lista-2-solucoes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lista de Exercícios 2 \n",
    "\n",
    "Solucionário matemático e computacional de exercícios selecionados da Lista de Exercícios 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import metodosRaizes as rz\n",
    "import numpy as np\n",
    "import sympy as sy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q12 - L2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiramente, recorramos à análise gráfica da função."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import cos, exp\n",
    "\n",
    "# funcao \n",
    "p = lambda x: 2*cos(x) - exp(x)\n",
    "\n",
    "# plotagem\n",
    "x = np.linspace(-1,1,30)\n",
    "plt.plot(x,p(x),x,0*p(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que a raiz está próxima de $x= 0.5$. Assim, qualquer valor próximo a este é razoável como aproximação inicial. \n",
    "\n",
    "Agora, antes de aplicar o método de Newton, vamos calcular a derivada da função simbolicamente. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - e^{x} - 2 \\sin{\\left(x \\right)}$"
      ],
      "text/plain": [
       "-exp(x) - 2*sin(x)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# derivada simbolica \n",
    "xsym = sy.Symbol('x')\n",
    "sy.diff(2*sy.cos(xsym) - sy.exp(xsym),xsym)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resolvamos com a nossa função programada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimativa inicial: x0 = 0.2\n",
      "\n",
      "i\t x\t\t f(x)\t\t df(x)\t\t ER\n",
      "0\t 0.200000\t 0.738730\t -1.618741\t -\n",
      "1\t 0.656361\t -0.343328\t -3.148240\t 6.952896e-01\n",
      "2\t 0.547307\t -0.020734\t -2.769371\t 1.992555e-01\n",
      "3\t 0.539820\t -0.000096\t -2.743662\t 1.386900e-02\n",
      "4\t 0.539785\t -0.000000\t -2.743542\t 6.499799e-05\n",
      "Solução obtida: x = 0.5397851616\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0 = 0.2\n",
    "tol = 1e-3\n",
    "f = '2*cos(x) - exp(x)'\n",
    "df = '-2*sin(x) - exp(x)'\n",
    "xr = rz.newton(x0,f,df,tol,10,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verificação:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.1118811144305027e-09"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*cos(xr) - exp(xr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q16 - L2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.90617985 -0.53846931  0.90617985  0.53846931  0.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = lambda x: x**5 - 10/9*x**3 + 5/21*x\n",
    "x = np.linspace(-1,1,50,endpoint=True)\n",
    "plt.plot(x,p(x),x,0*p(x))\n",
    "\n",
    "xr = np.roots([1,0,-10/9,0,5/21,0])\n",
    "print(xr)\n",
    "\n",
    "plt.scatter(xr,0*xr,c='r');\n",
    "plt.grid(True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "tol = 1e-3\n",
    "nmax = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### item b.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimativa inicial: x0 = -0.8\n",
      "\n",
      "i\t x\t\t f(x)\t\t df(x)\t\t ER\n",
      "0\t -0.800000\t 0.050733\t 0.152762\t -\n",
      "1\t -1.132103\t -0.517006\t 4.179132\t 2.933506e-01\n",
      "2\t -1.008392\t -0.143443\t 2.018543\t 1.226817e-01\n",
      "3\t -0.937329\t -0.031683\t 1.169040\t 7.581417e-02\n",
      "4\t -0.910227\t -0.003604\t 0.908555\t 2.977501e-02\n",
