{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#1\" data-toc-modified-id=\"1-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>1</a></div><div class=\"lev2 toc-item\"><a href=\"#1(b)\" data-toc-modified-id=\"1(b)-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>1(b)</a></div><div class=\"lev1 toc-item\"><a href=\"#2\" data-toc-modified-id=\"2-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>2</a></div><div class=\"lev2 toc-item\"><a href=\"#2(b)\" data-toc-modified-id=\"2(b)-21\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>2(b)</a></div><div class=\"lev1 toc-item\"><a href=\"#3(a)\" data-toc-modified-id=\"3(a)-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>3(a)</a></div><div class=\"lev2 toc-item\"><a href=\"#3(b)\" data-toc-modified-id=\"3(b)-31\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>3(b)</a></div><div class=\"lev1 toc-item\"><a href=\"#4\" data-toc-modified-id=\"4-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>4</a></div><div class=\"lev2 toc-item\"><a href=\"#3(b)\" data-toc-modified-id=\"3(b)-41\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>3(b)</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"text-align: center;\">\n",
    "   <font size=\"5\"> 2018年度　数式処理演習　pre試験問題 </font>\n",
    "</div>\n",
    "   <div style=\"text-align: right;\">\n",
    "   <font size=\"3\"> cc by Shigeto R. Nishitani</font>\n",
    "</div>\n",
    "\n",
    "* file: ~/symboic_math/exams/18_pre/exam18_0_pre_ans.ipynb\n",
    "\n",
    "\n",
    "# 1線形代数\n",
    "## 1(a)\n",
    "関数$\\sin x \\cos^3 x$を15次程度までTaylor展開し，両方の関数をx=0..Pi/2 で同時にplotせよ．また，最初の関数を x=0..x で積分して得られた関数を示せ．さらに得られた関数を最初の関数とともに0..2*Piでplotせよ．(20点)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sin{\\left(x \\right)} \\cos^{3}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "          3   \n",
       "sin(x)⋅cos (x)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "x = symbols('x')\n",
    "f = sin(x)*cos(x)**3\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "fs = f.series(x,0,15)\n",
    "f0 = fs.removeO()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{8194 x^{13}}{6081075} - \\frac{82 x^{11}}{6237} + \\frac{257 x^{9}}{2835} - \\frac{26 x^{7}}{63} + \\frac{17 x^{5}}{15} - \\frac{5 x^{3}}{3} + x$"
      ],
      "text/plain": [
       "      13       11        9       7       5      3    \n",
       "8194⋅x     82⋅x     257⋅x    26⋅x    17⋅x    5⋅x     \n",
       "──────── - ────── + ────── - ───── + ───── - ──── + x\n",
       "6081075     6237     2835      63      15     3      "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf71854520>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(f,f0,(x,0,pi/2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = integrate(f,(x,0,x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf719d9730>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(f,g,(x,0,2*pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1(b)\n",
    "資料を参考にして，次の2重積分を求めよ．(10点)\n",
    "\\begin{equation*}\n",
    "\\int \\int_D \\sqrt{x^2-\\frac{1}{2}y^2}\\hspace{2mm}dxdy,\\hspace{5mm} D:0\\leqq y \\leqq x \\leqq 1 \n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\sqrt{x^{2} - \\frac{y^{2}}{2}}$"
      ],
      "text/plain": [
       "     _________\n",
       "    ╱       2 \n",
       "   ╱   2   y  \n",
       "  ╱   x  - ── \n",
       "╲╱         2  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "y = symbols('y')\n",
    "x = symbols('x',positive = True)\n",
    "f = sqrt(x**2-Rational(1/2)*y**2)\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} x^{2}}{4} + \\frac{\\sqrt{2} \\pi x^{2}}{8}$"
