBJcuXSpRvnTp0hKtbo7uc/jw4QwfPtzuWLPZbLt/Hx8f1q9fb7c/IyODJu3aMfe//ou5L70ESUmQlmb0IWvb1hijTBIyIYQQtVS9TMTc5ejRo4SGhtq24+LiGDVqlMO3ARs2bEh2drbd8ceOHSM5ORkfHx+7pCsnJwdvb2+7uuVtEVNljE7fqVOnMu/Lz8+PCxcu2LYTExPx8/MrUW/fvn1lnguc36czju7fat26dYUbjRtDly5w86aRkF28aEyh1K4dtGkjCZkQQohap14mYmW1XLmKj48PP/30EwCxsbFs3ryZefPmERgYyPr16ykoKOCRRx5h9uzZtGzZEovFQnZ2Nt7e3iQnJzN16lR27NjB3Llz2bNnD6NGjSI1NZXWrVvj6elpd63ytojpMkam79Chgy0GZwYMGMDJkyc5e/Ysfn5+bNu2jQ8++KBc1y/O2X064+z+S2VNyDIzjYQsMdF4w1ISMiGEELWMdNavRtOnTyc6OpqePXuyYcMGAgICCAwMBOzfBrQaOXIkX3/9Nbdu3WLixIm8+eabBAcHs3DhQhYvXgzA/v37GTt2bKVjunDhAuHh4YSEhNC9e3fWrFljt98ag9VDDz3E4MGDOXHiBP7+/mzYsAEPDw/WrVvH/fffT3BwMA8++CDdu3evcCyl3aczVbr/Jk1snfqtb1kSF2e0ksnAsEIIIWoDrXWdW/r166eLi4+PL1FW0zIyMmzry5cv1/Pnzy9RZ8yYMbb1I0eO6GnTppV6zt/85jf6xIkTlY4pKSlJHzlyRGutdXp6uu7SpYs+fvx4hWJwp6rev530dK1//FHrw4e1jo3V+vJlrS2WKp+2Nnz3hBBC1F5AtHaS09TLR5PusmrVKrZt24anpye/+tWvWLlyJeD4bUCAvn37Eh4ejsVicTiWWG5uLhMmTKBr166Vjql9+/a0b98egKZNmxIcHMzFixcJCQkpVwzuVB33b6dpU2McsowMo//Yzz8bjyzbtwcfH2O+SyGEEKIGKV1GH6LaqH///jo6OtquLCEhgeDgYDdFVDecO3eOsLAw4uLiaNasmbvDcS+tjamTkpKMzv0NGsBddxnzXJbxgkNx8t0TQghRGqXUEa11f0f7pEXsDpGZmcmkSZNYvXq1JGFgJFvNmxuj9aelGS1kZ89CcjL4+UGLFhVOyIQQQoiKkkTsDpCXl8ekSZOYOnUqEydOdHc4tYtSRtLVvDlcv260kJ0+bXTu9/MzEjVJyIQQQriIJGL1nNaamTNnEhwczPPPP+/ucGovpYzHki1bQmqq0TJ28qTx5qWfn9G/TAghhKhm0ju5njt48CB///vf+eKLLwgNDSU0NJTPP//c3WHVXkpB69bQvTt07Ag5OXDiBPz0k9GXTAghhKhG0iJWzw0ZMqTMQV2FAyaTMT2Sjw9cvWq8XZmQYLSY+flBKQPgCiGEEOUliZgQpTGbjRH5W7c2BoK9fNnoS9a6tfGWpZeXuyMUQghRh0kiJkR5eHgYLWG+vkb/satXjb5kvr5gsbg7OiGEEHWU9BEToiI8PY2+Yz16GI8tL182hr5YskT6kAkhhKgwScSEqIwGDSAgwOjU7+0NCxfC3XfDX/8KeXnujk4IIUQd4dJETCnVQSm1XykVr5Q6rpR61kGd4UqpNKVU7O1lkStjEqJaNWxoPJ48eNCYYHzOHAgOhm3bZGJxIYQQZXJ1i1g+8AetdQjwC2COUirEQb0DWuvQ28ufXByTENXvl7+EL7+EnTuNwWAfeggGDoR//cvdkQkhhKjFXJqIaa2Ttdbf317PABIAP1deszrIcA+iUpSCsWMhJgbee8/o0B8RAaNGQWysu6MTQghRC9VYHzGlVADQB/jOwe7BSqkflFK7lVLdnRz/e6VUtFIq+urVqy6MFK7eukrspViOXznOydSTnLtxjqSMJK7evEpadhpZeVnkF+RLwiYcM5vhkUeMgWBXrIBDh6BvX5g+Hc6fd3d0QgghapEaScSUUk2A/wWe01qnF9v9PdBJa90bWAt85ugcWuu3tdb9tdb927Rp49J4G3o0pKV3Sxp4NCCvII+07DSSMpI4n3aek9dOcvzqcWIvxRJzKYa4K3GcSDnB2etnSUxP5MrNK9zIusHN3JvkWfLqTLI2Y8YMfH196dGjR4l9e/bsoVu3bgQFBbFs2TI3RFdHeXvDH/4AZ87Aiy/Cxx9Dt27G+vXr7o5OCCFELaBcnSgopTyBncA/tNYry1H/HNBfa53irE7//v11dHS0XVlCQgLBwcFVjNa5Al1AniWPPEseuQW55FpyjXXL7fUCY5/G/uepUHiaPfEye+Fpuv3pYNuk3PsC61dffUWTJk145JFHiIuLs5VbLBa6du3K3r178ff3Z8CAAWzdupWQEEdd/e5M5f7u/fwzLFoE779vTDS+YIHRub9BA9cHKYQQwm2UUke01v0d7XPpgK5KKQVsABKcJWFKqXbAZa21VkoNxGilS3VlXJVhUiYaeDSggYfzX5paa/IL8guTtGIJW1Z+Fmk5aRTokm/TeZg8HCZrXqbCdbPJ7LL7CwsL49y5cyXKDx06RFBQEIGBgQBMmTKFHTt2SCJWGR07wqZN8B//AfPmGa1lf/4zvPYa/O53xrRKQggh7iiuHln/V8B04JhSytpb+RWgI4DWej0wGZitlMoHsoApuq48zytGKaP1y9Ps6bSO1hqLtpRoTSuasN3Mu0l+QX6JY03KZJesOWpd8zB5YOS/1ePixYt06NDBtu3v78933znq5ufcmTNnWLp0KWlpaXzyySe28vfff59Lly5x8uRJ0tPTmTlzJiNHjqy22Gut3r1hzx7Yuxf++Ed4+GFYtcroTxYW5u7ohBBC1CCXJmJa66+BUrMCrfU6YJ0r46hNlFJ4KA88TB6QD+PGjOOLL77AbLZv7SooKCAzO5PRI0ez/fPtaJO2S9YycjPIteSWPL+DR6H5uflMmziNz//xOd5e3i5/FJqbm0tERARffPEFHh4eBAYGsmHDBiZPnmxXLzo6mjVr1qCU4vr167zwwgt3RiJmNWIEHDkCmzfD/PkwbBiMHw+vv270JRNCCFHvyVyTbrRx40YmTpxYIgkDMJlMNGvUjJEjRrLv//YxderUEnW01ra+aY5a1qyPQre9u41fjPgFJ2+ctB1b/FGol9mLa1nXKNAFZOVl2R6F+vn5ceHCBdtxiYmJ+PmVPgKJl5cX9913Hx9++KHDuAHy8vLw8ChsvVuyZAlz5swp18+tXjGb4dFH4be/hdWrYdkyY/qkWbPgP//TmFxcCCFEvSWdUqpZQkICYWFh9OrVizfeeIOgoCCndbds2cL48eNt2+Hh4ezduxeABQsW8MwzzzBhwgS2bNni8HilFF5mLxp7NaZlw5b4NvbFv5k/nVt2plvrbvTw7UGfdn04sPMATzz0BF1adaFT807c1fQuWni3wNPkSa4ll+vZ17mYcZHE9ERyLDkcv3qcmEsxxCTH0LBTQ+JPxHPghwOcTTnL5g82M/z+4dzKu1XqW6GlxQ1w4MABhgwZgtaaefPmMXr0aPr27VueH3H91KgRvPIKnDoFTzwBb70FQUHwxhuQne3u6IQQQriItIhVo/z8fKZOncqGDRvo06cPs2fPdjgcBBiP786cOUNAQICtbPHixSxatIgrV64QExNDZGQkAIcPHy5x/NChQ8nIyChRvmLFCiIiImzbeXl5nD1zlnu63FNq7FOmTOHLL78kJSWFcQPG8cIrLzB52mRyLbnMf20+0yZOw2KxMO534/Bs59ovnJ4AACAASURBVEn81XjAeBRq93LB7VY2v7v9OHT4ELmWXNKvp7NgwQJiYmJ47bXXePnll9m7dy/z589n7dq17Nu3j7S0NE6dOsWsWbPK/DnXa76+xnyVTz9tDHPx4ovG9rJl8OCDxqCxQggh6g1JxKrR9u3b6d27N3369AEgJCQEX19fh3VTUlJo0aKFXVlYWBhaa1auXElUVJTtkaWXlxcZGRk0bdrUVvfAgQPlisnRdRzZtm2b031BDwUx66FZtkehRR9/WrdzLbnczL3Jdct12xAeJg8T357+lsZNGvPU4qd49r+excvsxc9pP3P52mVyzbnMeHIGTz71ZK0YwqNWCQkxpkvat894u3LKFOMNy1WrjKmThBBC1Av1MhE7efI5MjOrd0qZJk1C6dJldal1jh49SmhoqG07Li6OUaNGAXDz5k2GDRvGq6++ygMPPEDDhg3JLvbI6dixYyQnJ+Pj42OXdOXk5ODt7W1Xt7wtYkWvU51vU5blZu5NLHkWgnyDwAS5BUbyZu239tR/PsWZ62fsjvE0eZZoWSv+dugdl6xFRMD33xvDXsyfD4MGGW9ZvvaaMRyGEEKIOq1eJmLu4uPjw08//QRAbGwsmzdvZt68eQC8/vrrPPjgg7a6LVu2xGKxkJ2djbe3N8nJyUydOpUdO3Ywd+5c9uzZw6hRo0hNTaV169Z4etoPiVHeFrGi16nJUUFSU1Np07oNfi1KduwvbQiPXEsuOfk5ZORkYNGWEsc6esmg3idrZjPMnGk8mnz9dXjzTdi+HV54wRiPrEkTd0cohBCikuplIlZWy5WrTJ8+nbFjx9KzZ0+GDx9OQEAAgYGB7N27l5CQkBItYCNHjuTrr7/ml7/8JRMnTuTNN98kODiYhQsXMm/ePEaNGsX+/fsZO3ZsleKyXsfaUmaxWOjfvz9+fn7s3LmzSud2prS4iw7h0dCzodNzWAosJZK0oslbZm7mnZWsNW0KS5bA738PL79srG/YYLSOTZ8uA8IKIUQdVC8TMXfx9va2DXb6xhtv8Jvf/AaAqKgobt68SXx8PA0bNmTMmDGYTCbmzJnDqlWriIiI4Ntvv7WdJywszLb9wQcfVHl+x6LXAVizZg3BwcGkpxef9tNeVFQUmzZtYtOmTRW+ZnXEbTaZaWhqSENKT9aKzmJQ0WStxFJkJoOafJRbIR07wpYtRof+556Dxx6DdeuM4S9+9St3RyeEEKICJBGrRqtWrWLbtm14enryq1/9ipUrjVmdli5dCsCmTZto3bo1ptstF3379iU8PByLxeJwLLHc3FwmTJhA165dqxRX0eskJyeza9cu5s+fb4uvssLDw3nllVcYMWIECxYsIC0tjbVr11Zb3OVhNpkxm8x44+20jqNkrTyPQZ21qlmX6p7FoMIGD4Zvv4UPPoCXXoIhQ4ypkl5/HTp1cl9cQgghys3lk367gjsm/a4vJk+ezMsvv0xGRgYrVqwo9dFkWS1iX331FYsWLeKJJ57ggw8+IDIy0mFCWRdYH4PaLQW55OYXrhf/f8U6dEfqz6m8l/QeHZt1pEPzDnRs3pGOzTvSoVkHGns1rpkbuHnTGHNs+XLQunDoi8Y1dH0hhBBOuW3Sb1G77Ny5E19fX/r160dUVJTTeoMGDSInJ4fMzEyuXbtmexP09ddf5/7777fVczbcRl1kewzqpM9a8Qndcyw5toQthRT2nt5LUkaSbegOK5+GPnRq0clIzpp1tCVp1rK2jdtWT6ta48bw6qswY4bRgf9Pf4KNG43EbMoUGX9MCCFqKUnE7iAHDx4kMjKSzz//nOzsbNLT05k2bRqbN2+2q2ft51ZWi5iz4Tbqo9ImdM+9nEvi84nkWfJIykjifNp5LqRd4Oe0n40l/WdOpp7kX2f+RUau/ZAjDcwN6NC8A52ad6JT8062JK1T804EtAjAv5l/qZPIl9CxI2zdCnPmwLPPGkNdrFtnjEHWr19VfwxCCCGqmSRiDty4ASkphdvWxoSin47KKvpZ1boVrf/qq6/x6quvoRR8+WUUq1evYNOmzeTnOz6mNM6G27iTeZo9jSSqhfP+WTeyb/Bz2s+cv3Ge82nnjfW085y/cZ7PT33OpcxLdvVNysRdTe+yJWa2zxbGZ8fmHfH2cNA/bsgQOHzYGH/s5ZdhwABjCIylS43R+4UQogK01hQUFGCxWLBYLOTn59vWHS3F95e17ai8rPXinxVZL3rsiy++yJAhQ9z2s5VEzIG0tBTS0y8DysFiKlGmtaN6zssLFyic7rOseqVtFy8r25kzkJ4OsaWMe3viBKSmGuOJQmGylpV1i1mzJjJnzpvk5QXz8MPGcBv+/qNKJHSlrZe1XdnjHG2Xt05Fjq2MFt4taOHdgl5tezncn5Ofw4X0C7ZE7dyNc7ZE7eCFg2yL21bixYL2TdoT0CKgxNK5RWc6PjKVBpMmwX/9F6xZAx9/bEwm/vTT4FmBljYhapmCggLbYrFYSv0sT52in8XXK1u3rH3l2S7PUpljylqKJ0oFBQXu/k9eJg8PD8xms22xbhct9/DwKFF+69Ytt8YtnfUdSEk5R0pKClpjWwC77bLK3Klka5hyUK7sEgprmaPjCuuUtq2KJSjKaT3H60W3VZGfYXmOLWvd+f6qXkcpSE4+z6uvHkQphdlsQikTJpMJs1lhMhllJpN1AZPJjNmsbu834eFhul1P2Y4zmwvLCz/NKFVAjs4iKz+TTEsamXnppOelk55/nRs510nLTcVCHpjy0aYCtLLQrGETWjdtia+5EW1PnafdmUTaN2yJ3+RptBt8Lw0aeODhofDwULaYjf9mJRdrudbGf1fj5+foDwuD9d+Xov/OFC0rvt/ZvqJL8TJHdSq7FBQUVLq8vOvWbUefpe0rrU7x8vJuO1rKU8dRElQd+xwlTs721xfWfxusiULR9fIulTnGw8PD6XHFE5rK1HGWFJW27uwcjs5VfJ+plo+jKJ31K6hlyzY0bWp93FM0qyqeYZXcLvx9Y/3HuugvCefl9vsdb0PRckd1itazXy8aW8l9zrZLHuMo2XR+jpJ1iq/XBzk5N/jqqxfcHYZTl4GTJUovwoGXaj4YUe1MJmvyDFA0mTaSZeMPBGVbtyba1rLC44tum+zKi27bl1n/iDAZ/Sg9rX+IKLt9JpPH7eNMtj9YjCTA+LQvM9vOb/9HTOFi/EIuXC/6aSzm29c2314vei4zHh7m238QmVHKdHvbhNlsn5xY61jLi/7SL6zrYavr4WGta61f9FjPYnU9MJnMKGUu8YdPadtKmUrZV4XmeuE2kog5YDY3xmyW1/5dzVlrSEXLCreL7tclElBrElwkAlsd+/PaH2PsK1wvud/C5s0rAWuLgvHXemFLiLVM22Kz/kVfuM+6bv203kPhuQoKoKBA25b8fKO+xaJt+y0W+3pa69v7jcVSUEB2Xg5ZObfITrlKVkYaOWbIbeBFrgksBQWACaUVCoVJeeClPPE0eWFWnniYPDDjgVmZMClzkT8AuH29wp+j9frWn11BgbFPKX07adC3kwVHZfblSt2eSN5Usp7JpG3bZrPGZDJmhTLWrdvats9k0re3se03yrCrY19egMlkxFH0OLO5wO66Rny62Hn07WMLz1EYf4HtHq33AYX1jXX7nxMU2N2z9Rjrd6zo96ywvPg+67aoCK0hP9/dUZSH48StMGkzFUnayqpb2rapAnUrnlhWz3bZ99Shwx9o3tx9g2FLIibcpvCRad3+K+7y5WtMnfof7g6jchITjfHGtm6FTp3IeGMpZ4f24MyNs5y5fobT105z5obxee7GOfIK8myHepm96NyiM0Gtgri75d0EtQqyLQEtApy+7WmxQF4e5OYaS14e5OQYn0XLrfuKfhZfz801jnVWnpcHWVmFdaxl1u2ixxc/NieneltvlYIGDRwv3t7l22ddd/RZVlnR7aIjzRRP+q0JW/GkrWhyV/a+0pLC4ucwzuP4/FW7Xunbzq5ZtWtU78+xorGXt27RRLyy53V1jOXbLv5HbsW+d8ZisWTiTpKICXEn8/c3RuafNQueeYamD06j14gR9Fq7FgZPsKtqKbCQmJ7I6eunOX3tNKevn+bUtVOcunaKL89/SWZu4T9mZmUmoEUAQa2C6NKqC118utg+A1oE4O3tgbfzyRBqBaO10T6JK/5ZfL20svIumZn229nZ9uvV0T3Kw6NocqZuLya8vaFhQ/vErXiZdb20sqKf1sVat47/3SVEtZNETAgBYWFw5Ai89RYsXAg9e8Lzz8OCBdCkCWAMemsdnuPezvfaHa615srNK7bE7OS1k7bPby58Yzd+mofJg7tb3k1Xn662pZtPN7r6dKVdk3a1poVUKSNh8fCoXRMU5OeXTM6s29bWv6IJXPGy7OzCMut28bLMTGMIn6wsx3WroniCVtrSqJH9Z/GystY95DecqAPkrUkhqqjeffcuXzbGHnv3XfDzgxUrjDksK5kgWZO0k9dOcjL1JD+l/sTJa4Wf2fmFv9mbNWhGN59udGvdjW4+3bin9T0Etw4mqFUQDTwaVNcdiiooKCiZ1FmXomXF9zkrc7TculXyuMrw8ipMzEpbGjcu/2fRpWFDaeET5VPaW5OSiAlRRfX2u/ftt8Z4Y99/D/fea4zQX833WaALSExP5ETKCU6knrB9/pjyIxfSL9jqmZSJwJaBBLcOJrh1MCFtQghpE8I9re+haYP6PauDMJK/7Gz7BO3WrcLtop9Fl+JlN28aZTdvOi6raMKnlOMErUmTkutFP4uvF18aN4ZaPhqDqCAZvkIIUXGDB8OhQ/D22/DKK9Crl/G4cuFC2+PKqjIpk23+zRF3j7DbdzP3Jj+l/kRCSgI/pvxIQkoCCVcT2HNqj91LAx2bdySkTQjd23Snh28PurfpTkibkJqbcF24nMlU2HrlSgUFhUmZNVmzrjvatpZlZpYsT0kxPq37MjMr9vJHo0b2yVnTpmV/Fl+aNStcl8e0tZe0iAlRRXfEd+/qVXjpJWMicX9/WLUKJk1yy3OZ/IJ8Tl87TfzVeBJSEjh+9bixfjWBHEsOAApF55ad6enbk15te9k+g1oFYTbV3cnpRd2ldWH/O2tiVnw9MxMyMhyXFV/PyDCW8g6n0bChfXLWrFnJdUdL8+aFn82bG2/dyuPYipNHk8JlEhISWLNmDSkpKdx3333Mnj27Rq772WefsWvXLtLT05k5cyYjR46skes6ckd99779Fp56ypgb6/77jceVQUHujgowErQz188QdyWO41eOc+zKMY5dOcZPqT9RcHtIAW8Pb3r69qR3296Etguld7ve9Grbi2YNmrk5eiEqTmujv541KSttSU8vuZ6ebr/k5JR9TU/PwqTM0dKiRclP62KtcyfOriaJmHC5goICHnnkETZv3lzpc1gsFvr374+fnx87d+4s1zHXr1/nhRdeYMOGDZW65owZM9i5cye+vr7ExcXZyvfs2cOzzz6LxWLh8ccf56WXnI9Cf8d99/LzjbcrFyww/uV+6SWYN8/4k7sWysrLIiElgWOXj/HD5R/44fIPxF6K5VrWNVudLq260O+ufvRt15e+7fvSp30fWjVs5caohah51qSuaHKWllbys7QlPb3sR7CNG0PLlkZyZv20rhddWrUqud6gjr6zI4mYcKnIyEjeeustpk+fzsMPP+ywTlRUFJs2bWLTpk1Oz7Ny5Uqio6NJT08vdyL2hz/8galTp9K3b9/KhM5XX31FkyZNeOSRR2yJmMVioWvXruzduxd/f38GDBjA1q1bCQkJcXiOO/a7l5wMf/wjbNkCgYFG69jo0e6Oqly01iSmJ/LD5R+ISY4h5lIM3yd/z/m087Y6d7e8mwF+Axh410AG+A2gb/u+NPJ0cSclIeq4ggIjmbtxw1isCZp1+/p1Y/v6dfsy65KeXvr5GzUykrKii49P4WfR9datC7fd3UdOOuuLahEeHs4rr7zCiBEjWLBgAWlpaaxdu5Zx48Yxbtw4xo4d6zQRK0tiYiK7du1i/vz5rFy5sszr/vnPf+all15i9OjRlU7CAMLCwjh37pxd2aFDhwgKCiIwMBCAKVOmsGPHDqeJ2B2rfXvYvBlmzjQeV44ZY/QbW73a6EdWiyml6NC8Ax2ad+CBrg/YylNvpRJzKYbopGgOJx3m4M8H2Ra3DTAGqe3VtheD/QczuMNgBvsPJrBlYK0Z90yI2sBkKnwE2alTxY/Pzy9M1KzLtWuF66mphWXXrsGPPxpl164Zs2Y407y5kZg5WiZMgHvuqfw9V5UkYqLcFi9ezKJFi7hy5QoxMTFERkYSFRXF9u3bycnJYcyYMZU+93PPPcfy5cvJyMgosc/RddeuXcu+fftIS0vj1KlTzJo1qyq3ZufixYt06NDBtu3v7893331Xbeevd8LD4Ycf4M034U9/gn/8w/h85hn3/xlaQT6NfIgIjCAiMMJWdinzEocvHubQxUN8m/gt7x99n79G/xUA38a+DOk4hLCOYQwLGEZP357yMoAQVeDhUdiyVRFaGy85WJOylBRjPTW1cD0lxViSkuDoUeMdpOxs6NpVEjFRR4SFhaG1ZuXKlURFRWE2mxk+fDjDhw93esygQYPIyckhMzOTa9euERoaCsDrr7/O/fffD2Dro9WvXz+ioqLKdd25c+cyd+5cp9eNiIjg0qVLJcqXLl3K+PHjK3bjomxeXsYgsFOmGGOPPf88vPcerF8Pv/iFu6OrknZN2vHrbr/m191+DRhTPR2/epxvL3zLwQsHOfDzAbYnbAeghXcLhnQcQnhAOCPvHkn3Nt2lxUyIGqBU4VAfFWmJu3XLfu5Vd5BEzI2ysrIYNWoUX3zxBWYH34Tc3FwiIiL44osv8KgFLQvHjh0jOTkZHx8fmjYt3yCa1pak0vqIHTx4kMjISD7//HOys7NJT09n2rRpto7/lbnuvn37yndTDvj5+XHhQuFgoomJifj5+VX6fHeUzp1h50749FN49ln45S/hySfhv//b6GlbD5hNxiPKXm178WT/JwH4Oe1nvjr/FV+d/4ovz3/Jzp+MPo7tm7RnxN0jGBE4gpF3j8S3sa87QxdCFOPqsenKQ8budaONGzcyceJEh0kYgJeXF/fddx8ffvhhDUdWUnJyMlOnTmXHjh00adKEPXv2VNu5X3vtNRITEzl37hzbtm3j3nvvtSVhrryuMwMGDODkyZOcPXuW3Nxctm3bxrhx41x+3XpDKZg4ERIS4D/+A955x2j3/+CDio1oWYd0bN6Rab2m8fav3+bE0yf4+bmf2TBuA2Gdwtj10y6mfzqddivaMfTdoaz4ZgWnrp1yd8hCiNpCa13nln79+uni4uPjS5S5Q3x8vB46dKju2bOnXr58ub777rud1h08eLA+e/asbXv48OH6n//8p9Za6/nz5+unn35ax8bG6tGjR1cpJkfnrYibN2/qX/ziF7ZzfPnll/oXv/hFhc6xf/9+/eijj5ar3tixY6vtumWZMmWKbteunfbw8NB+fn76b3/7m9Za6127dukuXbrowMBAvWTJklLPUVu+e7VWTIzWAwdqDVqPGKH1yZPujqhGWQosOvpitH51/6s6dH2o5lU0r6JD/hKiF36xUJ9KPeXuEIUQLgZEayc5jQxfUY3y8/MZOHAgGzZsoE+fPsyePZvk5GQ+++yzEnVzc3Pp2LGjXT+mr776ikWLFvHEE0/wwQcfEBkZCUC7du24evWq3fFDhw512LF9xYoVRERE2JU5Oq+zVjhRcbXhu1frWSxGf7FXXjEGK1qwAF580ehbdoc5d+MckSci+fTHT/ny3JdoNMM6DeP/hf4/JodMlqmZhKiH7rhxxJ577jliY2Or9ZqhoaGsXr261DofffQRu3fv5t133wVg7dq1pKSksHjx4hJ1k5KSuPfee/nxxx/tyocNG0ZmZiZRUVG2/lB+fn78+OOP5e4f5Yij84J0aq8OkohVQFKS8bjyo4+MCcTffhuGDHF3VG6TmJ7I+z+8z8aYjZy+fpomXk2Y2nMqC8IW4N+sdg8BIoQoPxlHrIYcPXrU9lYgQFxcHKNGjSIqKoqFCxfSvXt3pkyZwvDhw2nYsCHZ2dl2xzvrlJ6Tk4O3t7dd3Yq0iJXW2b28ndrlzS97dfEPmFrhrrvgww/h0UeNsceGDoXHH4fly+tNZ/6K8G/mzytDX+HlIS/z9c9fszF2I+/Gvst7P7zHs4Oe5aUhL9HCu4W7wxRCuJKzZ5a1eamtfcRWrlypn3rqKa211jExMbpRo0b69OnTOioqSo8aNUo/+uij+mSR/jH+/v46KytLa611UlKS7tmzp46Pj9cRERF69+7dWmutU1JSdLdu3Sodk7PziupTG757dVJmptYvvKC12ay1r6/WW7dqXVDg7qjc7uz1s3ra9mmaV9GtXm+lV36zUmfnZbs7LCFEFVBKHzG3J1WVWWprInb16lU9cOBA3aNHD/3000/rkJAQrbXWFotFa631pUuX9MMPP2yrP2PGDL13795SO6V//PHH+vnnn69UPDXR2b06ffrpp/rxxx/XDz74oP7HP/7h7nDKrTZ89+q0mBit+/c3/jkaPVrrIi+w3Mm+T/pej3h/hOZVdMDqAH38ynF3hySEqCRJxGpIRkaGbX358uV6/vz5dvtzcnL0pEmTbNtHjhzR06ZNK/Wcv/nNb/SJEyeqN9AakJWVpQcMGKB79eqlQ0JC9KJFi8p97LVr1/SMGTMqfe2VK1fqkJAQ3b17dz1lyhRbq6Or1IbvXp2Xn6/16tVaN26sdaNGWq9cqXVenrujqhX+eeqfetzWcTorz7XfYyGE65SWiLl8HDGl1Cil1Aml1Cml1EsO9jdQSn14e/93SqkAV8fkKqtWraJ79+6EhoZy7tw5Fi5cCMD27dt58sknmT59Ok8//bStft++fQkPD8disTg8X25uLhMmTKBr1641En91atCgAV988QU//PADsbGx7Nmzh3//+9/lOnbJkiXMmTPH4b6oqCgee+wxp8devHiRP//5z0RHRxMXF4fFYmHbtm2VuQVRk8xmYwDY+HhjyqTnnzdG5I+JcXdkbjfi7hHsmLIDbw/vsisLIeoclyZiSikz8BdgNBACPKSUKj5z8kzgutY6CFgFvO7KmFxp4cKFHD9+nNjYWP7yl7/QoEEDACZOnMj//M//8OGHH5aYDmjGjBmlDuj6yCOPuDpsl1BK0aRJEwDy8vLIy8uzdfgPDw9n7969ACxYsIBnnnkGMFpn582bV+WJvPPz88nKyiI/P59bt25x1113lXpdUYt07Aj/939Gh/7ERBgwAF56CbKy3B2ZEEK4hKtbxAYCp7TWZ7TWucA2oPiYCOOB926vfwLcp+QVvXrBYrEQGhqKr68vI0aMYNCgQYAxiffSpUvZsmULMTExtmFBrBN5f/LJJ6xfv75S1/Tz8+OFF16gY8eOtG/fnubNmzNy5MhSrytqGaXgwQeNkfkfewxefx169oT9+90dmRBCVDtXJ2J+wIUi24m3yxzW0VrnA2lAiXnXlVK/V0pFK6Wiiw9uKmons9lMbGwsiYmJHDp0iLi4OMB+Eu9t27bZWgTnzp3LkSNHWL9+PbNmzbI716BBgwgNDeXxxx8nMjKS0NBQQkND+cc//mFX7/r16+zYsYOzZ8+SlJTEzZs3bdMlObuuqKVatoS//Q3+9S9j+957jaEurl93b1xCCFGN6sxck1rrt7XW/bXW/du0aePucEQFtGjRgvDwcNs8kdZxzby8vCo0eXhsbCx/+9vfGDduHLGxscTGxnL//ffb1du3bx+dO3emTZs2eHp6MnHiRL755ptKX1fUAvfeC0ePGiPxb9oEISHwv//r7qiEEKJauDoRuwh0KLLtf7vMYR2llAfQHEh1cVzCxa5evcqNGzcAyMrKYu/evdxzzz0un8S7Y8eO/Pvf/+bWrVtorfnXv/5FcHCwWyYPF9WoUSPjEeXhw9C+PUyeDJMmQXKyuyMTQogqcXUidhjoopTqrJTyAqYAkcXqRAKP3l6fDHxx+1VPUYclJycTHh5Or169GDBgACNGjODee+9l4sSJvPnmmwQHB7Nw4UKH0z9VxaBBg5g8eTJ9+/alZ8+eFBQU8Mgjj7j8uqKG9OkD330Hy5bB558brWMbN4L8kyGEqKNcPtekUmoMsBowAxu11kuVUn/CGFMjUinlDfwd6ANcA6Zorc+Uds7aOum3uDPJd89NfvoJnngCvvoK7rsP3nkHOnd2d1RCCFFCaXNNuryPmNb6c611V6313VrrpbfLFmmtI2+vZ2utf6u1DtJaDywrCRNCCAC6djXepFy/Hg4dgh49YM0acDIunxBC1EZ1prO+EEKUYDLBk0/C8eMwfDg89xyEhcGPP7o7MiGEKBdJxIQQdV+HDrBzJ7z/vpGEhYbCa69Bfr67IxNCiFLVq0RM+viLmibfuVpEKZg+3Zgm6de/hldeMaZJOnbM3ZEJIYRT9SYR8/b2JjU1VX4xihqjtSY1NRVvb5kDsFZp2xY+/hg++QQuXIB+/eBPf4LcXHdHJoQQJbj8rUlXcPTWZF5eHomJiWRnZ7spKnEn8vb2xt/fH09PT3eHIhxJSTEmE//gA+jVC959F6owj6kQQlRGaW9NetR0MK7i6elJZ3l1XQhRVOvWsGUL/O53MGsWDBwIL78MCxeCl5e7oxNCiPrzaFIIIZwaN854s3LqVFiyBPr3h++/d3dUQgghiZgQ4g7RsiW89x783/8ZjywHDjRaxqTvmBDCjSQRE0LcWR54wGgdmzZNWseEEG4niZgQ4s7TsiVs2mSMPZaaCoMGwauvSuuYEKLGSSImhLhzjR0LcXHw0EOweLGRkP3wg7ujEkLcQSQRE0Lc2Vq2NEbk/+wzSE6GAQOMR5Z5ee6OTAhxB5BETAghAMaPN/qOTZpkdOL/5S+NUfqFEMKFJBETQggrHx/YLpTCtwAAHqVJREFUutUYmf/sWWPw1zffBIvF3ZEJIeopScSEEKK4yZON1rHRo+GFF2DYMDh1yt1RCSHqIUnEhBDCkbZtYft2o/9YXBz07g1vvQV1cFo4IUTtJYmYEEI4oxRMn24kYkOGwFNPwahRkJjo7siEEPWEJGJCCFEWf3/Yswf++lf4+mvo2dOYw1Jax4QQVSSJmBBClIdSMHu2Mc5YSIgxMv9vf2tMlySEEJUkiZgQQlREUBB89RUsWwaRkdCjB+za5e6ohBB1lCRiQghRUWYzzJsH0dHg62vMX/nkk5CZ6e7IhBB1jCRiQghRWb16weHD8Mc/wjvvQGgofPONu6MSQtQhkogJIURVNGgAy5dDVJQx8OvQoTB/vkwgLoQoF0nEhBCiOoSFGR35H3sM/vu/YfBgSEhwd1RCiFpOEjEhhKguzZrBhg3w6afw88/GFEnr1skwF0IIpyQRE0KI6jZhAhw7BuHh8MwzxiCwSUnujkoIUQtJIiaEEK7Qrp0xrMVbb8GBA8YgsNu3uzsqIUQtI4mYEEK4ilIwaxbExEBgIEyaBDNnQkaGuyMTQtQSkogJIYSrdetmDGsxfz5s2mQMc/Htt+6OSghRC0giJoQQNcHTE5YsKRzmYsgQ+M//hPx8d0cmhHAjScSEEKImDR1qDHMxdSr86U/GsBdnzrg7KiGEm0giJoQQNa15c3j/ffjgA4iPNx5V/v3vMsyFEHcgScSEEMJdHnrIaB0LDYVHHoGHH4YbN9wdlRCiBkkiJoQQ7tSpE+zfb/Qf+/hj6N0bvv7a3VEJIWqIJGJCCOFuZrPxRuU33xid+ocNk478QtwhJBETQojaYuBAY8yx6dONjvzDhsHZs+6OSgjhQpKICSFEbdK0qTHW2AcfQFyc0X9s61Z3RyWEcBFJxIQQojayduTv0cPoxP/YYzIivxD1kCRiQghRWwUEwJdfGv3F/v536NcPjhxxd1RCiGrkskRMKfWGUupHpdRRpdSnSqkWTuqdU0odU0rFKqWiXRWPEELUSR4e8OqrxpuVWVkweDC8+SYUFLg7MiFENXBli9heoIfWuhfwE/ByKXXDtdahWuv+LoxHCCHqrrAw41HlAw/ACy/AmDFw+bK7oxJCVJHLEjGt9T+11tZ3r/8N+LvqWkIIcUdo1Qr+939h/XrjkWXv3rB3r7ujEkJUQU31EZsB7HayTwP/VEodUUr93tkJlFK/V0pFK6Wir1696pIghRCi1lMKnnwSDh8GHx8YORJeegny8twdmRCiEqqUiCml9iml4hws44vUmQ/kA1ucnGaI1rovMBqYo5QKc1RJa/221rq/1rp/mzZtqhK2EELUfT16GMnY738Pr79uTCYuY44JUedUKRHTWkdorXs4WHYAKKUeAx4ApmrteDZbrfXF259XgE+BgVWJSQgh7hiNGsH//A989BH8+KMx5tjHH7s7KiFEBbjyrclRwIvAOK31LSd1GiulmlrXgZFAnKtiEkKIeum3v4XYWAgOhgcfhFmzjDcshRC1niv7iK0DmgJ7bw9NsR5AKXWXUurz23XaAl8rpX4ADgG7tNZ7XBiTEELUTwEBcOAAvPii0Uo2aBAkJLg7KiFEGZSTJ4a1Wv/+/XV0tAw5JoQQDu3ZA488Ajdvwrp1xqj8Srk7KiHuWEqpI86G6JKR9YUQor4ZNcp4VDloEMyYYSRlmZnujkoI4YAkYkIIUR/ddZcxxtjixcYE4v36wdGj7o5KCFGMJGJCCFFfmc2waBH861/GhOEDB8Lbb0Md7JIiRH0liZgQQtR3w4cbjyqHDTMGg334YUhPd3dUQggkERPi/7d371FWV/X/x59vGCHUb8BXyUoUXejPzMrbSCgoiuAFk4nkomSaopRCmaUpulRcmV+1TMukFEwiL5iKSnInxQt4Ac28dqG85CUjK8NQCN2/Pz5jTjrAyHBmn8vzsdYs5pzzmTMv+CyYF5+9P3tLteFDH4JZs+D884u1xnbfvShnkrKyiElSrWjXDsaNgwULinXGevculrpwqFLKxiImSbWmb1/41a+KIcsvf7kYqly+PHcqqSZZxCSpFnXrBjNnwre/XWyRtPvu8Otf504l1RyLmCTVqnbt4Iwz4I47inXGeveGSZMcqpTakEVMkmpdv37FxP2+feH44+Hoo4tV+SWVnEVMklTcVTl7NowfD9dcU6w55l6VUslZxCRJhfbt4ZxzYM4cWLYM9tgDrr02dyqpqlnEJEn/beDA4q7KXXeFI4+EE0+ElStzp5KqkkVMkvReW25ZTOI/9VT40Y+gTx945pncqaSqYxGTJDVvo43goovglltg6VLYbTe4/fbcqaSqYhGTJK3dZz8LDz0EPXrAoYcWS16sXp07lVQVLGKSpHXr2RMWLYLjjoP/+z844AB4+eXcqaSKZxGTJLVMp04wcSJcfTXcd18xVLlwYe5UUkWziEmS3p8vfrEoYp06FftVXnqpq/FL68kiJkl6/3bZBZYsgUGD4OSTYcQINw6X1oNFTJK0frp0Ke6ovOACuPlmV+OX1oNFTJK0/tq1g9NOg3nz4JVXijJ20025U0kVwyImSWq9/v3h4Ydhp51g2DA45RSXuJBawCImSdowuneHu+4qtkS6+GLYf3/4859zp5LKmkVMkrThdOwIl18OP/sZLF4Mu+9e3GEpqVkWMUnShnfkkUUB+8AHoF8/mDDBJS6kZljEJEmlsfPOxRIXAwfCmDHF+mOvv547lVRWLGKSpNLp2hV+8Qs45xyYMgX22guefjp3KqlsWMQkSaXVrh2MHw+3316UsPr6YrkLSRYxSVIbOeSQYqjyox+Fgw6Ciy5y3phqnkVMktR2ttuumMQ/dGixEOyIEfDaa7lTSdlYxCRJbWvTTWHqVPjOd4qtkXr3ht//PncqKQuLmCSp7UUUq+/PnVss+rrHHjBrVu5UUpuziEmS8tl//2Le2LbbFnPIzj/feWOqKRYxSVJe22wDCxfCEUfAmWcW88eWL8+dSmoTFjFJUn4bbwzXXFPsUXnrrc4bU82wiEmSykMEfP3rxRpjL78MvXrB7Nm5U0klZRGTJJWX/v2LeWM9esCgQXDhhc4bU9WyiEmSys/b88aGD4fTT4eRI2HFityppA2uZEUsIsZHxAsR8Ujjx6A1HHdQRPw2IpZGxOmlyiNJqjCbbALXXw8XXAA33AB9+sAzz+ROJW1Qpb4idklKaZfGj5nvfjEi2gOXAwcDHweOiIiPlziTJKlSRBQr8M+c+c4+lQsW5E4lbTC5hyZ7AUtTSn9MKa0CpgINmTNJksrNQQfB4sXQrRsMHAgTJjhvTFWh1EVsbEQ8GhE/iYiuzby+JfCnJo+fb3zuPSJidEQsiYgly5YtK0VWSVI52357uP9+OPBAGDMGvvxlWLUqdyqpVVpVxCJifkQ83sxHA/AjoCewC/AScHFrvldK6cqUUn1Kqb5bt26teStJUqXq3Bluuw3GjYMrryxW5v/LX3KnktZbXWu+OKU0oCXHRcRE4PZmXnoB2KrJ4+6Nz0mS1Lz27YutkHbeGY45ppg3dtttsOuuuZNJ71sp75r8SJOHQ4DHmzlsMbB9RGwbER2Aw4HppcokSaoiI0bAvfcWn/ftCzfemDePtB5KOUfsooh4LCIeBfYDTgaIiI9GxEyAlNJqYCwwB3gK+HlK6YkSZpIkVZPddism8e+yS7Hm2DnnwFtv5U4ltVikCrzrpL6+Pi1ZsiR3DElSuVi5Ek44Aa6+GoYMgSlTYNNNc6eSAIiIh1JK9c29lnv5CkmSWq9jR7jqKrjkkmK+2F57ufirKoJFTJJUHSLga1+DWbPguedgjz3emUMmlSmLmCSpuhxwADzwAHTtWmwgftVVuRNJa2QRkyRVnx12KMrYvvvCccfB178Oq1fnTiW9h0VMklSdunYt9qj86leLuWOHHgqvvpo7lfRfLGKSpOpVVwff/z5ccQXMnw977gl/+EPuVNJ/WMQkSdVv9GiYOxf+/Gfo1Qvuuit3IgmwiEmSasV++xXzxrp1gwEDnMSvsmARkyTVju23h/vvL+6mfHsS/5tv5k6lGmYRkyTVli5dYMYM+MpXikn8DQ2wfHnuVKpRFjFJUu2pq4Mf/AAuvxxmz4Y+feDZZ3OnUg2yiEmSateJJ76zEn+vXsWwpdSGLGKSpNo2cCDcd1+xSfi++8LUqbkTqYZYxCRJ2nHH4o7KXr3giCPg3HMhpdypVAMsYpIkAWy+OcybB0cfDePHw5FHwhtv5E6lKleXO4AkSWWjY0e4+upir8ozzoBnnoFbby3WHpNKwCtikiQ1FQHjxsGNN8LDD8OnPw1PPpk7laqURUySpOYMHVpshbRiBey1V7FXpbSBWcQkSVqTXr3gwQdh663h4INh0qTciVRlLGKSJK3N1lvDvfcW+1Mefzycdhq89VbuVKoSFjFJktblgx+EX/wCTjgBLroIhg8vhiylVvKuSUmSWqKurtgSafvt4RvfgD/9CaZPhy22yJ1MFcwrYpIktVQEnHwy3HILPP64d1Sq1SxikiS9Xw0NcPfdsHJlcUflHXfkTqQKZRGTJGl97L57sUl49+5w4IEweXLuRKpAFjFJktZXjx6wcGGxWfgxx8BZZ7lHpd4Xi5gkSa3RuTPMnAmjRsF558EXvlAMWUot4F2TkiS11kYbwcSJ0LNnsUfl888XE/q7ds2dTGXOK2KSJG0Ib+9Ree21cN99xST+p5/OnUplziImSdKGNHIkzJsHL78MvXvD4sW5E6mMWcQkSdrQ9tkHFi2CjTcuJvJPn547kcqURUySpFL42MeK5S122gmGDClW5ZfexSImSVKpbLEF3HknHHIIjB3rhuF6D4uYJEmltMkmMG3aOxuGf/7zLm+h/3D5CkmSSu3tDcN79IDTT4cXX4Rbb3V5C3lFTJKkNhFRDE2+vbxFnz7w7LO5Uykzi5gkSW1p5EiYO7e4Kta7NzzySO5EysgiJklSW9t332KPyro62HvvYt0x1SSLmCRJOey0U7G8xbbbwqBBMGVK7kTKoGST9SPiBmCHxoddgH+klHZp5rhngOXAm8DqlFJ9qTJJklRWttwS7rkHPvc5OProYo/KceOK+WSqCSUrYimlEW9/HhEXA6+u5fD9Ukp/LVUWSZLKVufOMGsWHHssnHlmUcYuuwzat8+dTG2g5MtXREQAw4H+pf5ekiRVpA4diqHJ7t3hwgvhpZfguuugU6fcyVRibTFHbG/g5ZTS79fwegLmRsRDETF6TW8SEaMjYklELFm2bFlJgkqSlE27dnDBBfCDH8Btt8GAAfC3v+VOpRJrVRGLiPkR8XgzHw1NDjsCuH4tb9M3pbQbcDAwJiL2ae6glNKVKaX6lFJ9t27dWhNbkqTy9ZWvwM9/DkuWuNZYDWjV0GRKacDaXo+IOuBzwO5reY8XGn/9S0TcAvQC7m5NLkmSKtrQodCtGzQ0wJ57wuzZ8KlP5U6lEij10OQA4DcppeebezEiNomI/3n7c+AA4PESZ5Ikqfz16wf33ltM2t97b1iwIHcilUCpi9jhvGtYMiI+GhEzGx9uAdwbEb8GHgRmpJRmlziTJEmV4ROfgEWLikn8Bx4IN96YO5E2sJLeNZlS+mIzz70IDGr8/I/AzqXMIElSRdtqq2KtscGDYcQIePllGDs2dyptIK6sL0lSufvf/y22QRo8uJjMf+aZkFLuVNoALGKSJFWCTp3gpptg9Gg4/3wYNQpWr86dSq1U8gVdJUnSBlJXBz/+MXzkI3DuubBsGdxwA2y8ce5kWk9eEZMkqZJEwPjxMGECzJgBBxzgwq8VzCImSVIlOuGEYuHXxYthn32KPSpVcSxikiRVqqFDi8Ven3sO9toLfvOb3In0PlnEJEmqZPvtB3fdBatWQd++8OCDuRPpfbCISZJU6XbdFRYuhM6doX9/mDs3dyK1kEVMkqRq0LNnUca22w4+8xm4/vp1f42ys4hJklQtPvzhYphyzz3h85+Hyy7LnUjrYBGTJKmadO4Mc+ZAQwN89atw9tmuwl/GLGKSJFWbD3yg2CB81Cj41rdgzBh4883cqdQMV9aXJKka1dXBxImw+eZw4YXFoq9TpkCHDrmTqQmLmCRJ1SoCLrgANtsMvvlN+PvfYdo02GST3MnUyKFJSZKq3amnwlVXwfz5sP/+8MoruROpkUVMkqRacOyxcNNN8KtfQb9+8OKLuRMJi5gkSbVjyJBiS6Rnn4U+fWDp0tyJap5FTJKkWrLffnDHHbB8ebEl0qOP5k5U0yxikiTVmj32gHvuKe6s7NcPFi3KnahmWcQkSapFO+5YbInUrRsMGFAMWarNWcQkSapVPXoUV8Z22AEGDy4WgVWbsohJklTLttgC7rwTevWCww8vlrlQm7GISZJU67p0gblzYeBAOO44uPji3IlqhkVMkiTBxhvD9OkwbBiccgqcdZabhbcBtziSJEmFDh3g+uvhgx+E886Df/wDvv99aOd1m1KxiEmSpHe0b19sFt6lSzFE+c9/FvPG6qwMpeCfqiRJ+m8R8J3vQOfOcPbZ8NprcN110LFj7mRVx2uNkiTpvSKKeWKXXgrTpkFDA6xYkTtV1bGISZKkNTvppGJoct48OPBAePXV3ImqikVMkiSt3bHHwtSp8MAD0L8//PWvuRNVDYuYJElat2HD4Lbb4Mkni/0pX3opd6KqYBGTJEktc/DBMGsWPPcc7L03PPts7kQVzyImSZJabt99Yf58eOWVooz97ne5E1U0i5gkSXp/Pv1pWLAA3ngD9tkHHnssd6KKZRGTJEnv3847w913Fwu99usHixfnTlSRLGKSJGn9fOxjcM89xSr8AwbAwoW5E1Uci5gkSVp/225bXBn78IfhgAPgl7/MnaiiWMQkSVLrdO9elLGePeGQQ2DGjNyJKoZFTJIktd4WW8Cdd8InPwlDhsDNN+dOVBFaXcQiYlhEPBERb0VE/bteGxcRSyPitxFx4Bq+ftuIeKDxuBsiokNrM0mSpAw226xY2qJXLxg+HK65Jneisrchrog9DnwOuLvpkxHxceBwYCfgIGBCRLRv5usvBC5JKW0H/B0YtQEySZKkHDp3hjlzivXGjjoKJk3KnaistbqIpZSeSin9tpmXGoCpKaWVKaWngaVAr6YHREQA/YGbGp/6KfDZ1maSJEkZbbIJ3H57sUn48cfD5ZfnTlS2SjlHbEvgT00eP9/4XFObAf9IKa1eyzEARMToiFgSEUuWLVu2wcNKkqQNqFMnuPVWaGiAsWPhu9/NnagstaiIRcT8iHi8mY+GUgd8W0rpypRSfUqpvlu3bm31bSVJ0vrq2BFuvLGYL3bqqXDeebkTlZ26lhyUUhqwHu/9ArBVk8fdG59r6hWgS0TUNV4Va+4YSZJUqTbaCK69tihlZ50Fr79eFLKI3MnKQimHJqcDh0dEx4jYFtgeeLDpASmlBNwJDG186mjgthJmkiRJba2uDiZPhuOOg/PPL66OpZQ7VVnYEMtXDImI54E9gRkRMQcgpfQE8HPgSWA2MCal9Gbj18yMiI82vsVpwNcjYinFnLGrWptJkiSVmXbt4Ior4MQT4eKL4aSTLGO0cGhybVJKtwC3rOG1bwPfbub5QU0+/yPvuptSkiRVoXbt4Ic/LIYpL7kEVq2CCROK52tUq4uYJElSi0UUV8Q6doQLLijK2MSJ0L65pUarn0VMkiS1rYhirljHjnDuuUUZmzy5mEtWY2rvdyxJkvKLgPHjoUMHOPNMePNN+NnPaq6M1dbvVpIklZczziiWuPjmN+Hf/4brry8e14janR0nSZLKw6mnwve+BzffXCz+umpV7kRtxiImSZLyO/lkuOyyYlukww6DlStzJ2oTFjFJklQexo6FH/+42DD8s5+FN97InajkLGKSJKl8fOlLMGkSzJlTbBj++uu5E5WURUySJJWXUaPgqqtg3jwYPBhWrMidqGQsYpIkqfwccwxcfTX88pdw6KHwr3/lTlQSFjFJklSejj4apkyBBQvgM5+pyjJmEZMkSeXryCOLhV7vvhsGDYLXXsudaIOyiEmSpPI2ciRcdx0sXFh1ZcwiJkmSyt+IEUUZW7QIDj4Yli/PnWiDsIhJkqTKMHx4sQXSffdVTRmziEmSpMoxbFhRxu6/vyrKmEVMkiRVlmHDYOrUoowddFBFlzGLmCRJqjxDh8INN8ADD1R0GbOISZKkynTYYe+UsQodprSISZKkynXYYe8MUw4aVHFlzCImSZIq29Ch79xNWWHrjFnEJElS5Rs2DK69tuLKmEVMkiRVhxEj4JprihX4K2RvSouYJEmqHocfXuxNec89cOihsGJF7kRrZRGTJEnVZeRI+OlPYcECGDwYXn89d6I1sohJkqTqc+SRMHky3HEHNDSUbRmziEmSpOp01FHwk5/A/PkwZAi88UbuRO9hEZMkSdXri1+EiRNhzpximYuVK3Mn+i8WMUmSVN1GjYIrroAZM2D4cFi1Knei/7CISZKk6jd6NPzwhzB9OhxxBPz737kTARYxSZJUK8aMgUsvhWnTisn8q1fnTkRd7gCSJElt5qSTigJ2yilQVwdTpkD79tniWMQkSVJt+cY3iqHJceOgX79i2DITi5gkSao9p58OO+5YbIWUkUVMkiTVpoaG3AmcrC9JkpSLRUySJCkTi5gkSVImFjFJkqRMWlXEImJYRDwREW9FRH2T5wdGxEMR8Vjjr/3X8PXjI+KFiHik8WNQa/JIkiRVktbeNfk48Dnginc9/1fg0JTSixHxCWAOsOUa3uOSlNJ3W5lDkiSp4rSqiKWUngKIiHc//6smD58AOkVEx5RSeW15LkmSlFFbzBE7DHh4LSVsbEQ8GhE/iYiua3qTiBgdEUsiYsmyZctKk1SSJKkNrbOIRcT8iHi8mY91roIWETsBFwJfWsMhPwJ6ArsALwEXr+m9UkpXppTqU0r13bp1W9e3liRJKnvrHJpMKQ1YnzeOiO7ALcBRKaU/rOG9X25y/ETg9vX5XpIkSZWoJEOTEdEFmAGcnlJauJbjPtLk4RCKyf+SJEk1obXLVwyJiOeBPYEZETGn8aWxwHbA2U2WpvhQ49dMarLUxUWNS1w8CuwHnNyaPJIkSZUkUkq5M7xv9fX1acmSJbljSJIkrVNEPJRSqm/uNVfWlyRJysQiJkmSlElFDk1GxDLg2RJ/m80pdghQefG8lB/PSXnyvJQfz0l5aovz0iOl1OzaWxVZxNpCRCxZ03iu8vG8lB/PSXnyvJQfz0l5yn1eHJqUJEnKxCImSZKUiUVsza7MHUDN8ryUH89JefK8lB/PSXnKel6cIyZJkpSJV8QkSZIysYhJkiRlUvNFLCJ+EhF/iYhmNxyPwg8iYmlEPBoRu7V1xlrTgnPy+cZz8VhELIqInds6Y61Z1zlpctweEbE6Ioa2VbZa1pLzEhH7Nu73+0RE3NWW+WpRC/796hwRv4iIXzeek2PaOmOtiYitIuLOiHiy8c/8pGaOyfazvuaLGDAZOGgtrx8MbN/4MRr4URtkqnWTWfs5eRrol1L6JPAtnADbFiaz9nNCRLQHLgTmtkUgAes4LxHRBZgADE4p7QQMa6NctWwya/+7MgZ4MqW0M7AvcHFEdGiDXLVsNfCNlNLHgd7AmIj4+LuOyfazvuaLWErpbuBvazmkAZiSCvcDXSLiI22Trjat65yklBallP7e+PB+oHubBKthLfh7AvAV4GbgL6VPJGjReRkJTEspPdd4vOemxFpwThLwPxERwKaNx65ui2y1KqX0Ukrp4cbPlwNPAVu+67BsP+trvoi1wJbAn5o8fp73nkDlMwqYlTtErYuILYEheMW43Pw/oGtELIiIhyLiqNyBxA+BHYEXgceAk1JKb+WNVDsiYhtgV+CBd72U7Wd9XVt8E6kUImI/iiLWN3cWcSlwWkrpreI/+ioTdcDuwP5AJ+C+iLg/pfS7vLFq2oHAI0B/oCcwLyLuSSn9M2+s6hcRm1Jctf9aOf15W8TW7QVgqyaPuzc+p4wi4lPAJODglNIrufOIemBqYwnbHBgUEatTSrfmjVXzngdeSSn9C/hXRNwN7AxYxPI5BrggFYt4Lo2Ip4GPAQ/mjVXdImIjihJ2bUppWjOHZPtZ79Dkuk0Hjmq8o6I38GpK6aXcoWpZRGwNTAO+4P/sy0NKaduU0jYppW2Am4ATLWFl4Tagb0TURcTGwKcp5scon+corlASEVsAOwB/zJqoyjXOx7sKeCql9L01HJbtZ33NXxGLiOsp7lzZPCKeB84BNgJIKf0YmAkMApYCKyj+N6MSasE5ORvYDJjQeAVmdUqpPk/a2tCCc6IM1nVeUkpPRcRs4FHgLWBSSmmtS5CodVrwd+VbwOSIeAwIiiH9v2aKWyv6AF8AHouIRxqfOwPYGvL/rHeLI0mSpEwcmpQkScrEIiZJkpSJRUySJCkTi5gkSVImFjFJkqRMLGKSJEmZWMQkSZIy+f+tSnflY/npsQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2160x1440 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "x = np.linspace(1,2,100)\n",
        "plt.plot(x,x-x**3-4*x**2+10, 'r', label='$g_1(x)=x-x^3-4x^2+10$')\n",
        "plt.plot(x,(10/x-4*x)**0.5, 'g', label='$g_2(x)=(\\dfrac{10}{x}-4x)^{1/2}$')\n",
        "plt.plot(x,0.5*(10-x**3)**0.5, 'b', label='$g_3(x)=\\dfrac{1}{2}(10-x^3)^{1/2}$')\n",
        "plt.plot(x,(10/(4+x))**0.5, 'y', label='$g_4(x)=(\\dfrac{10}{4+x})^{1/2}$')\n",
        "plt.plot(x,x-((x**3+4*x**2-10)/(3*x**2+8*x)), 'black', label='$g_5(x)=x-\\dfrac{x^3+4x^2-10}{3x^2+8x}$')\n",
        "plt.legend(loc='upper left')\n",
        "plt.rcParams['figure.figsize'] = [30, 20]\n",
        "f = plt.figure()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "\n",
        "# setting the axes at the centre\n",