      "5\t -0.906261\t -0.000070\t 0.873137\t 4.376698e-03\n",
      "6\t -0.906180\t -0.000000\t 0.872424\t 8.905774e-05\n",
      "Solução obtida: x = -0.9061798789\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-0.9061798789481786"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Aproximacao de xi1 pelo MNR\n",
    "x0 = -0.8\n",
    "p = 'x**5 - 10/9*x**3 + 5/21*x'\n",
    "dp = '5*x**4 -10/3*x**2 + 5/21'\n",
    "plotar = True\n",
    "rz.newton(x0,p,dp,tol,nmax,True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.03303209894521281, 0.4870085727669044)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ff = lambda x: x**5 - 10/9*x**3 + 5/21*x\n",
    "dff = lambda x: 5*x**4 - 30/9*x**2 + 5/21\n",
    "\n",
    "xx = 0.857\n",
    "ff(xx),dff(xx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### item b.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=1 a=-0.750000 b=-0.250000 xm=-0.500000 f(a)=0.052874 f(b)=-0.043139 f(xm)=-0.011409 b-a=0.500000\n",
      "i=2 a=-0.750000 b=-0.500000 xm=-0.625000 f(a)=0.052874 f(b)=-0.011409 f(xm)=0.027090 b-a=0.250000\n",
      "i=3 a=-0.625000 b=-0.500000 xm=-0.562500 f(a)=0.027090 f(b)=-0.011409 f(xm)=0.007512 b-a=0.125000\n",
      "i=4 a=-0.562500 b=-0.500000 xm=-0.531250 f(a)=0.007512 f(b)=-0.011409 f(xm)=-0.002211 b-a=0.062500\n",
      "i=5 a=-0.562500 b=-0.531250 xm=-0.546875 f(a)=0.007512 f(b)=-0.002211 f(xm)=0.002605 b-a=0.031250\n",
      "i=6 a=-0.546875 b=-0.531250 xm=-0.539062 f(a)=0.002605 f(b)=-0.002211 f(xm)=0.000183 b-a=0.015625\n",
      "Solução encontrada: -0.5390625\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-0.5390625"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Aproximacao de xi2 pelo MB\n",
    "\n",
    "var = 'x'\n",
    "a,b = -0.75, -0.25 \n",
    "rz.bissecao(p,a,b,tol,100,var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### item b.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=1 a=-0.350000 b=0.250000 xm=-0.057823 f(a)=-0.040947 f(b)=0.043139 f(xm)=-0.013553 b-a=0.600000\n",
      "i=2 a=-0.057823 b=0.250000 xm=0.015767 f(a)=-0.013553 f(b)=0.043139 f(xm)=0.003750 b-a=0.307823\n",
      "i=3 a=-0.057823 b=0.015767 xm=-0.000181 f(a)=-0.013553 f(b)=0.003750 f(xm)=-0.000043 b-a=0.073590\n",
      "Solução encontrada: -0.00018060189341005293\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-0.00018060189341005293"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Aproximacao de xi3 pelo MFP\n",
    "a,b = -0.35, 0.25 \n",
    "rz.falsa_posicao(p,a,b,tol,100,var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### item b.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i\t x\t\t f(x)\t\t ER\n",
      "0\t 0.400000\t 0.034367\t 2.500000e+00\n",
      "1\t 0.074501\t 0.017281\t 4.369086e+00\n",
      "2\t 0.071429\t 0.016604\t 4.299795e-02\n",