      ],
      "text/plain": [
       "    2         2\n",
       "√2⋅x    √2⋅π⋅x \n",
       "───── + ───────\n",
       "  4        8   "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int1 = integrate(f,(y,0,x))\n",
    "int1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2}}{12} + \\frac{\\sqrt{2} \\pi}{24}$"
      ],
      "text/plain": [
       "√2   √2⋅π\n",
       "── + ────\n",
       "12    24 "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(int1, (x,0,1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2\n",
    "## 2(a)\n",
    "資料を参考にして，$\\boldsymbol{R^n}$のベクトル$\\boldsymbol{a,b,c}$が一次独立のとき，$\\boldsymbol{a}+\\boldsymbol{b}, \\boldsymbol{a}-\\boldsymbol{b}+\\boldsymbol{c}, \\boldsymbol{a}-3\\boldsymbol{b}+2\\boldsymbol{c}$は一次独立であるかどうか調べよ．(15点)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 1 & 1\\\\1 & -1 & -3\\\\0 & 1 & 2\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  1   1 ⎤\n",
       "⎢         ⎥\n",
       "⎢1  -1  -3⎥\n",
       "⎢         ⎥\n",
       "⎣0  1   2 ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=Matrix([[1,1,1],[1,-1,-3],[0,1,2]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAA9klEQVR4nJ3SvyvFYRTH8dfl/gcGs90fcWWyGMiIgU1JGZRS30w2KcVguP+ADCIWEpNSBkkyyOImKZPBz+H7qNO3b/d++dTTOZ3nvE/n8/TUsizzV3WFvAfT2MEd3vCKM0zF3nqAxrCBRxzjAb0YwRaGUs93hG4xjD18hfoizjGaBmzH9Y6wWwCghc2UN4qe2uk9xY+qUB0TKT+oCq2gH/s4rALNYh43GP8ttoNmsIZrDOClEzSHdVwloBUvy6AFrOIyAU/FhiK0JDd+gUE8l60Rf8QklvGJU/kjFHWPZoT6UuyWeyrTCZpxvQy1DqdR5qmS/gX9ALg2MQ/Qmy4sAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle 2$"
      ],
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.rank()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2(b)\n",
    "資料を参考にして，グラム・シュミットの直交化法により，つぎのベクトルから$\\boldsymbol{R}^3$の正規直交基底をつくれ．(15点)\n",
    "\\begin{equation*}\n",
    "\\boldsymbol{x}_1 = (1,1,0), \\hspace{5mm}\n",
    "\\boldsymbol{x}_2=(1,0,-1), \\hspace{5mm}\n",
    "\\boldsymbol{x}_3=(0,-1,1)\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1=Matrix([1,1,0])\n",
    "x2=Matrix([1,0,-1])\n",
    "x3=Matrix([0,-1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡√2⎤\n",
       "⎢──⎥\n",
       "⎢2 ⎥\n",
       "⎢  ⎥\n",
       "⎢√2⎥\n",
       "⎢──⎥\n",
       "⎢2 ⎥\n",
       "⎢  ⎥\n",
       "⎣0 ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1=x1\n",
    "a1=y1/y1.norm()\n",
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2=x2-(x2.T*a1)[0]*a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1\\\\0\\\\-1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1 ⎤\n",
       "⎢  ⎥\n",
       "⎢0 ⎥\n",
       "⎢  ⎥\n",
       "⎣-1⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2}\\\\\\frac{1}{2}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1/2⎤\n",
       "⎢   ⎥\n",
       "⎢1/2⎥\n",
       "⎢   ⎥\n",
       "⎣ 0 ⎦"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2a = (x2.T*a1)[0]*a1\n",
    "x2a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2}\\\\- \\frac{1}{2}\\\\-1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1/2 ⎤\n",
       "⎢    ⎥\n",
       "⎢-1/2⎥\n",
       "⎢    ⎥\n",
       "⎣ -1 ⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y2 = x2-x2a\n",
    "y2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{6}}{6}\\\\- \\frac{\\sqrt{6}}{6}\\\\- \\frac{\\sqrt{6}}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ √6 ⎤\n",
       "⎢ ── ⎥\n",
       "⎢ 6  ⎥\n",
       "⎢    ⎥\n",
       "⎢-√6 ⎥\n",
       "⎢────⎥\n",
       "⎢ 6  ⎥\n",
       "⎢    ⎥\n",
       "⎢-√6 ⎥\n",
       "⎢────⎥\n",
       "⎣ 3  ⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2=y2/y2.norm()\n",