        "\n",
        "\n",
        "# plot the function\n",
        "plt.plot(x,x-x**3-4*x**2+10, 'r', label='$g_1(x)=x-x^3-4x^2+10$')\n",
        "plt.legend(loc='upper left')\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "nXOvzKagSBMG",
        "outputId": "f9ab4ddb-fe92-48bd-a8f0-bb38177971cc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 819
        }
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 2160x1440 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# setting the axes at the centre\n",
        "\n",
        "# plot the function\n",
        "plt.plot(x,(10/x-4*x)**0.5, 'g', label='$g_2(x)=(\\dfrac{10}{x}-4x)^{1/2}$')\n",
        "plt.legend(loc='upper left')\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "V9E1GCX1SsNr",
        "outputId": "09197b85-037e-48d1-fdb7-f7a2d83ae77c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 865
        }
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in sqrt\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 2160x1440 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# setting the axes at the centre\n",
        "\n",
        "\n",
        "# plot the function\n",
        "plt.plot(x,0.5*(10-x**3)**0.5, 'b', label='$g_3(x)=\\dfrac{1}{2}(10-x^3)^{1/2}$')\n",
        "plt.legend(loc='upper left')\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "ojbj7TZlUQcD",
        "outputId": "6a7674f4-9f04-4c49-e85a-0161f3b294d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 826
        }
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 2160x1440 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# setting the axes at the centre\n",
        "\n",
        "# plot the function\n",
        "plt.plot(x,(10/(4+x))**0.5, 'y', label='$g_4(x)=(\\dfrac{10}{4+x})^{1/2}$')\n",
        "plt.legend(loc='upper left')\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "wQyzll44UW4N",
        "outputId": "7ef96753-c228-443f-b459-28e9f15fcd81",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 824
        }
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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g6YlaAAAAAAAAND1RCwAAAAAAgKb3/wGJoMPnnAQHhwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 2160x1440 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 100 linearly spaced numbers\n",
        "x = np.linspace(1,2,100)\n",
        "\n",
        "# setting the axes at the centre\n",
        "\n",
        "\n",
        "# plot the function\n",
        "plt.plot(x,x-((x**3+4*x**2-10)/(3*x**2+8*x)), 'black', label='$g_5(x)=x-\\dfrac{x^3+4x^2-10}{3x^2+8x}$')\n",
        "plt.legend(loc='upper left')\n",
        "\n",
        "# show the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "fZrAiYAOUa3J",
        "outputId": "d0a21ee4-7d3e-44b2-c196-e3f2bf24c9ec",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 823
        }
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 2160x1440 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def abs(x):\n",
        "   if x >= 0:\n",
        "      return x\n",
        "   return -x \n",
        "\n",
        "def absolute_error(p, p2):\n",
        "  return abs(p-p2)\n",
        "\n",
        "def fixed_point_iteration(g,p0,N):\n",
        "  if N == 0:\n",
        "    return p0\n",
        "  for i in range(N):\n",
        "    try:\n",
        "      p = g(p0)\n",
        "      if isinstance(p, complex):\n",
        "         return float(\"nan\")\n",
        "      p0 = p\n",
        "    except OverflowError:\n",
        "      return float(\"nan\")\n",
        "  return p"
      ],
      "metadata": {
        "id": "Swl8VKi4dVQo"
      },
      "execution_count": 216,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fixed_point_iteration(lambda x: (10/x-4*x)**0.5, 1.5, 10)"
      ],
      "metadata": {
        "id": "7b8s35_neXqs",
        "outputId": "9d60e588-e8d8-43e2-9fd4-748a5cbaa83e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 217,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nan"
            ]
          },
          "metadata": {},
          "execution_count": 217
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "n=np.arange(0, 30)\n",
        "\n",
        "def g1(n):\n",
        "  return fixed_point_iteration(lambda x: x-x**3-4*x**2+10, 1.5, n)\n",
        "\n",
        "def g2(n):\n",
        "  return fixed_point_iteration(lambda x: (10/x-4*x)**0.5, 1.5, n)\n",
        "\n",
        "def g3(n):\n",
        "  return fixed_point_iteration(lambda x: 0.5*(10-x**3)**0.5, 1.5, n)\n",
        "\n",
        "def g4(n):\n",
        "  return fixed_point_iteration(lambda x: (10/(4+x))**0.5, 1.5, n)\n",
        "\n",
        "\n",
        "def g5(n):\n",
        "  return fixed_point_iteration(lambda x: x-((x**3+4*x**2-10)/(3*x**2+8*x)), 1.5, n)\n",
        "\n",
        "df=pd.DataFrame([np.vectorize(g1)(n),np.vectorize(g2)(n),np.vectorize(g3)(n),np.vectorize(g4)(n),np.vectorize(g5)(n)],[\"g1\", \"g2\", \"g3\", \"g4\", \"g5\"])\n",
        "df.T"
      ],
      "metadata": {
        "id": "u5-VuZYkZKbI",
        "outputId": "6fb5809e-44ca-47a3-d4f4-1dc061f6f70d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        }
      },
      "execution_count": 224,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-2f2b8456-a3e1-436f-8332-f4820b3f5394\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>g1</th>\n",
              "      <th>g2</th>\n",
              "      <th>g3</th>\n",
              "      <th>g4</th>\n",
              "      <th>g5</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.500000e+00</td>\n",
              "      <td>1.500000</td>\n",
              "      <td>1.500000</td>\n",
              "      <td>1.500000</td>\n",
              "      <td>1.500000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-8.750000e-01</td>\n",
              "      <td>0.816497</td>\n",
              "      <td>1.286954</td>\n",
              "      <td>1.348400</td>\n",
              "      <td>1.373333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>6.732422e+00</td>\n",
              "      <td>2.996909</td>\n",
              "      <td>1.402541</td>\n",
              "      <td>1.367376</td>\n",
              "      <td>1.365262</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-4.697200e+02</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.345458</td>\n",
              "      <td>1.364957</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.027546e+08</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.375170</td>\n",