      "3\t 0.071429\t 0.016604\t 1.829703e-06\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.07142912925875246"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UplIqCLgW2NKRikops1Iq/Ohn4GLgGxfEZIgHH3yQQYMGMWzYMA4cOMCcOXNalg0fPpzRo0ef8oayyZMn069fv54IVwjD1bz/Afsuv5zyjRuJ/u1vydqymbDzzzM6LJ+jtO5ML047K1FqAvAQjstH12utFymlbgHQWq9RSiUBO4AIoBmoAQYCcTiOAsBx4nqj1nrRqb4vOztb79ix45h53377LQMGDOhyWzyNr7ZbeDZ7RQWFi++jcvNmgrKySF64kNCzhhsdltdTSn3W1iX6LrmPQGv9BvDGcfPWtPpcgKPL6HhVwFBXxCCE8AxVb22lYMEC7JWVxN7yB+JuvVUGiTOYDDonhOgRTUVFFC5YSPW2bZgGDiR93eOY5GjWLUgiEEJ0K601lS+/QuH996MbG0m4YyYx06ahAmTz4y7klxBCdBtrfj4Fc++h9j//IST75yQvWEBwZqbRYYnjSCIQQricttspf24jRQ89hAKS7plL1K9/jfKTcS7dkSQCIYRLNe7bh2V2DvVffol51AUk5+YS2KuX0WGJk5BEIIRwCd3UROkTT1Dy6Cr8QkPp9cD9RFx+uQwS5wEkEQghuqz+m11YZs+m8fvvCR9/KUk5OQTExhodlugg6bBzoZ07d3LeeT/dFfn5558zZsyY01pXew+uEcKdNDc0ULR0KQd+/WvsZWWkPvIwqQ8+KEnAw3jlEUHBvffS+K1rH0wTPKA/SXfffdIygwYNYt++fdjtdvz9/Zk5cybLli07pswFF1xAdXX1CXWXLl3K2LFjW6bbe3CNEO6ibvt2LDlzsB48SOTV/0Xi3/6Gf0SE0WGJ0+CVicAofn5+DBo0iF27drFnzx7S09M566yzjinz/vvvd2hd7T24Rgij2WtqKFq2jIrnXyAwNZX0J9djPvdco8MSXeCVieBUe+7daeTIkXz44YesWrWKt95664TlHT0iONmDa4QwSs2//oUldx62ggJipt5A/J//jF9oqNFhiS7yykRgpJEjRzJt2jRuu+02Utp4rmpHjghaP7jm9ttvZ+vWrVxyySXdEa4QHWIrL6dw8WKqtrxK0Bl9yHh+IyGtnsYnPJucLHax/v37ExwczJ13nt7jMk/14BohepLWmqo33yTvsolUvfEmcX/8I5kvvyxJwMvIEYGLrVixgsWLF2M2m0+r/tEH1xx1/INrhOgpTYVFFMyfT80772AaPJj0J9djkmdleCU5InCRffv20b9/f+rr65k6darR4Qhx2rTWVLz0EnkTJ1L7wQck/PWvZLzwvCQBLyZHBC7Sp08fvvvOtZesCtHTrIcOYZkzl7qPPyZ0xAiSFy4gqHdvo8MS3UwSgRDCMUjcs89S9NAKlJ8fSbm5RP3qGhkkzkdIIhDCxzXu2cORnBwavvqasAsvJGleLoFJSUaHJXqQVyUCrbVPDXDliudNC9+lrVZKHn+ckjWP4W8202vJA0RMnOhT/4eEg9ckApPJRGlpKbGxsT7xD1lrTWlpKSaTyehQhAeq37kTy+wcGn/4gYjLLiNx9t0ExMQYHZYwiNckgtTUVPLz8ykuLjY6lB5jMplITU01OgzhQZrr6yl++BHKnnqKgPh4UletInzMaKPDEgbzmkQQGBhIpjwCT4h21X7yKZa5c2g6+CNRv/oVCX+9A38ZvkTgRYlACNE2e3U1RUuXUbFpE4Hp6aQ/9RTmkecYHZZwI5IIhPBi1e++S0HuPGzFxcTceCPxf5qBX0iI0WEJNyOJQAgvZCsro3DRvVS9/jrBffuS+vBKQoYMMTos4aZccreIUupSpdT3Sqm9SqlZbSzvr5T6SCnVqJS6ozN1hRAdp7Wm8rXXHYPEvf02cX+aQeb/viRJQJxUl48IlFL+wKPAOCAf2K6U2qK13t2qWBlwOzD5NOoKITqgqaCAgtx51Lz3HqYhQ0hfuADTz35mdFjCA7iia+hsYK/WOg9AKfUCMAlo2ZhrrYuAIqXUZZ2tK4Q4Od3cTMWLL1G0ZAnaZiNh1p3EXH89Sp5qJzrIFYkgBTjUajof6OglCR2uq5SaDkwHSE9P73yUQngh68GDjkHiPv2U0JEjSV4wn6C0NKPDEh7GFYmgrdt4Ozr2QYfraq3XAmsBsrOzZWwF4dO0zUbZ0xsoXrkSFRhI0oL5RF19tU/cVS9czxWJIB9ovQuSChzpgbpC+KSG73/AkpNDw86dhI0ZQ9I9cwlMTDQ6LOHBXJEItgN9lVKZwGHgWuC6HqgrhE9ptlopXfMYJWvX4h8RQcryZYSPHy9HAaLLupwItNY2pdQMYCvgD6zXWu9SSt3iXL5GKZUE7AAigGal1H8DA7XWVW3V7WpMQnib+q++wpKTQ+OevURccTmJd91FQHS00WEJL+GSG8q01m8Abxw3b02rzwU4un06VFcI4dBcV0fxipWUbdhAQGIiaY+tIezCC40OS3gZubNYCDdV+9FHWObMpSk/n6jfXEvCzJn4h4UZHZbwQpIIhHAz9qoqipYsoeLFlwjq3Zvez2wgdMQIo8MSXkwSgRBupPqddxyDxJWWEnvzTcTNmIGfPHxIdDNJBEK4AVtpKYWLFlH1xpsE9+tH6qpVhJw52OiwhI+QRCCEgbTWVL36KoWL7qW5ro74P99O7M03owIDjQ5N+BBJBEIYpOnIESy5udT++31Chg0jedFCgvv0MTos4YMkEQjRw3RzMxWbNlG0ZClaaxLvvpvoKdfJIHHCMJIIhOhBjfv3Y5kzh/odn2H+xbkkzZ9PUGqbt9gI0WMkEQjRA7TNRtlTT1H88COo4GCSFy0i8qorZXgI4RYkEQjRzRq++w7L3bNp2L2b8HFjSZwzh8CEBKPDEqKFJAIhukmz1UrJ6tWUPr4O/8hIUh56iPBLLpajAOF2JBEI0Q3qPv8CS04O1rw8IidNImHWnTJInHBbkgiEcKHm2lqKHlpB+bPPEpCcRNrjawm74AKjwxLipHwqEfzvD//Lh0c+NDoM4aVSdpdwwXPfEF5az65f9mb75J/RZH8F3nvF0Li0dv0D/XQHH0LYme/u8DrbKtdO1bbKtjnvuDhblzmhvG673PHraXMd7dTV6Ja6R+e3F9PM7JkMjR96Qhu6wqcSQUl9CXkVeUaHIbyIUgpTnZ0JrxeRvaOS4vggNt6SzsHMEGg8BI1GR9h9OnquQ7X5RNqulW3ruzv1PR2o33r6+PLHlD1uVcfUa2Md7cWplKLlj1KgfirbUkeBH37ttOr0qe7YW+hu2dnZeseOHUaHIQRV27ZRMH8+9rJyYm+6ibjb/ohfcLDRYQnRJqXUZ1rr7OPn+9QRgRCuYispoWDBQqq3biV4wADS1qwhZNAgo8MS4rRIIhCiE7TWVG7eTOHi+9D19cT/5S/E3vg7GSROeDRJBEJ0UNPhw1juyaX2gw8IOesskhcuIDgry+iwhOgySQRCnIJubqb8+ecpXrYcDSTm5BB93W9Qfq4/aSeEESQRCHESjXn7seTkUP/555jPP5/kebkEpqQYHZYQLiWJQIg26KYmStc/Scmjj6JCQkhevJjIyZNkeAjhlSQRCHGcht27OZKTQ+Pubwm/5BKScmYTEB9vdFhCdBtJBEI4NTc2UvLoKkqfeAL/6GhSVq4g4uKLjQ5LiG4niUAIoO7zz7HMzsG6