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "x3a1 = (x3.T*a1)[0]*a1\n",
    "x3a1\n",
    "x3a2 = (x3.T*a2)[0]*a2\n",
    "x3a2\n",
    "y3=x3-x3a1-x3a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2}{3}\\\\- \\frac{2}{3}\\\\\\frac{2}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡2/3 ⎤\n",
       "⎢    ⎥\n",
       "⎢-2/3⎥\n",
       "⎢    ⎥\n",
       "⎣2/3 ⎦"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{3}}{3}\\\\- \\frac{\\sqrt{3}}{3}\\\\\\frac{\\sqrt{3}}{3}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ √3 ⎤\n",
       "⎢ ── ⎥\n",
       "⎢ 3  ⎥\n",
       "⎢    ⎥\n",
       "⎢-√3 ⎥\n",
       "⎢────⎥\n",
       "⎢ 3  ⎥\n",
       "⎢    ⎥\n",
       "⎢ √3 ⎥\n",
       "⎢ ── ⎥\n",
       "⎣ 3  ⎦"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3 = y3/y3.norm()\n",
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[0]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3.T*a1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3\n",
    "座標平面上で，放物線$\\displaystyle y=\\frac{1}{2}x^2+\\frac{1}{2}$を$C_1$とし，放物線$\\displaystyle y=\\frac{1}{4}x^2$を$C_2$とする．\n",
    "\n",
    "## 3(a)\n",
    "実数$a$に対して，2直線$x=a,x=a+1$と$C_1,C_2$で囲まれた図形$D$の面積$S$は\n",
    "\\begin{eqnarray*}\n",
    "S &=& \\int_{a}^{a+1} \\left(\\frac{1}{\\fbox{ ア }}x^2 + \\frac{1}{\\fbox{ イ }}\\right) dx \\\\\n",
    "&=& \\frac{a^2}{\\fbox{ ウ }}+\\frac{a}{\\fbox{ エ }}+\\frac{\\fbox{ オ }}{\\fbox{ カキ }}\n",
    "\\end{eqnarray*}\n",
    "である．$S$は$\\displaystyle a=\\frac{\\fbox{ クケ }}{\\fbox{ コ }}$で最小値$\\displaystyle \\frac{\\fbox{ サシ }}{\\fbox{ スセ }}$をとる．\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "\n",
    "a, x = symbols('a x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2}}{2} + \\frac{1}{2}$"
      ],
      "text/plain": [
       " 2    \n",
       "x    1\n",
       "── + ─\n",
       "2    2"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C1 = Rational(1/2)*x**2 + Rational(1/2)\n",
    "C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2}}{4}$"
      ],
      "text/plain": [
       " 2\n",
       "x \n",
       "──\n",
       "4 "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C2 = Rational(1/4)*x**2\n",
    "C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{2}}{4} + \\frac{a}{4} + \\frac{7}{12}$"
      ],
      "text/plain": [
       " 2         \n",
       "a    a   7 \n",
       "── + ─ + ──\n",
       "4    4   12"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S = expand(integrate(C1-C2,(x,a,a+1)))\n",
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{1}{2}$"
      ],
      "text/plain": [
       "-1/2"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0 = solve(diff(S,a),a)[0]\n",
    "S0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{25}{48}$"
      ],
      "text/plain": [
       "25\n",
       "──\n",
       "48"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.subs({a:S0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3(b)\n",
    "4点$(a,0),(a+1,0),(a+1,1),(a,1)$を頂点とする正方形を$R$で表す．$a$が$a\\geqq0$の範囲を動くとき，正方形$R$と(a)の図形$D$の共通部分の面積を$T$とおく．$T$が最大となる$a$の値を求めよう．\n",
    "\n",
    "直線$y=1$は$C_1$と$\\left(\\pm \\fbox{ ソ },1\\right)$で，$C_2$と$\\left(\\pm \\fbox{ タ },1\\right)$で交わる．したがって，正方形$R$と図形$D$の共通部分が空集合にならないのは，$0 \\leqq a \\leqq \\fbox{ チ }$のときである．\n",
    "\n",
    "$\\fbox{ ソ } \\leqq a \\leqq \\fbox{ チ }$のとき，正方形$R$は放物線$C_1$と$x$軸の間にあり，この範囲で$a$が増加するとき，$T$は\\fbox{ ツ　減少する }．\n",
    "\n",
    "したがって，$T$が最大になる$a$の値は，$0 \\leqq a \\leqq \\fbox{ ソ }$の範囲にある．\n",
    "\n",
    "$0 \\leqq a \\leqq \\fbox{ ソ }$のとき，(a)の図形$D$のうち，正方形$R$の外側にある部分の面積$U$は\n",