              "      <td>1.365265</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>-1.084934e+24</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.360094</td>\n",
              "      <td>1.365226</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1.277056e+72</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.367847</td>\n",
              "      <td>1.365231</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>-2.082713e+216</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.363887</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365917</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.364878</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365410</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365138</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365277</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365206</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365242</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365224</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365233</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365228</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365231</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2f2b8456-a3e1-436f-8332-f4820b3f5394')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "          const element = document.querySelector('#df-2f2b8456-a3e1-436f-8332-f4820b3f5394');\n",
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
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              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "               g1        g2        g3        g4        g5\n",
              "0    1.500000e+00  1.500000  1.500000  1.500000  1.500000\n",
              "1   -8.750000e-01  0.816497  1.286954  1.348400  1.373333\n",
              "2    6.732422e+00  2.996909  1.402541  1.367376  1.365262\n",
              "3   -4.697200e+02       NaN  1.345458  1.364957  1.365230\n",
              "4    1.027546e+08       NaN  1.375170  1.365265  1.365230\n",
              "5   -1.084934e+24       NaN  1.360094  1.365226  1.365230\n",
              "6    1.277056e+72       NaN  1.367847  1.365231  1.365230\n",
              "7  -2.082713e+216       NaN  1.363887  1.365230  1.365230\n",
              "8             NaN       NaN  1.365917  1.365230  1.365230\n",
              "9             NaN       NaN  1.364878  1.365230  1.365230\n",
              "10            NaN       NaN  1.365410  1.365230  1.365230\n",
              "11            NaN       NaN  1.365138  1.365230  1.365230\n",
              "12            NaN       NaN  1.365277  1.365230  1.365230\n",
              "13            NaN       NaN  1.365206  1.365230  1.365230\n",
              "14            NaN       NaN  1.365242  1.365230  1.365230\n",
              "15            NaN       NaN  1.365224  1.365230  1.365230\n",
              "16            NaN       NaN  1.365233  1.365230  1.365230\n",
              "17            NaN       NaN  1.365228  1.365230  1.365230\n",
              "18            NaN       NaN  1.365231  1.365230  1.365230\n",
              "19            NaN       NaN  1.365230  1.365230  1.365230\n",
              "20            NaN       NaN  1.365230  1.365230  1.365230\n",
              "21            NaN       NaN  1.365230  1.365230  1.365230\n",
              "22            NaN       NaN  1.365230  1.365230  1.365230\n",
              "23            NaN       NaN  1.365230  1.365230  1.365230\n",
              "24            NaN       NaN  1.365230  1.365230  1.365230\n",
              "25            NaN       NaN  1.365230  1.365230  1.365230\n",
              "26            NaN       NaN  1.365230  1.365230  1.365230\n",
              "27            NaN       NaN  1.365230  1.365230  1.365230\n",
              "28            NaN       NaN  1.365230  1.365230  1.365230\n",
              "29            NaN       NaN  1.365230  1.365230  1.365230"
            ]
          },
          "metadata": {},
          "execution_count": 224
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "n=np.arange(0, 30)\n",
        "\n",
        "def relative_error(p, p2):\n",
        "  return absolute_error(p,p2)/abs(p)\n",
        "\n",
        "def g1(n):\n",
        "  return relative_error(fixed_point_iteration(lambda x: x-x**3-4*x**2+10, 1.5, n), 1.365230013)\n",
        "\n",
        "def g2(n):\n",
        "  return relative_error(fixed_point_iteration(lambda x: (10/x-4*x)**0.5, 1.5, n), 1.365230013)\n",
        "\n",
        "def g3(n):\n",
        "  return relative_error(fixed_point_iteration(lambda x: 0.5*(10-x**3)**0.5, 1.5, n), 1.365230013)\n",
        "\n",
        "def g4(n):\n",
        "  return relative_error(fixed_point_iteration(lambda x: (10/(4+x))**0.5, 1.5, n), 1.365230013)\n",
        "\n",
        "\n",
        "def g5(n):\n",
        "  return relative_error(fixed_point_iteration(lambda x: x-((x**3+4*x**2-10)/(3*x**2+8*x)), 1.5, n), 1.365230013)\n",
        "\n",
        "df=pd.DataFrame([np.vectorize(g1)(n),np.vectorize(g2)(n),np.vectorize(g3)(n),np.vectorize(g4)(n),np.vectorize(g5)(n)],[\"g1\", \"g2\", \"g3\", \"g4\", \"g5\"])\n",
        "df.T"
      ],
      "metadata": {
        "id": "QDixbe7qnCOq",
        "outputId": "fd8e3f4d-1fab-4e17-af36-3460b86d872b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        }
      },
      "execution_count": 228,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-ac82f996-3cb0-4e92-b4db-3867f72909b5\">\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>g1</th>\n",
              "      <th>g2</th>\n",
              "      <th>g3</th>\n",
              "      <th>g4</th>\n",
              "      <th>g5</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.089847</td>\n",
              "      <td>0.089847</td>\n",
              "      <td>8.984666e-02</td>\n",
              "      <td>8.984666e-02</td>\n",
              "      <td>8.984666e-02</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.560263</td>\n",
              "      <td>0.672058</td>\n",
              "      <td>6.082289e-02</td>\n",
              "      <td>1.248168e-02</td>\n",
              "      <td>5.900476e-03</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.797216</td>\n",
              "      <td>0.544454</td>\n",
              "      <td>2.660229e-02</td>\n",
              "      <td>1.569691e-03</td>\n",