fz+RV15J4qw78Y+MNDosIXqEJALh0+w1tRQ/+CDlGzcS2KsXaU+sI+y884wOS4ge5ZLr35RSlyqlvldK7VVKzWpjuVJKrXQu/1opdVarZQeUUjuVUl8qpWTcCNFjat7/gLwrLqd840aif/tbsrZsliQgfFKXjwiUUv7Ao8A4IB/YrpTaorXe3arYeKCv83UOsNr5ftRorXVJV2MRoiPsFRUULr6Pys2bCcrKovdzzxF61nCjwxLCMK7oGjob2Ku1zgNQSr0ATAJaJ4JJwAbtGOHuY6VUlFIqWWttccH3C9FhVW9tpWDBAuyVlcTe8gfibr1VBokTPs8ViSAFONRqOp9j9/bbK5MCWHCM0P22UkoDj2mt17b1JUqp6cB0gPT0dBeELXxJU1ERhQsWUr1tG6aBA0lf9zimAQOMDksIt+CKRNDWHTbHj219sjLnaa2PKKUSgG1Kqe+01v8+obAjQawFxzDUXQlY+A6tNZUvv0Lh/fejGxtJuGMmMdOmoQLkOgkhjnLF/4Z8IK3VdCpwpKNltNZH34uUUq/g6Go6IREI0VnW/HwK5s6l9j8fEZL9c5IXLCA4M9PosIRwO664amg70FcplamUCgKuBbYcV2YLcIPz6qGRQKXW2qKUMiulwgGUUmbgYuAbF8QkfJi22ynb8Ax5l19B/ZdfkXTPXHpv2CBJQIh2dPmIQGttU0rNALYC/sB6rfUupdQtzuVrgDeACcBeoA74nbN6IvCKc/yWAGCj1vqtrsYkfFfjvn1YZudQ/+WXmEddQHJuLoG9ehkdlhBuTR5VKbyCbmqi9IknKHl0FX5mM4l330XE5ZfLIHHCY2mtaWhqprK+6ZjX8PQo4sJO70o3eVSl8Fr13+zCMns2jd9/T8SE8STOnk1AbKzRYQkBODbo1Y02KmqbKK+zUlHfREWdlfJaK+V1js8Vzo18VcsG30ZVfRNWe/MJ63vydyMY3S/BpTFKIhAeq7mhgZJHHqF0/ZMExMaS+ugjhF90kdFhCS/XaLNTXttEaW0jZbXWY16ltVbKaqyU1TmmK+qsVNQ1YWtuv+clwhRAVGgQkSGBRIYEkhwZQoTzc0RIQMv8o6/MOLPL2ySJQHikuu3bseTMwXrwIFHXXE3CX/+Kf0SE0WEJD6S1pqrBRklNI6U1Vud7I8U1Vkpbz6u1UlLdSHWjrc31+CmIDg0ixhxEtDmIvglhRIUGER0aSHRoEFGt3o/OjwwJJMDf+CfdSSIQHsVeU0PRsmVUPP8CgamppD+5HvO55xodlnBDVlszJTWNFFU3UtzqVVTd4Phc00hRlePdajuxC0Y5N+xxYUHEmoMZnBJJrNkxHWMOJsYc1PKKNTv26P38PPOclCQC4TFq/vUvLLnzsBUUEDN1KvF/vh2/0FCjwxI9zGZvpqTGSmFVg+NV3UiR83NRdSOFVY7p0lprm/VjzEHEhwUTHx7M2Zlm4sODiQ8LJi48iLiwYGLNjs8xoUFusbfeEyQRCLdnKy+ncPFiqra8StAZfch4fiMhw4YZHZboBvVWOwVVDVgq6ymsasBS2UBhpfPdOV1S08jxXe5+CuLCgkmMMJESZWJ4ehSJ4SYSIoJJCHds9OPDHRv5oADf2Lh3hiQC4ba01lS/+SYFCxdhr6oi7o9/JPaWP+AXFGR0aOI0NDTZKahs4EhlPZYKx8b+SGUDlop6LM6NfWV90wn1wk0BJEeaSIww0S8pnKQIE4mRJhLDHfMSI4KJDQvG30O7ZdyBJALhlpoKiyiYN4+af/4T0+DBpD/5JKZ+PzM6LNGO5mZNSW0jh8vrOVLRwJGKeg47Xxbnhr+trproUMdVMqnRIWRnRJMcGUJShMmx4Y80kRRhwhwsm6nuJn/Dwq1oral46SWKHliCtlpJ+NvfiLnhehkkzmBN9mYsFQ3kl9eRX1HP4XLHRv7oBt9S0XDCNe9hwQH0ijKRHBnCmSmRJEeGkBxpoleU4z05MoSQIH+DWiRak/9dwm1YDx3CMmcudR9/TOiIESQvXEBQ795Gh+UTrLZmjlTUk19eT355HYdbfc4vd/TXt+6XVwoSw030ijIxJDWKSwebSIkKoVdkCCnRIfSKCiHCFCB3dnsISQTCcNpup+yZZyh+aAXK35+k3FyifnUNyk9O6rmKvVlTUNVAflkdh8rrOVRWx6HyOvLL6jlUXkdBVQOtR5vxU7R02ZzbJ5bU6FBSox3TqVGhJEWa5KSrF5FEIAzVuGcPR3JyaPjqa8IuvJCkebkEJiUZHZZHqqxv4lBZHT+2eh2dPlJRT5P9py29UpAUYSItOpRz+8SS5tzQp8WEkhIVQlKkiUAfuXRSSCIQBtFWKyWPP07JmsfwDwuj19KlRFw2QboSTsLerDlSUc+PZXUcLD12Q/9jWd0JV9xEhwaSHhPK4JRIxg9OJi0mhLToUNJiQukVZSI4QPrnhYMkAtHj6nfuxHL3bBr37CHisstInH03ASDDd7EAABKZSURBVDExRoflFhqa7C0b+oOltcds9PPL647Zqw/0V6Q6N+xD0yJJjwklPcYxnRYTSoQp0MCWCE8iiUD0mOb6eopXPkzZ008TEB9P6qpVhI8ZbXRYPa6m0cbB0loOltZxoLSWgyXO91JHX31r4cEBpMeGMiA5nEsGJdE7NpTeMaGkx4aSHBki184Ll5BEIHpE7cefYJkzh6ZDh4j69a9JuGMm/uHhRofVbaobmjjg3MAfKKnlgHMP/0BpHSU1jceUjQsLJiM2lF+cEUvvGDMZcY49+96xZqJDA6W7THQ7SQSiW9mrqylaspSKv/+dwPR00p96CvPIc4wOyyVqGm3OjbxjY7+/5OjGvpaSmmNvnkqKMNE7NpSL+ifQOy6UjFizY+8+1kyY3DAlDCb/AkW3qX73XQpy52ErLibmxhuJ/9MM/EJCjA6rUxqa7BwsrWN/SQ37S+qcG/xa9pfWUlx97J59YkQwGbFmxg5IpHesmcy4UDLizPSOMcuNU8KtSSIQLmcrK6Nw0b1Uvf46wX37kvrwSkKGDDE6rHbZ7M0cKq9nf0kNecWOPfr9JbUcKKnjSGX9MdfXx4UFkxkXyuh+8WTEmcmMNdM71tGdExok/52EZ5J/ucJltNZUvfY6hYsWYa+tJe5PM4j7/e9RbjBInNaaoupG8oqde/QlNewvqSWvpJYfS+uOeYJUhCmAzPgwzs6MIcO5kc+KCyMjLpRwuRJHeCFJBMIlmgoKKMidR81772EaOoTeCxcS3Ldvj8dR02hjf3Etec69+7yjG/3iWmqt9pZywQF+ZMaZ6ZcYzqWDksiMM5MVbyYj1kyMOUhO0AqfIolAdIlubqbi7