    "\\begin{equation*}\n",
    "U = \\frac{a^3}{\\fbox{ テ }} + \\frac{ a^2 }{\\fbox{ ト }}\n",
    "\\end{equation*}\n",
    "である．よって，$0 \\leqq a \\leqq \\fbox{ ソ }$において\n",
    "\\begin{equation}\n",
    "T = - \\frac{a^3}{\\fbox{ ナ }} - \\frac{a^2}{\\fbox{ ニ }} + \\frac{a}{\\fbox{ ヌ }} + \\frac{ オ }{\\fbox{ カキ }}\n",
    "\\end{equation}\n",
    "である．(1)の右辺の増減を調べることにより，$T$は\n",
    "\\begin{equation}\n",
    "a = \\frac{ \\fbox{ ネノ } + \\sqrt{\\fbox{ ハ }}} {\\fbox{ ヒ }}\n",
    "\\end{equation}\n",
    "で最大値をとることがわかる．(10点)\n",
    "\n",
    "(2016年度大学入試センター試験　本試験　数学II・B第2問)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ -1, \\  1\\right]$"
      ],
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(C1-1,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ -2, \\  2\\right]$"
      ],
      "text/plain": [
       "[-2, 2]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(C2-1,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uSwaQZpIQEa/T1mPnzpe38dH+Bm6ZlcWPLxijZTL8kAJKRLzK/mMdfG9pCdWtPdxzSR7XFmfqGUo/pYASEa+xYlctP3l1B5GhQbz03WmaidzPKaBExOMcThePrTnMg+8doCAjjseuK2So7jf5PQWUiHhUY6eV21/axieHm7j93Bx+eG6O7jcJoIASEQ/adrSFH7ywleYuG3+4YiLfKsrwdEniRRRQIjLgTNPkhU1H+c3bexgWG8brt84gLy3W02WJl1FAiciA6rY5+OUbu/nH1mrOGZPEH79dQFxEiKfLEi+kgBKRAVPW0Mmtz5cSFRbMneeP4vZzRxEQoCHkcmIKKBEZEMt31vLz13cSHGhw14JczhmT7OmSxMspoETErWwOF/eu2Mczn5QzKTOOP18zmdS4cE+XJYOAAkpE3KaqpZsfvriNHZWt3HRWFr+YP5aQIM1CLn2jgBIRt/hgXx1/+uAgZQ1d/PXaycyfkOLpkmSQUUCJSL+yOVzcv/JTnlh3hNmjEnnrP2aSlRjp6bJkEFJAiUi/qWzu5rYXt7Kjqo0bpg/nrgW5hAVrVgg5PQooEekXK3b1jtIDdElP+oUCSkTOiMXu5LfL97F0YwX5GXE8evUkMuIjPF2W+AAFlIictkP1nfz4le3sqGrju7Oy+OkFGqUn/UcBJSJfm2mavFpaxa/f3MPUrCE8eUMR5+UO9XRZ4mMUUCLytbT12Pnvf+5i2c5apmcn8PvL8xkWq7WbpP8poESkz0ormrn9pe0ca7fw0wvG8P2zRxKoufTETRRQInJKDqeLZzeUc++KT0mNC+PV709ncuYQT5clPk4BJSJfqbK5mzv/vp3SihZunpXF7eeNIiYs2NNliR9QQInICZmmyetbq7n7rT0YBjx8VQHfLEjzdFniRxRQIvIlrd02/vufu1m+q5apWfE8dGU+6UP0bJMMLAWUiPyLjWVN3Pnydho7rfxs3hi+N1sDIcQzFFAiAvTOCPG7dz7l+Y3lzMhJ5G/fKGJCeqynyxI/pke+RYSdVa1c+Ke1PPNJOddNG8Hj1ymcpJdpmny0v55v/nk9tW09A3ps9aBE/Jjd6WLphgruXbGPxKhQli6eyqxRSZ4uS7zE7uo27l2xj08ONzE8IYJjbRZSYgduNWQFlIifOlDXwY9f2cG+2jauLh7OT+aOITZCw8eldyXkB989wD+3VTMkIphfXzSOa4uHD/g8iwooET/jdJn8bW0ZD717gOiwIB69ZjLz8rQ0hvSO3vzzR4coKW9hb207t54zklvPGemx594UUCJ+pKyhk5+8uoOtR1uZN34Y91yaR2JUqKfLEg+z2J08vb6cv6w+RKfVwWWT0nj0msmkDRm4y3knooAS8QNOl8nT64/w4qajdNkcPHxVARfnp2IYGj7uz5wukze2V/PAqv3UtlmYMyaJn88fy9hhMZ4uDVBAifi8Q/Wd/Oy13l7T+blD+e2leQyN0ezj/sw0Td7bW8cfVu0nJjyI5OhQHrqygOkjEzxd2r9QQIn4KIfTxRPrjvDQeweICAlUr0kA2FTWxO9XfsrWo61kJ0Zy01lZLJiQ4pXfF24LqMrKShYtWsSxY8cICAjglltu4Y477nDX4UTkC/bVtvOrN3dT2dzDnDFJ/N8leSRHq9fkz/bWtLN0Yzkvba5kaEwo9102gW8VphMU6L2Pw7otoIKCgnjwwQeZPHkyHR0dFBYWMnfuXMaNG+euQ4r4PavDyaMfHuKvqw8TGx7MPZfmMW/8MK/861gGxpHGLh567wBv76hhzLAofj5vDDfOyCI8JNDTpZ2S2wIqJSWFlJTeoavR0dHk5uZSXV2tgBJxk9KKZn7++i4O1Xdy2eQ0/ufCcQyJDPF0WeIhtW09/OmDg7xSUkVIYAA/nDOSW2aPJDZ88DzrNiD3oMrLy9m2bRvFxcUDcTgRv9JhsfOX1Yd4bE0ZqbHhPHvTVM4erdkg/FVjp5XHVh9mX207m8ubuX7acH4wZ+SgvMTr9oDq7Ozk8ssv549//CMxMV8eurhkyRKWLFkCQENDg7vLEfEpq/Yc49dv7iE+MoQbpo/gpxeMITJUY5/8UVu3nSVrD/P0+nIsdidXT83kd5dPJCN+8C6TYpimeab7OOkO7HY7Cxcu5IILLuBHP/rRKXdUVFRESUnJmdYj4vNq23r49Zt7eHdvHWOHRXPfZROYpCXY/VKn1cHT646wZG0ZHRYHF+Wncuf5oxiZFOXp0r5Kn26Kuu1PLdM0Wbx4Mbm5uX0KJxE5NafL5LkN5Tywaj9O0+QX88eyeGYWwV48Ekvco8fm5NWSSv74wUGau2zMHTeUH80dTW6Kdzxk2x/cFlDr169n6dKlTJgwgYKCAgDuvfdeFixY4K5Divi0XVVtPLGujDe31zB7dBL3fDOPzITBe/lGTo/F7uSFTUf56+rDxEcGMz41hp98Ywz5GXGeLq3fuS2gZs6cST9cPhTxe209dh56dz9LN1YQHxnCX66ZzPwJGjrub6wOJy9vruTPHx2ivsPK9OwE/nPuaKZmxXu6NLfR3VQRL2WaJm9ur+Ge5fto7rJy/bTh/OgbYwbVMGE5c1aHk7e31/DgeweobbMwdUQ8D181yeumJXIHBZSIFzpY185vl3/K6gMN5KfH8