lista-2-solucoes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "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": [
    "# Lista de Exercícios 2 \n",
    "\n",
    "## Descrição \n",
    "\n",
    "Solucionário matemático e computacional da Lista de Exercícios 2.\n"
   ]
  },
  {
   "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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\n",
      "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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\n",
      "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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\n",
      "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": {
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "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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\n",
      "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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\n",
      "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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\n",
      "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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\n",
      "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\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",
    "$$P = \\dfrac{Et}{12\\left( 1 - \\dfrac{1}{\\left(1 + \\frac{t}{12}\\right)^{12a}} \\right)}.$$\n",
    "\n",
    "Determine a taxa $t$ de um empréstimo de R\\$ 170.000,00 por 20 anos se o pagamento mensal for de R\\$ 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problema \n",
    "\n",
    "Um jogador de futebol americano está prestes a fazer um lançamento para outro jogador de seu time. O lançador tem uma altura de 1,82 m e o outro jogador está afastado de 18,2 m. A expressão que descreve o movimento da bola é a familiar equação da física que descreve o movimento de um projétil:\n",
    "\n",
    "$$y = x\\tan(\\theta) - \\dfrac{1}{2}\\dfrac{x^2 g}{v_0^2}\\dfrac{1}{\\cos^2(\\theta)} + h,$$\n",
    "\n",
    "onde $x$ e $y$ são as distâncias horizontal e verical, respectivamente, $g=9,8 \\, m/s^2$ é a aceleração da gravidade, $v_0$ é a velocidade inicial da bola quando deixa a mão do lançador e $\\theta$ é o Ângulo que a bola faz com o eixo horizontal nesse mesmo instante. Para $v_0 = 15,2 \\, m/s$, $x = 18,2 \\, m$, $h = 1,82 \\, m$ e $y = 2,1 \\, m$, determine o ângulo $\\theta$ no qual o jogador deve lançar a bola. \n",
    "\n",
    "Resolva aplicando bisseção, Newton ou secantes.\n",
    "\n",
    "#### Solução computacional:"
   ]
  }
 ],
 "metadata": {
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   "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
  },
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