y9StGQJ2m4nYdadxFx/Pcq/+/rEbfZm8svrj9nY5xU79vALq37qt1cKUqNDyIwLI7t3DFnxZjLjHK9ekSEe+zQpIVxNEoE4bdaDBx2DxH36KaEjR5K8YD5BaWkuW395rZW8khr2Fdc6NvjFNeSV1HKwtPaYG6uiQx0P9L6gbzyZcWb6xJvJig8jPSYUU6CcpBXiVCQRiE7TNhtlT2+geOVKVGAgSQvmE3X11afVndJkb+ZgaR15xUc3+DUte/jldT8NmRDor+gdayYrznFVTla8c4MfF0a02fhzEEJ4MkkEolMavv8BS04ODTt3EjZmDEn3zCUwMfGU9cpqrewrrnFs6ItrnZ9rOVhWh73Vidq4sGCy4s1cOjiJPvFhZDk39qnRIT7z/FgheppLEoFS6lJgBeAPrNNa33fccuVcPgGoA6ZprT/vSF3hHpqtVkrXPEbJ2rX4R0SQ8uBywi+99JijgPb27vcV11DRau8+KMCPzFgz/ZLCGX/m0Q1+GJlxZiJD5KocIXpalxOBUsofeBQYB+QD25VSW7TWu1sVGw/0db7OAVYD53SwrjBY/ZdfciQnB+vefURccTmmP9/BD00B5O3IZ1+rjf6PZcdehhkfHkyfeDMTzkwmK85Mn4Qw+sSFkRItY+QI4U5ccURwNrBXa50HoJR6AZgEtN6YTwI2aK018LFSKkoplQxkdKCu67w5Cwp2dsuqvY1GU1dno+T9cuq+rAGzH81jwrGEvo/tsX8DkA70BiYE+hMS6I8pzvEeEuiPKdCPgKMPlqlwvvYa1BghvEnSmTDetR0nrkgEKcChVtP5OPb6T1UmpYN1AVBKTQemA6Snp3ctYtHC1txMfZOdhqZm6q1252c7TfmNhOyow69W09gnCPuwEEzmAGJaNvT+hAT5Exzgh0L27oXwZK5IBG1tBXQHy3SkrmOm1muBtQDZ2dltljklF2dRT2Fv1uSX17WcpG3dndN6cLRAf0X/MMX1u7Zw5pfv0ZiUAvPuJnPMBUSGSt+9EN7KFYkgH2h98XgqcKSDZYI6UFd0UGV90wlX5eSV1HCgpA6rvbmlXIw5iD7xZi7qn0ifBMdVOX0Swoj+4iOK58/HVlpK7M03ETdjBn4mk4EtEkL0BFckgu1AX6VUJnAYuBa47rgyW4AZznMA5wCVWmuLUqq4A3VFK8ffVfvT3n3tMePcB/gp0mND6RMfxuj+CfSJC3Nee3/idfe2khIKFuVgefMtgvv3J3X1akIGD+rppgkhDNLlRKC1timlZgBbcVwCul5rvUspdYtz+RrgDRyXju7Fcfno705Wt6sxeYPKuib2ldSwr+inG6yOjox5/F21feLDGNM/nqz4sJZr79NjQk/58HGtNVWvvkrhontprqsj/r//TOxNN6ECpRtICF+itD697nYjZWdn6x07dhgdRpdZbc38WFZ3zN20+0sce/eltcf23afHhJIV/9NefVfvqm06cgRLbi61/36fkGHDSF60kOA+fVzVNCGEG1JKfaa1zj5+vtxZ3M201hRXN7LPOfxx643+ofL6Nu+qHTcwsWWDnxUfRpoL76rVzc1UbNpE0ZKlaK1JvPtuoqdc162DxAkh3JskAhc5fvhjx1j37Q9/PLBXBBOH9HIModBDd9U27t+PZc4c6nd8hvkXvyBp/jyCUlO79TuFEO5PEkEnNNrsHCqra9nQHyitbflcVO2+wx9rm43SJ5+k5OFHUCYTyffeS+SVk2XMfSEEIIngBPZmzeHyeva3PJD8p4ebHC6vp/mYxxYGkRFrZtTP4lsGRzt6otZdhj9u+O47LHfPpmH3bsLHjSVxzhwCExKMDksI4UZ8MhE0N2sKqhqcjyx0bPCPPqf2x7K6Y67KCQsOIDPOzLC0aK4cnkqWc88+w80HSGtubKRk9WpK1z2Bf1QUKStWEHHJxUaHJYRwQz6VCB7/dx4vfZbPgdJaGm0/3WAVHOBHRqyZMxLCGDcwicy4UDJizWTGm4kPC/a4LpS6z7/AkpODNS+PyMmTSZx1J/5RUUaHJYRwUz6VCAL9FWkxIVzQN46MOMdDTjLizCRFmLzisYXNtbUUPbSC8mefJSA5ibTHHyfsgvONDksI4eZ8KhFMOy+TaedlGh1Gt6j58EMK5t5D05EjRF93HfF/+Qv+YWajwxJCeACfSgTeyF5ZSeH9D1D58ssEZWbS+9lnCP35z40OSwjhQSQReLCqt9+mYMEC7GXlxE6fTtxtf8QvONjosIQQHkYSgQeyFRdTsGAh1W+/TfCAAaQ/9himgQONDksI4aEkEXgQrTWV/9hM4X33oevrif+f/yH2d9NkkDghRJdIIvAQTYcPY7knl9oPPiDk5z8necECgrO888S3EKJnSSJwc7q5mfKNz1O0fDkKSJyTQ/RvfoPyc80gdEIIIYnAjTXm7ceSk0P9559jPv98kuflEpiSYnRYQggvI4nADemmJkrXP0nJo4+iQkJIvm8xkZMmedwdzkIIzyCJwM007N7Nkdk5NH77LeGXXELSnBwC4uKMDksI4cUkEbiJ5sZGSh55lNL16/GPiSbl4ZVEjBtndFhCCB8gicAN1H32GZbZOVgPHCDyv64i8W9/wz8y0uiwhBA+QhKBgew1tRQvX075xo0EpqSQvv4JzL/4hdFhCSF8jCQCg9S8/wGWe+ZisxQQff31JPz3n/EzyyBxQoieJ4mgh9krKihcfB+VmzcTlJVF7+eeI/Ss4UaHJYTwYZIIeojWmuqtzkHiKiuJvfUW4m69Fb+gIKNDE0L4OEkEPaCpqIjCBQuo3vZ/mAYNIv2JdZj69zc6LCGEACQRdCutNZUvv0Lh/fejGxtJuGMmMdOmoQLkr10I4T5ki9RNrPn5FMydS+1/PiIk2zlIXKYMEieEcD9dGrlMKRWjlNqmlNrjfI9up9ylSqnvlVJ7lVKzWs3PVUodVkp96XxN6Eo87kDb7ZRteIa8y6+g/quvSbpnLr03bJAkIIRwW10dwnIW8I7Wui/wjnP6GEopf+BRYDwwEPiNUqr1U1Qe1FoPc77e6GI8hmrcu5eDU35L4b33Ejoim6zXXpWRQoUQbq+rXUOTgF86Pz8NvAfceVyZs4G9Wus8AKXUC856u7v43W5DNzVRum4dJatW42c202vJA0RMnCiDxAkhPEJXd1UTtdYWAOd7QhtlUoBDrabznfOOmqGU+loptb69riUApdR0pdQOpdSO4uLiLobtOvXf7GL/1ddQvGIl4ePGkvX6a0RefrkkASGExzhlIlBK/Z9S6ps2XpM6+B1tbRG183010AcYBliAZe2tRGu9VmudrbXOjo+P7+BXd5/mhgaKli