vSNU7TCrZ+xOpy8UlLFXz86RHuPnfzMOB74Vj4zRib4Te9ZASXiRTqtDv70wUGeWneEGTmJ3HNJHldPzSQwwD9+IcnxYNpSyV9WH6a2zcLkzDh+f8VEZuYk+k0wfUYBJeIFTNPkrR01/Hb5Puo7rHy7KIOfzRtDgtZq8hsWu5PXSip57OMyqlp6KBw+hPv9NJg+o4AS8bC9NW385u29bDrSzMT0WJYsKqLAB0dkyYn12Jy8uPkoj685TH2HlSsmp3HJZemcleM/l/JORgEl4iHNXTYefHc/L20+yuxRSdx32QSuLMrQ5Tw/0WV1sHRjBU+sLaOx08a07Hj+eFUB07MVTJ9RQIkMMLvTxdINFfzx/QN02ZzcMGMEd543mtgIjc7zB209dp77pJy1hxrZfKSZWaMSuf28UUwZ4bvDxU+XAkpkAK3ZX8//Ld/HofpOZo1K5FcLxzFqaLSny5IB0NRp5cl1R1i6oYIOq4NvT0nnrvljNUXVV1BAiQyAQ/Ud/Hb5Prptzt6VbhcVcV5usi7l+IHath6WfFzGS5uPYnW4WJCXwg/mjGR8qh4bOBUFlIgbNXVa+eP7B3lx81EiQgK587xRXDd9OKFB3r9YnJyZI41dPL7mMLuq2/j0WAeXFKRx6zkjyUn26klcvYoCSsQNLPbeiTzvX7mfbruT64ozueP80cRrAUGft7u6jb+uPsyK3bUEBwZwy6xsHruucFAve+EpCiiRfuRymby5o5oHVh2gy+ZgRk4CP71gDDnJus/ky0zTZGNZM39dc5iPDzQQHRrE988eyU1nZZEUrWfZTpcCSqSfrDvYyL0r9rG3tp28tBj+cMVEZuQkeroscSOXy+TdvXU8tuYQLd12uqwOfjZvDNdNG05MmEZlnikFlMgZ2l3dxnMbynmlpIq0uHAevqqAiyamEqDnmXyW1eHkn1urWfJxGWWNXWTGR/Af5+ZwUX4qYcG6v9hfFFAip6m8sYsH3t3Psp21xIYH8ZuLx3PV1AwNgPBhbd12nt9UzhvbajhY30leWgyPXjOJeeOHEaRFI/udAkrka6pvt/DwBwf5+5ZKggMDuG1ODrecna1LOj6ssrmbp9Yf4e9bKum2OblmaiZ3Xzzer2YW9wQFlEgfNXfZeHzNYXbXtLGprJlrijO57dwckqPDPF2auMmuqlaWrD3Cil21GMDF+ancPCubcam+s6y6N1NAiZxCW4+dJ9eW8eS6I3TbnVxZmM69Pz6b4QmRni5N3MDlMvng03qeWFuGacLe2nYWz8zixhkjSI0L93R5fkUBJXISnVYHz6w/wpKPy2i3OLhwQgp3nj9KUxP5qG6bg9dLq3hqfTlHGrtIjQ1j8cwsnrixSJdvPUQBJfJvOq0OnttQzrqDjXxyuInzc5P5z7mjNTWNjzrWZuHZDeW8uOkobT128jPieOTqSczP08AHT1NAiRzXYbHz3IYK/ra2jNZuO2ePTuSNH86gIEOTefqiHZWtPL3+CPtqOzhY38EF44dx86wsJmcO0cAHL6GAEr/XbrHz7Ppynlh3hLYeO3PGJHH7eaM0y7QPsjtdrNx9jKfXH2Hr0VaiQoO4ZVY2l0wqIjNBUxF5GwWU+K3WbhvPrC/nta1VVLX0cN7YZG4/bxT5Ws3W57R02Xhx81Ge31hBbZuF4QkR/PqicVxRmE607i95LQWU+J36dgtPrDvC8xsr6LY5uWHGcK6YnMGEdN1j8jV7a9p59pMjbDrSTHlTNzNzErnnkjzmjEnWTB+DgAJK/EZlczePrTnMqyVVOFwuLspP5dZzRjJ2mJ5p8SV2p4tVe47x3CcVbC5vJjw4kMWzRnDRxDTGDNMIzMFEASU+b3d1G0s+LqO+w8LWilYuL0zn+2dn6zkmH1PfYeHtHbUs+fgwde1WMuMj+OWFuXyrMIPYCF3GG4wUUOKTTNNk3aFGHl9TxrpDjUSFBnHjjBH88duTGBarmR98hWmabD7SzNKNFazcfYyc5CjGDIvhvsuGc/boZAJ1GW9QU0CJT7E7XazYVcvja8rYW9tOcnQoP583lmuKM4kN11/RvqLDYueNbdUs3VjBgbpOYsKCuGHGCK4tziQ7SSvW+goFlPiEtm47L205yrOflJMSG4bN6eL+yyfyzUmpml3ch+yrbWf5zlqeXn+ELpuTvLQY7r98IhflpxIeonb2NQooGdQON3T2DhUvraLH7mTGyAS+OyuLs0drlJavsNidLN9ZywubKth6tJWI4AC+OSmNb0/JJD89Vg/V+jAFlAw6pmmyoayJJ9Ye4cNP6wkJDOCbBal856wszTLtQw7WdfBKSSWvb62muctGdmIkv7wwl8snpzMkMsTT5ckAUEDJoNFhsfN6aRXPbaygx+bE4TK58/xRXFs8nKToUE+XJ/3AYneyYlctL20+ypbyFoIDDa4tzuSC8SlMy45Xb8nPKKDE6x2s6+C5DRX8Y2sVXTYn+Rlx3DYnhwV5wwgL0bewL9hX287ft1Syr7adTUeaGZEQwV3zx3J5YTqJUfrjw1/pp1u8ks3h4t29x1h7oIG/l1QREhTARRNTWTR9uKYi8hEdFjvv7qnjuY0V7KhsJSQwgPl5Q3nx5mKmZSfoHqIooMS7VDR18dLmSl4rraSx00Z+eiw/nzeWb0/JIF73HQY90zTZUt7CKyWVLN9Zy7jUGHpsDn61cByXTkrTvSX5Fwoo8Tirw8l7e+tYs7+BV0urCAwwOG9sMtcUZzJ7VJL+kvYBde0W3txew0ubj3KksYvIkEAumZTKtwozmJQZp3tLckJuC6ibbrqJZcuWkZyczO7du911GBnEPrvv8Mb2alq77cwalciP5o7myqIMzfbgAyx2J+/vq+O10io+PtCAy4QFE1L4wTkjuXBiChG6fyin4LbvkBtvvJHbbruNRYsWuesQMgi1ddtZubuWFzYfZWdVGyGBAcwdP5RvF2VwVk6ipqYZ5EzTZFd1G6v2HOP5jb0r1KbEhnHrOSO5ojCDrETNfyh9Z5imeab7OOkOysvLWbhwYZ97UPHDc5n7X0+daT3iZUx6115q7LTS0mUnKiwIh9MkOTqUxOhQghRKg57N6aKxw0pDpxWL3UV0WBAhgQEkRYdqiikf8vfvTe+vXfXph97jfewlS5awZMkSAOx2u4erkf7UZXXQ2GmlsdOGw2USFGCQHBNKUlQokaEe/9aTM+QyTZq7bLRbHDR0WAGICg0iKzGchMgQ9YbljHlVD6qoqIiSkpIzrUc86HBDJ29tr+HtHTU4XC6OtVk5f1wyl01K5+wxSQQHBni6RDkDDqeL9Yeb+OfWKlbtqaPH7mR6djxTRsRz2eR0RugSnvTN4OhByeBX09rDsp01vLWjht3V7RgGTMtK4OKCVObnDSMuQkOHBzPTNNld3c4b26s53NDJ6v0NxIQFccmkNC6bnEbR8CEahSduoYCS01LT2sPK3cd4Z3ctB+s6ae2xk58eyy8vzGXhxFSNwvMB5Y1dvLm9hjd3VFPW0EVIYACXTU7jsesmM2dssmaJF7dzW0BdffXVrF69msbGRtLT0/nNb37D4sWL3XU4GQCVzd28s7uWFbuOsb2yFYCxw6K54/xRnDMmWSO0fMCxNgvLdvZeog0LDmRzeTPFWfHcMiub+XkpWplWBpRb70F9XboH5V1M0+RQfSefHG7ktdJqdlW3AZCXFsP8vBTm5w3T4nA+oLnLyopdx3h7Rw2by5sxTZiQFsvlk9O4IG8YKbHhni5RfI/uQcnX53C6KK1o4b29dby/r47ypm5GJUcSGRrMfy0Yy/y8FDLiIzxdppyh1m4b7+6p4+2dNZSUNxMYEMDQmFDuPG80F+Wn6A8P8QoKKKG128bHBxsprWjmre01tHTbCQkMYPrIBG6elc35uUN1T8kHtPXYeW9vHct21rDuYCMOl0lmfAQ3npXFxfmpjB0WrcEO4lUUUH7INE321LSzen89q/c3sPVoCy4T4iOCmTtuKOeMSWb26CSi9KzSoNfabeO9vXWs2FXLsXYL+2o7SIsLZ/HMLBZOTCUvLUahJF5Lv4H8RH2HhfWHGll7sJGa1h42ljUDvfcabpuTwzljk8lPj9PDlT6gsdPK+3vrWLH7GJ8c6u0ppcWFc01xJvddlqhl0mXQUED5qE6rg9KKFtYdbGDtwUY+PdYBwJCIYC6bnM4VhRmcPTpJK9H6iJrWHlbtOcbK3cfYUt5MfGQIkaFB3DwrmwUThjEhTaEkg48Cykd0WR2UVLSwsayJDYeb2FXdhoFJZGgw41Nj+Nm8MczKSWJ8aoyWr/ARh+o7+fhAPW9ur2FHVe8Iy9FDo7htTg7z81IYm6J7SjK4KaAGqZYuG6UVLWypaKampYd3dh/7fL67/Iw4vn92NtOzE5k8PE7LGvgIl8tke1Ur7+6p4929xyhr6KI4Kx4Mg5/PG8sF44dq9J34FP3mGgRcLpOyxi62V7ZQWtFKSXkzB+s7AQgONLg4P5VbZmczLTuBohFDFEg+pMfmZP2hRt7fV0d1aw9rDzYSFGAwfWQCN84Ywfm5Q0mN03NK4pv0m8wL1XdY2FfTTmlFC9sqW9le2UqHxQFAVmIkIxIiuGRS7xxo+RlxhAVryhlfUt9uYc2BBlbtqWPdoQYsdhdRoUFcUZjGFYXpnDMmWUtYiF9QQHmQaZrUd1jZVdXGruo29tT0vq9rtzJlxBBKK1oYMyyGi/JTKciIY3JmHFkJkQRqRnCf4nK52FPTwQef1vHhp/XsrGqjICOOhg4rV03J5LzcZIqzEggJUruLf1FADZAem5MDdR3sP9bB/uPvAw2DNQcbADAMGJkUxYyRiYxPjSE/PY5xqTFaN8lHtVvsrDvYyEef1rN6fz1OE1q6bUzKiOOnF4zhvLHJjNGDs+Ln9Nuvn3VaHZQ1dFLW0EVlcze7a9rYf6yDiuZuPpv2MCw4gNFDoykaHs85Y5OYkBZLborCyJeZpsmnxzpYc6CBTWVNrD0+k0NMWBCzRydxwfhhzBiZQEKUhv2LfEa/EU9Dl9VBRVM3R5u7OdrcRbvFQWl5C2WNndS1Wz/fLjw4gNS4cHJTYrhkUhpjh0UzZlgMmfEReiDWD7R221h3qJE1+xv4+GDD598bCyYM47uzs5kzJpnJmXEE6ZKtyAkpoP6Ny2XS3G2jrs1CdWsPNa091Bz/2GZ3sq2ylcZO27/8mykjhmB3mszMSSI7KZKRSZGMTIoiMyFCa+b4EbvTxfbKVtYeaOh9Fq2mDYvdRWx4MDNHJXL26CTOHp3E0BjNayjSF34RUDaHi7YeO63dNpq6bDR39b5v6rTS2m2nurWH+g4r9e0WGjqsOFwmseHBtPXYAQgNCiAtLpysxEjOzx1KZkIEmfERDI+PJDMhQiOq/JRpmpQ1drL+UBMfH2hkY1kTnVYHAQZMTI/jzvNGMyUrnvz0WPWSRE6D1wRUQ4eVbpuTrUdbMM3eH36Hy8TudOFwmticLhwOF1anC4vdRY/dicXuxGp3YnO6aO2202l10GV1EB8Zyp6aNlq77bT12OmxOwEIDw78/OPPjEuJxumC5JhQcpISGRoTSnJ0KKlx4QyLDSM1LpyEyBDdrBagdwj4+sONrDvYxCeHG6ltsxAdFkRcRDAXF6QyKyeRGSMTtbCfSD/wmoBatrOGww2dXPaXTwCIjwyhuct2in/Va0RCBF02J1GhQUSGBhIfGUJmfAQT0oKJDe99i4sIJj4y9Pj7EBIiQxgSGUKw/rKVr9DcZft8+qjKlm5W7+8ddRkXEcyMkQnclpPIWSMTGJGoGRxE+pvXrKhb2dzN+bNn8Njr7xJgGAQAgQEGwUEBBAUYBAcGEBwYQEigQXhIEGHBAYQFBxIaFKDejfSb1m4bW4+2svZg732kzybZjQgJZFp2PMVZCZyVk8i4FM1pKHIG+vTD4zUBBVryXQZeY4eFLeUtbDrSzMayJvbXdTAuJYZD9Z0UjRjC9OwEpo9MYGJ6nHrbIv1HS76LfJFpmlS19LClvJkt5c1sPtJMXEQIpRUthAcHUjh8CBdOSGFqVjwFmXEagSniYQoo8VkOp4tPj3VQWtFCZXM3y3b2rioLEB0WRNHwIcwZk8x/LchlQlqsphIS8TIKKPEZrd02dla1UVLeTOnRFrYfbaXL1jtqc/rI3pnep2bFM2VEPKOHRuthaREvp4CSQcnhdLG/roNtR1t73ypbKGvoIjosiB6bkzHDormiMJ3Jw4dQNCKeNC1JITLoKKDE631272hHVSs7q9rYXtlKdUsP1a09ACRGhVCQMYTLJ6czKTOOiWlxRIXpW1tksNNPsXidunYLu6ra2Fndxq6qVurareytbQcgJDCAcakxXFGYTnZSJJMzh5A+JFyPGoj4IAWUeIxpmtS0WdhT3cbumnb2VLdR0dTNoYbe1YIDDBiVHM05Y5O4ujiTgvQ4xgyL1mAGET+hgJIB4XC6KGvsYm9NO3tr22npsvH+vjpaunvnOww4vh7W2WMSuXZaJhPTe5cg0fL1Iv5LP/3S7xo7LByo62TfsQ721bZz4Fg7hxu76LL2jqgLCQqgOCueb4wbRl5aDOPTYskdFkN4iJ47EpH/RwElp63DYudgXWfvSsF1HcdXDO4kKjSQ8qZuAJKiQxk7LJrFZyWTlRTJuJRYspMiNSuDiJySAkpOqbnLxqH6Tqpautld3c7B+g4O1XdS22YhMz6Co83dhAcHMnpoFHPGJDEpM47hCZGMGRZNolaIFZHTpIASAKwOJ0ebuilr7OJIYxftPXY2H2nmcEPn5/eJirPi2VnVRk5yFNOzE8gZGkXusBhGJkWRPiRck6eKSL9SQPkRi91JVUs3FU3dlDd1U9HUhdNlsvZgI1Ut3bi+MO3vzJxEAgIM5uWlkJMcxcikSLKTIkmPi1AQiciAUED5EJfLpL7TQlVzD5Ut3VQ291DZ3M3R5m6iw4L44NN6vjh5fXRoELNHJ5KfEcclk9LITowkKzGSEYmRWiVYRDxOATWI9Nic1Lb1UNdupbKlm+qWHmpae2dUqG7tobbVwojECA7UdX7+b4bGhJIxJILsxEjyzhvFiIRIhidEMDwhkiERwXrAVUS8lgLKCzhdJk1dVurbrdR3WKhrt1LXbsHuMNlb20Ztm4Vj7RZaj98LGpEQQXlTN4YBydGhpMWFMzE9jvl54WTGh5MSF07GkAjSh4QTFqyh2yIyOLk1oFauXMkdd9yB0+nk5ptv5he/