              "      <td>2.344010e-05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.002906</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.469510e-02</td>\n",
              "      <td>2.000045e-04</td>\n",
              "      <td>6.710567e-10</td>\n",
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              "      <th>4</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>NaN</td>\n",
              "      <td>7.228370e-03</td>\n",
              "      <td>2.544203e-05</td>\n",
              "      <td>3.033166e-10</td>\n",
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              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>NaN</td>\n",
              "      <td>3.776077e-03</td>\n",
              "      <td>3.236710e-06</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.913193e-03</td>\n",
              "      <td>4.121454e-07</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>NaN</td>\n",
              "      <td>9.846924e-04</td>\n",
              "      <td>5.209512e-08</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>5.027542e-04</td>\n",
              "      <td>6.969938e-09</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>2.577489e-04</td>\n",
              "      <td>5.448736e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.318638e-04</td>\n",
              "      <td>4.112313e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>6.753335e-05</td>\n",
              "      <td>2.895867e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>3.456846e-05</td>\n",
              "      <td>3.050634e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.769894e-05</td>\n",
              "      <td>3.030943e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>9.061189e-06</td>\n",
              "      <td>3.033449e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>4.638635e-06</td>\n",
              "      <td>3.033129e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>2.375230e-06</td>\n",
              "      <td>3.033171e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.215575e-06</td>\n",
              "      <td>3.033165e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>6.227838e-07</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>3.183831e-07</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.634583e-07</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>8.322574e-08</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>4.306695e-08</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>2.159001e-08</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.151185e-08</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>5.435018e-09</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>3.241122e-09</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.200726e-09</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.073328e-09</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>9.089934e-11</td>\n",
              "      <td>3.033166e-10</td>\n",
              "      <td>3.033166e-10</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ac82f996-3cb0-4e92-b4db-3867f72909b5')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
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              "  </svg>\n",
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              "      \n",
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              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
              "      height: 32px;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-ac82f996-3cb0-4e92-b4db-3867f72909b5 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-ac82f996-3cb0-4e92-b4db-3867f72909b5');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
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              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "          g1        g2            g3            g4            g5\n",
              "0   0.089847  0.089847  8.984666e-02  8.984666e-02  8.984666e-02\n",
              "1   2.560263  0.672058  6.082289e-02  1.248168e-02  5.900476e-03\n",
              "2   0.797216  0.544454  2.660229e-02  1.569691e-03  2.344010e-05\n",
              "3   1.002906       NaN  1.469510e-02  2.000045e-04  6.710567e-10\n",
              "4   1.000000       NaN  7.228370e-03  2.544203e-05  3.033166e-10\n",
              "5   1.000000       NaN  3.776077e-03  3.236710e-06  3.033166e-10\n",
              "6   1.000000       NaN  1.913193e-03  4.121454e-07  3.033166e-10\n",
              "7   1.000000       NaN  9.846924e-04  5.209512e-08  3.033166e-10\n",
              "8        NaN       NaN  5.027542e-04  6.969938e-09  3.033166e-10\n",
              "9        NaN       NaN  2.577489e-04  5.448736e-10  3.033166e-10\n",
              "10       NaN       NaN  1.318638e-04  4.112313e-10  3.033166e-10\n",
              "11       NaN       NaN  6.753335e-05  2.895867e-10  3.033166e-10\n",
              "12       NaN       NaN  3.456846e-05  3.050634e-10  3.033166e-10\n",
              "13       NaN       NaN  1.769894e-05  3.030943e-10  3.033166e-10\n",
              "14       NaN       NaN  9.061189e-06  3.033449e-10  3.033166e-10\n",
              "15       NaN       NaN  4.638635e-06  3.033129e-10  3.033166e-10\n",
              "16       NaN       NaN  2.375230e-06  3.033171e-10  3.033166e-10\n",
              "17       NaN       NaN  1.215575e-06  3.033165e-10  3.033166e-10\n",
              "18       NaN       NaN  6.227838e-07  3.033166e-10  3.033166e-10\n",
              "19       NaN       NaN  3.183831e-07  3.033166e-10  3.033166e-10\n",
              "20       NaN       NaN  1.634583e-07  3.033166e-10  3.033166e-10\n",
              "21       NaN       NaN  8.322574e-08  3.033166e-10  3.033166e-10\n",
              "22       NaN       NaN  4.306695e-08  3.033166e-10  3.033166e-10\n",
              "23       NaN       NaN  2.159001e-08  3.033166e-10  3.033166e-10\n",
              "24       NaN       NaN  1.151185e-08  3.033166e-10  3.033166e-10\n",
              "25       NaN       NaN  5.435018e-09  3.033166e-10  3.033166e-10\n",
              "26       NaN       NaN  3.241122e-09  3.033166e-10  3.033166e-10\n",
              "27       NaN       NaN  1.200726e-09  3.033166e-10  3.033166e-10\n",
              "28       NaN       NaN  1.073328e-09  3.033166e-10  3.033166e-10\n",
              "29       NaN       NaN  9.089934e-11  3.033166e-10  3.033166e-10"
            ]
          },
          "metadata": {},
          "execution_count": 228