7lwK9+hb2sjNRHHyFl+XICYmONDk0IITrllF1DWuux7S1TShUqpZK11halVDJQ1EaxfCCt1XQqcMS57sJW63oceK2jgRup9tNPKZgzF+vBg0Rdcw0Jf70D/4gIo8MSQojT0tVzBFuAqcB9zvfNbZTZDvRVSmUCh4FrgesAjiYRZ7krgW+6GE+3stfUULR0KRUvbCIwLY30p57EPHKk0WEJIUSXdDUR3Af8XSl1E/AjcA2AUqoXsE5rPUFrbVNKzQC2Av7Aeq31Lmf9B5RSw3B0FR0A/tDFeLpNzb/+heWeXGxFRcRMm0b87X/CLzTU6LCEEKLLupQItNalwEVtzD8CTGg1/QZwwqWhWuvru/L9PcFWXk7hvYupevVVgs7oQ8aKjYQMHWp0WEII4TJyZ3E7tNZUv/kmBQsXYa+qIu6224j9w3QZJE4I4XUkEbShqbCQgnnzqfnnPzGdeSbpTz6Jqd/PjA5LCCG6hSSCVrTWVLz4IkUPLEHbbCT87W/ETL0B5e9vdGhCCNFtJBE4WX/8EcucudR98gmhZ59N8oL5BPXubXRYQgjR7Xw+ERwdJK54xQpUQABJ8+YRdc3VMj6QEMJn+HQiaPjhByw5c2j4+mvCfvlLknLvITApyeiwhBCiR/lkItBWKyVrH6fkscfwDwuj19KlRFw2QcYHEkL4JJ9LBPVff41ldg6Ne/YQMXEiiXffRUBMjNFhCSGEYXwqEZSsXk3xw48QEB9P6upVhI8ebXRIQghhOJ9KBIFp6Y5B4u6YiX94uNHhCCGEW/CpRBA58TIiJ15mdBhCCOFW5BpJIYTwcZIIhBDCx0kiEEIIHyeJQAghfJwkAiGE8HGSCIQQwsdJIhBCCB8niUAIIXyc0lobHUOnKaWKgYNGx9GGOKDE6CBczBvbBN7ZLmmTZzCyTb211vHHz/TIROCulFI7tNbZRsfhSt7YJvDOdkmbPIM7tkm6hoQQwsdJIhBCCB8nicC11hodQDfwxjaBd7ZL2uQZ3K5Nco5ACCF8nBwRCCGEj5NEIIQQPk4SQScppWKUUtuUUnuc79HtlLtUKfW9UmqvUmpWq/m5SqnDSqkvna8JPRd9x2JstVwppVY6l3+tlDqro3WN0sU2HVBK7XT+Ljt6NvL2daBN/ZVSHymlGpVSd3SmrlG62Ca3/J2gQ+2a4vx397VS6j9KqaEdrduttNby6sQLeACY5fw8C7i/jTL+wD4gCwgCvgIGOpflAne4QTvajbFVmQnAm4ACRgKfdLSup7XJuewAEGd0O06jTQnACGBR639bHv47tdkmd/2dOtGuXwDRzs/j3eX/lBwRdN4k4Gnn56eByW2UORvYq7XO01pbgRec9dxJR2KcBGzQDh8DUUqp5A7WNUJX2uSuTtkmrXWR1no70NTZugbpSpvcWUfa9R+tdblz8mMgtaN1u5Mkgs5L1FpbAJzvCW2USQEOtZrOd847aobz0HB9e11LPeBUMZ6sTEfqGqErbQLQwNtKqc+UUtO7LcrO6crftSf/Tifjjr8TdL5dN+E4Oj2dui7lUw+v7yil1P8BSW0smt3RVbQx7+h1uquBBc7pBcAy4MbOxugCJ4vxVGU6UtcIXWkTwHla6yNKqQRgm1LqO631v10aYed15e/ak3+nk3HH3wk60S6l1GgcieD8ztbtDpII2qC1HtveMqVUoVIqWWttcXYpFLVRLB9IazWdChxxrruw1boeB15zTdSd1m6MHSgT1IG6RuhKm9BaH30vUkq9guNw3egNTEfa1B11u1OX4nLT3wk62C6l1BBgHTBea13ambrdRbqGOm8LMNX5eSqwuY0y24G+SqlMpVQQcK2zHsf1R18JfNONsZ5MuzG2sgW4wXmlzUig0tkd1pG6RjjtNimlzEqpcACllBm4GON+m9a68nftyb9Tm9z4d4IOtEsplQ68DFyvtf6hM3W7ldFn2j3tBcQC7wB7nO8xzvm9gDdalZsA/IDjSoDZreY/A+wEvnb+0MkGtuWEGIFbgFucnxXwqHP5TiD7VO0z+nW6bcJxtcZXztcuD2tTEo49yiqgwvk5wsN/pzbb5M6/UwfbtQ4oB750vnacrG5PvWSICSGE8HHSNSSEED5OEoEQQvg4SQRCCOHjJBEIIYSPk0QghBA+ThKBEEL4OEkEQgjh4/4fICla9dXXNfYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Aproximacao de xi4 pelo MPF\n",
    "\n",
    "g = '( 0.9*(5/21 + x**5))**1./3.' \n",
    "#g = eval('lambda x:' + g)\n",
    "\n",
    "#plt.plot(x,g(x))\n",
    "rz.ponto_fixo(0.4,p,g,tol,nmax,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### item b.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimativas iniciais: xa = 0.8; xb = 1.0 \n",
      "\n",
      "i\t x\t\t f(x)\t\t ER\n",
      "1\t 0.857094\t -0.032986\t 1.667334e-01\n",
      "2\t 0.886562\t -0.015467\t 3.323813e-02\n",
      "3\t 0.912577\t 0.005764\t 2.850796e-02\n",
      "4\t 0.905514\t -0.000579\t 7.799970e-03\n",
      "5\t 0.906159\t -0.000018\t 7.112008e-04\n",
      "Solução obtida: x = 0.9061586909\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9061586908755153"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Aproximacao de xi5 pelo MS\n",
    "\n",
    "p = 'x**5 - 10/9*x**3 + 5/21*x'\n",
    "x0,x1=0.8,1.\n",
    "rz.secante(x0,x1,p,tol,nmax,True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemplos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=1 a=0.000000 b=1.000000 xm=0.500000 f(a)=3.000000 f(b)=-5.000000 f(xm)=-1.375000 b-a=1.000000\n",