+IU7D+dVrA4nzV02mjptNHf1vjV2Wmns/Oy9lYYOK1aHkyON3ThdX173sXB4HBa7i/Qh4RSNGEJKbDgpsWEMiw0jLS6clNhwzaogIj7LbQHldDr54Q9/yHvvvUd6ejpTpkzh4osvZty4ce46ZL9zukw6rXY6rU7ae+y9bxYH7T12Oqx2WrrstHbbaO2x09ptp6XbRmu3naZO6+fLPHxRaFAALtMkMSqUpOhQhsaEkRQVwgXjhzEsJoyk6DCGxvR+PTEqVOEjIn7NbQG1efNmcnJyyM7OBuCqq67izTffPO2AMk0Th8vE6Tr+3mnicLmwO13YnSY2pwubo/dzm8OF3eWix+bEYndhsfe+N02T1h47PTYnXTYHPTYn3cffDMOkvsNGp8VOp9VBp8VBl83JyKRIDjd0fameAKN3rfvo0CCGRIYQFx7MkIgQxgyNJiosiITIEOIjQ4mPDCEhKqT3fWQIseG67yMi0hduC6jq6moyMjI+/zw9PZ1NmzaddPulGyvYU9POmF++gwlggss0MYG81Bh2VLWd8N9Nzoxj69HWL329aPgQSipa/uVr2YmRlDV2EWBAREgQ4SGBRIYEEh4SRHxEMLHhwaTHhRMVGkRUWBBRoUEMiQwmPDiQmLBgYsJ7t+n9uPf1IM2IICLiFoZpfvnex9cxb948s7Gx8Utfb2lpob29neHDhwPQ1NREV1cXmZmZ/7JdQ0MDjY2NmIEhWHu6SBkx+nhl/2+bQMPAZZoYhoEBfNYBMQyDwOM9GQMDw+jt2Xz2sWEYvZ9/4X2gYeAtHZiGhgaSkpI8XcaA0fn6Pn87Z53v6SktLV1lmua8U213xgFFbz58yYYNG7j77rtZtWoVAPfddx8Ad91110l3FBkZSVfXly+n+aqioiJKSko8XcaA0fn6Pn87Z53vaetTN8Ft16emTJnCwYMHOXLkCDabjZdffpmLL77YXYcTEREf47Z7UEFBQTz66KNccMEFOJ1ObrrpJsaPH++uw4mIiI9x63NQCxYsYMGCBX3ePjEx0Y3VeJ9bbrnF0yUMKJ2v7/O3c9b5upfb7kGdDn+7nisi4qc8ew9KRETkTAx4QK1cuZIxY8aQk5PD7373uy+9bpomt99+Ozk5OUycOJGtW7cOdIn96lTnu3r1amJjYykoKKCgoID//d//9UCV/eemm24iOTmZvLy8E77ua+17qvP1tfatrKxkzpw55ObmMn78eB5++OEvbeNrbdyXc/aldrZYLEydOpX8/HzGjx/Pr3/96y9tM2BtbJrmmb71mcPhMLOzs83Dhw+bVqvVnDhxorlnz57PXy8sLDSXL19uzps3z3S5XOaGDRvMqVOnfp1DeJVTna9pmuZHH31kXnjhhR6qsP+tWbPGLC0tNcePH3/C132pfU3z1Ofra+1bU1NjlpaWmqZpmu3t7eaoUaO+9D3ta23cl3P2pXZ2uVxmR0eHaZqmabPZzKlTp5obNmz4l236oY37lC8D2oP64vRHISEhn09/9EVvvvkmixYtwjAMpk2bRmtrK7W1tQNZZr/py/n6mtmzZxMfH3/S132pfeHU5+trUlJSmDx5MgDR0dHk5uZSXV39L9v4Whv35Zx9iWEYREVFAWC327Hb7V+anm2g2nhAA+pE0x/9e0P3ZZvBoq/nsmHDBvLz85k/fz579uwZyBIHnC+1b1/5avuWl5ezbds2iouL/+XrvtzGJztn8K12djqdFBQUkJyczNy5cz3Xxn3tavXHG/At4IkvfH498MgXPl8JLAdmfuFrHwCFA1nnQJ3v8a/FAFHHP14AHPR03f1w3iOA3Sd5zWfat4/n63Pte/xcooBS4DJ/aOM+nLOvtnMc8BGQ54k2HuhBElVAxhc+TwdqPvvE7J2b6Su3GWROeS6mababptl5/OMVQLBhGL78QJgvte8p+WL7GoYRDLwOvGCa5j9OsInPtfGpztkX2xnANM1WYDXw7/PmDUgbD3RAbQFGGYaRZRhGCHAV8Na/bfMWsMjoNQ1oM01zsF7APuX5GoYxzDh+gdcwjKn0tknTgFc6cHypfU/J19r3+Lk8CewzTfOhk2zmU23cl3P2pXY2DCPJMIy44x+HA+cDn/7bZgPSxgO65Ltpmg7DMG4DVgGBwFOmae4xDOP7x19/DFhBbxf5ENANfGcga+xPfTzfK4BbDcNwAD3AVebxPvNgZBjGS8A5QKJhGFXAr4Fg8L32hT6dr0+1L3AWvZeqdxmGsf341/4LyATfbGP6ds6+1M4pwLOGYQTSG7SvmKa5zBO/p/tjJgkREZF+p5kkRETEKymgRETEKymgRETEKymgRETEKymgRETEKymgRETEKymgRETEKymgRERkQBiGMcUwjJ2GYYQZhhFpGMYewzBOvJgaelBXREQGkGEY9wBhQDhQZZrmfSfdVgElIiID5fi8pFsACzDDNE3nybbVJT4RERlI8fQuXRJNb0/qpNSDEhGRAWMYxlvAy0AWkGKa5m0n23ZAZzMXERH/ZRjGIsBhmuaLx2dL/8QwjHNN0/zwhNurByUiIt5I96BERMQrKaBERMQrKaBERMQrKaBERMQrKaBERMQrKaBERMQrKaBERMQrKaBERMQr/f/VMjkJiKc6eAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf6278b310>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from sympy.plotting import plot\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plot(C1,C2,1,(x,0,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](plot1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3}}{6} + \\frac{a^{2}}{2}$"
      ],
      "text/plain": [
       " 3    2\n",
       "a    a \n",
       "── + ──\n",
       "6    2 "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Su = expand(integrate(C1-1,(x,1,a+1)))\n",
    "Su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a^{3}}{6} - \\frac{a^{2}}{4} + \\frac{a}{4} + \\frac{7}{12}$"
      ],
      "text/plain": [
       "   3    2         \n",
       "  a    a    a   7 \n",
       "- ── - ── + ─ + ──\n",
       "  6    4    4   12"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S-Su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf71b2c3a0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(S-Su,(a,0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ - \\frac{1}{2} + \\frac{\\sqrt{3}}{2}, \\  - \\frac{\\sqrt{3}}{2} - \\frac{1}{2}\\right]$"