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "n=np.arange(0, 30)\n",
        "\n",
        "def g1(n):\n",
        "  return fixed_point_iteration(lambda x: x-x**3-4*x**2+10, 1.3, n)\n",
        "\n",
        "def g2(n):\n",
        "  return fixed_point_iteration(lambda x: (10/x-4*x)**0.5, 1.3, n)\n",
        "\n",
        "def g3(n):\n",
        "  return fixed_point_iteration(lambda x: 0.5*(10-x**3)**0.5, 1.3, n)\n",
        "\n",
        "def g4(n):\n",
        "  return fixed_point_iteration(lambda x: (10/(4+x))**0.5, 1.3, n)\n",
        "\n",
        "\n",
        "def g5(n):\n",
        "  return fixed_point_iteration(lambda x: x-((x**3+4*x**2-10)/(3*x**2+8*x)), 1.3, n)\n",
        "\n",
        "df=pd.DataFrame([np.vectorize(g1)(n),np.vectorize(g2)(n),np.vectorize(g3)(n),np.vectorize(g4)(n),np.vectorize(g5)(n)],[\"g1\", \"g2\", \"g3\", \"g4\", \"g5\"])\n",
        "df.T"
      ],
      "metadata": {
        "id": "RpWaaYNMZ1DC",
        "outputId": "378cbe96-ca4a-48e4-9f6a-8e6ee3386055",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        }
      },
      "execution_count": 226,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
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              "      <th></th>\n",
              "      <th>g1</th>\n",
              "      <th>g2</th>\n",
              "      <th>g3</th>\n",
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              "      <th>g5</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1.300000e+00</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>1.300000</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.343000e+00</td>\n",
              "      <td>1.578704</td>\n",
              "      <td>1.396693</td>\n",
              "      <td>1.373606</td>\n",
              "      <td>1.367421</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-2.247784e+01</td>\n",
              "      <td>0.139607</td>\n",
              "      <td>1.348648</td>\n",
              "      <td>1.364166</td>\n",
              "      <td>1.365232</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>9.323516e+03</td>\n",
              "      <td>8.430368</td>\n",
              "      <td>1.373591</td>\n",
              "      <td>1.365365</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-8.108220e+11</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.360916</td>\n",
              "      <td>1.365213</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>5.330605e+35</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.367430</td>\n",
              "      <td>1.365232</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>-1.514710e+107</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.364102</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365807</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.364934</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365381</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365153</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365270</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365210</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365240</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365225</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365233</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365229</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365231</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
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              "      <th>20</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "      <td>1.365230</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2ddcf498-e16f-42a4-ab16-44596a8bfe55')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-2ddcf498-e16f-42a4-ab16-44596a8bfe55 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-2ddcf498-e16f-42a4-ab16-44596a8bfe55');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "               g1        g2        g3        g4        g5\n",
              "0    1.300000e+00  1.300000  1.300000  1.300000  1.300000\n",
              "1    2.343000e+00  1.578704  1.396693  1.373606  1.367421\n",
              "2   -2.247784e+01  0.139607  1.348648  1.364166  1.365232\n",
              "3    9.323516e+03  8.430368  1.373591  1.365365  1.365230\n",
              "4   -8.108220e+11       NaN  1.360916  1.365213  1.365230\n",
              "5    5.330605e+35       NaN  1.367430  1.365232  1.365230\n",
              "6  -1.514710e+107       NaN  1.364102  1.365230  1.365230\n",
              "7             NaN       NaN  1.365807  1.365230  1.365230\n",
              "8             NaN       NaN  1.364934  1.365230  1.365230\n",
              "9             NaN       NaN  1.365381  1.365230  1.365230\n",
              "10            NaN       NaN  1.365153  1.365230  1.365230\n",
              "11            NaN       NaN  1.365270  1.365230  1.365230\n",
              "12            NaN       NaN  1.365210  1.365230  1.365230\n",
              "13            NaN       NaN  1.365240  1.365230  1.365230\n",
              "14            NaN       NaN  1.365225  1.365230  1.365230\n",
              "15            NaN       NaN  1.365233  1.365230  1.365230\n",
              "16            NaN       NaN  1.365229  1.365230  1.365230\n",
              "17            NaN       NaN  1.365231  1.365230  1.365230\n",
              "18            NaN       NaN  1.365230  1.365230  1.365230\n",
              "19            NaN       NaN  1.365230  1.365230  1.365230\n",
              "20            NaN       NaN  1.365230  1.365230  1.365230\n",
              "21            NaN       NaN  1.365230  1.365230  1.365230\n",
              "22            NaN       NaN  1.365230  1.365230  1.365230\n",
              "23            NaN       NaN  1.365230  1.365230  1.365230\n",
              "24            NaN       NaN  1.365230  1.365230  1.365230\n",
              "25            NaN       NaN  1.365230  1.365230  1.365230\n",
              "26            NaN       NaN  1.365230  1.365230  1.365230\n",
              "27            NaN       NaN  1.365230  1.365230  1.365230\n",
              "28            NaN       NaN  1.365230  1.365230  1.365230\n",
              "29            NaN       NaN  1.365230  1.365230  1.365230"
            ]
          },
          "metadata": {},
          "execution_count": 226
        }
      ]
    }
  ]
}

## notebook.ipynb

      
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