      "i=2 a=0.000000 b=0.500000 xm=0.250000 f(a)=3.000000 f(b)=-1.375000 f(xm)=0.765625 b-a=0.500000\n",
      "i=3 a=0.250000 b=0.500000 xm=0.375000 f(a)=0.765625 f(b)=-1.375000 f(xm)=-0.322266 b-a=0.250000\n",
      "i=4 a=0.250000 b=0.375000 xm=0.312500 f(a)=0.765625 f(b)=-0.322266 f(xm)=0.218018 b-a=0.125000\n",
      "i=5 a=0.312500 b=0.375000 xm=0.343750 f(a)=0.218018 f(b)=-0.322266 f(xm)=-0.053131 b-a=0.062500\n",
      "i=6 a=0.312500 b=0.343750 xm=0.328125 f(a)=0.218018 f(b)=-0.053131 f(xm)=0.082203 b-a=0.031250\n",
      "i=7 a=0.328125 b=0.343750 xm=0.335938 f(a)=0.082203 f(b)=-0.053131 f(xm)=0.014474 b-a=0.015625\n",
      "i=8 a=0.335938 b=0.343750 xm=0.339844 f(a)=0.014474 f(b)=-0.053131 f(xm)=-0.019344 b-a=0.007812\n",
      "i=9 a=0.335938 b=0.339844 xm=0.337891 f(a)=0.014474 f(b)=-0.019344 f(xm)=-0.002439 b-a=0.003906\n",
      "i=10 a=0.335938 b=0.337891 xm=0.336914 f(a)=0.014474 f(b)=-0.002439 f(xm)=0.006017 b-a=0.001953\n",
      "i=11 a=0.336914 b=0.337891 xm=0.337402 f(a)=0.006017 f(b)=-0.002439 f(xm)=0.001789 b-a=0.000977\n",
      "Solução encontrada: 0.33740234375\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.33740234375"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# exemplo bissecao\n",
    "rz.bissecao('x**3-9*x+3',0,1,1e-3,100,var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=1 a=0.000000 b=1.000000 xm=0.375000 f(a)=3.000000 f(b)=-5.000000 f(xm)=-0.322266 b-a=1.000000\n",
      "i=2 a=0.000000 b=0.375000 xm=0.338624 f(a)=3.000000 f(b)=-0.322266 f(xm)=-0.008790 b-a=0.375000\n",
      "i=3 a=0.000000 b=0.338624 xm=0.337635 f(a)=3.000000 f(b)=-0.008790 f(xm)=-0.000226 b-a=0.338624\n",
      "Solução encontrada: 0.33763504551140067\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.33763504551140067"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rz.falsa_posicao('x**3-9*x+3',0,1,1e-3,100,var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problemas aplicados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A temperatura $T$ (em graus Kelvin) de um semicondutor pode ser calculada como uma função da resistência $R$ (em ohms) pela equação de Steinhart-Hart: \n",
    "\n",
    "$$T = \\dfrac{1}{A + B\\ln(R) + C\\ln(R)^3},$$\n",
    "\n",
    "para constantes $A$, $B$ e $C$ dependentes do material. Supondo que $A = 1.4056 \\times 10^{-3}$, $B = 240.7620 \\times 10^{-6} K^{-1}$ e $C = 7.48 \\times 10^{-7}$, determine a resistência do semicondutor para uma temperatura de 135 graus Celsius.\n",
    "\n",
    "**Sugestão:** use o método da bisseção e tolerância de $10^{-6}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução computacional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Para 135.00 graus Celsius, a resistência é de 61.61 ohms\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import bisect\n",
    "\n",
    "# constantes\n",
    "A = 1.4056e-3\n",
    "B = 240.7620e-6\n",
    "C = 7.48e-7\n",
    "Tc = 135.0 # temperatura em Celsius\n",
    "Tk = Tc + 273.15 # temperatura em Kelvin\n",
    "\n",
    "# f(R) = 0\n",
    "f = lambda R: 1/(A + B*np.log(R) + C*np.log(R)**3) - Tk\n",
    "\n",
    "# localização \n",
    "R = np.linspace(1,100,50,True)\n",
    "plt.plot(R,f(R))\n",
    "plt.xlabel('$R$')\n",
    "plt.ylabel('$T$')\n",