      ],
      "text/plain": [
       "⎡  1   √3    √3   1⎤\n",
       "⎢- ─ + ──, - ── - ─⎥\n",
       "⎣  2   2     2    2⎦"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(S-Su,a),a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4\n",
    "\n",
    "前問3の$C_2$の放物線を$y=0.1x^2$と変えて問題を解け．ただし数値を変えたので， $\\fbox{ ウ }$，$\\frac{\\fbox{ オ }}{\\fbox{ カキ }}$\n",
    "等には，箱にこだわらず8桁程度の実数を求めよ．最後は$a=0.7165151384$になる．(30点)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "\n",
    "a, x = symbols('a x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{x^{2}}{2} + \\frac{1}{2}$"
      ],
      "text/plain": [
       " 2    \n",
       "x    1\n",
       "── + ─\n",
       "2    2"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C1 = Rational(1/2)*x**2 + Rational(1/2)\n",
    "C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 0.1 x^{2}$"
      ],
      "text/plain": [
       "     2\n",
       "0.1⋅x "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C2 = 0.1*x**2\n",
    "C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 0.4 a^{2} + 0.4 a + 0.633333333333333$"
      ],
      "text/plain": [
       "     2                            \n",
       "0.4⋅a  + 0.4⋅a + 0.633333333333333"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S = expand(integrate(C1-C2,(x,a,a+1)))\n",
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -0.5$"
      ],
      "text/plain": [
       "-0.500000000000000"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0 = solve(diff(S,a),a)[0]\n",
    "S0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 0.533333333333333$"
      ],
      "text/plain": [
       "0.533333333333333"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.subs({a:S0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ -1, \\  1\\right]$"
      ],
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(C1-1,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.16227766016838$"
      ],
      "text/plain": [
       "3.16227766016838"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 = solve(C2-1,x)\n",
    "s1[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf502e1ca0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from sympy.plotting import plot\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plot(C1,C2,1,(x,0,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3}}{6} + \\frac{a^{2}}{2}$"
      ],
      "text/plain": [
       " 3    2\n",
       "a    a \n",
       "── + ──\n",
       "6    2 "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Su = expand(integrate(C1-1,(x,1,a+1)))\n",
    "Su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{a^{3}}{6} - 0.1 a^{2} + 0.4 a + 0.633333333333333$"
      ],
      "text/plain": [
       "   3                                     \n",
       "  a         2                            \n",
       "- ── - 0.1⋅a  + 0.4⋅a + 0.633333333333333\n",
       "  6                                      "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S-Su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fbf71bf2460>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(S-Su,(a,0,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle \\left[ -1.11651513899117, \\  0.716515138991168\\right]$"
      ],
      "text/plain": [
       "[-1.11651513899117, 0.716515138991168]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(S-Su,a),a)"
   ]
  }
 ],
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