    "\n",
    "# refinamento a=1; b=100\n",
    "x = bisect(f,1,100,xtol=1e-6)\n",
    "print(\"Para {0:.2f} graus Celsius, a resistência é de {1:.2f} ohms\".format(Tc,x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- Gilat/Subramanian 3.22-->\n",
    "## Problema aplicado (revisar!)\n",
    "\n",
    "Quando se calcula o pagamento de uma hipoteca, a relação entre o montante do empréstimo $E$, o pagamento mensal $P$, a duração do empréstimo em anos $a$, e a taxa de juros anual $t$ é dada pela equação: \n",
    "\n",
    "$$P = \\dfrac{Et}{12\\left( 1 - \\dfrac{1}{\\left(1 + \\frac{t}{12}\\right)^{12a}} \\right)}.$$\n",
    "\n",
    "Determine a taxa $t$ de um empréstimo de R<span>&#36;</span> 170.000 00 por 20 anos se o pagamento mensal for de R<span>&#36;</span> 1.250,00. \n",
    "\n",
    "**Sugestão:** usar método de Newton como função programada pelo estudante ou função residente.\n",
    "\n",
    "### Solução computacional\n",
    "\n",
    "Resolver o problema $f(t) = 0$ com método de Newton."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0632479251521274, 'A taxa do empréstimo é de 6.32% a.a.')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import newton \n",
    "from sympy.utilities.lambdify import lambdastr\n",
    "\n",
    "E = 170000 # montante do empréstimo\n",
    "P = 1250 # pagamento mensal\n",
    "a = 20 # duração do empréstimo em anos\n",
    "\n",
    "# define função para computar \n",
    "# t: taxa de juros (incógnita)\n",
    "def taxa_anuidade(E,P,a):\n",
    "\n",
    "    Esym,t,asym,Psym = sy.symbols('Esym t asym Psym')\n",
    "\n",
    "    fsym = Esym*t/( 12*(1 - 1/(1 + t/12)**(12*asym) ) ) - Psym \n",
    "    dfsym = sy.diff(fsym,t)\n",
    "\n",
    "    f = fsym.subs({'Esym':E,'asym':a,'Psym':P})\n",
    "    df = dfsym.subs({'Esym':E,'asym':a,'Psym':P})\n",
    "\n",
    "    ft = eval(lambdastr(t,f))\n",
    "    dft = eval(lambdastr(t,df))\n",
    "\n",
    "    # Aplicação do método de Newton \n",
    "\n",
    "    # parâmetros \n",
    "    t0 = 1.0 # estimativa inicial\n",
    "    tole=1e-3 # tolerância de erro\n",
    "    nmax=50 # número máximo de iterações \n",
    "\n",
    "    # método de Newton \n",
    "    t = newton(ft,t0,dft,tol=tole,maxiter=nmax)    \n",
    "    msg = \"A taxa do empréstimo é de {0:.2f}% a.a.\".format(t*100)\n",
    "    \n",
    "    return (t,msg)\n",
    "\n",
    "# invoca função\n",
    "taxa_anuidade(E,P,a)\n",
    "# não sei se a equação do livro está correta: negativo até 12 \n",
    "# aa = np.arange(1,50)\n",
    "# tt = []\n",
    "# for i in aa:\n",
    "#     t=taxa_anuidade(E,P,i)\n",
    "#     print(t[1])\n",
    "#     tt.append(t[0])\n",
    "# tt = np.asarray(tt)\n",
    "# plt.plot(aa,tt)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "ipub": {
   "listcode": true,
   "listfigures": true,
   "listtables": true,
   "titlepage": {
    "author": "Gustavo P. Oliveira e Smith Lima",
    "email": "gustavo.oliveira@ci.ufpb.br",
    "institution": "Universidade Federal da Paraíba",
    "subtitle": "Soluções - Lista 02",
    "tagline": "Em preparação.",
    "title": "Cálculo Numérico"
   },
   "toc": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
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 },
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