wafuwafu13/math3.ipynb

## math3.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.61 関数 $y = \\dfrac{2x+1}{x-1}$ のグラフをかけ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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 0x7fd4ddddaac8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.plotting import plot\n",
    "from sympy import Symbol\n",
    "\n",
    "x = Symbol('x')\n",
    "\n",
    "plot((2*x + 1) / (x - 1), 2, ylim=(-10, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **p.64** 関数 $ y = \\dfrac{5}{x-3} $ のグラフと直線 $y = x+1$ との交点の座標を求めよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-2, -1), (4, 5)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, solve\n",
    "\n",
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "\n",
    "solve([y - (5 / (x - 3)), y - x - 1], [x, y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **p.67** 関数 $y = \\sqrt{2x+4}$ のグラフをかけ。"
   ]
  },
  {
   "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 0x7fe451970e80>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.plotting import plot\n",
    "from sympy import Symbol, sqrt\n",
    "\n",
    "x = Symbol('x')\n",
    "plot(sqrt(2*x + 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.71 関数 $y = 3x - 1$ の逆関数を求めよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x}{3} + \\frac{1}{3}$"
      ],
      "text/plain": [
       "x/3 + 1/3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, solve\n",
    "\n",
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "solve(y - 3*x + 1, x)[0].subs({y: x})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.75 次の関数 $f(x), g(x)$ に対して、合成関数 $\\left( g\\circ f\\right) \\left( x\\right), \\left( f\\circ f\\right) \\left( x\\right)$ を求めよ  \n",
    "### $f(x) = \\dfrac{2}{x-1}$&emsp;$g(x) = 2x+1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Symbol, simplify\n",
    "\n",
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "fx = 2 / (x - 1)\n",
    "gx = 2*x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1 + \\frac{4}{x - 1}$"
      ],
      "text/plain": [
       "1 + 4/(x - 1)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gx.subs({x: fx})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 \\left(1 - x\\right)}{x - 3}$"
      ],
      "text/plain": [
       "2*(1 - x)/(x - 3)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(fx.subs({x: fx}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.81 $\\displaystyle \\lim_{n \\to \\infty} (n^2 - 3n)$ &emsp; $\\displaystyle \\lim_{n \\to \\infty} (2\\sqrt{n} - n)$ の極限を調べよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\infty$"
      ],
      "text/plain": [
       "oo"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Limit, Symbol, S, sqrt\n",
    "\n",
    "n = Symbol('n')\n",
    "l = Limit(n*n - 3*n, n, S.Infinity)\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -\\infty$"
      ],
      "text/plain": [
       "-oo"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = Limit(2*sqrt(n) - n, n, S.Infinity)\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.107  $\\displaystyle \\lim_{x \\to 2+0} \\dfrac{x}{x-2}$ &emsp; $\\displaystyle \\lim_{x \\to 2-0} \\dfrac{x}{x-2}$ の極限を求めよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\infty$"
      ],
      "text/plain": [
       "oo"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Limit, Symbol\n",
    "\n",
    "x = Symbol('x')\n",
    "l = Limit(x/(x-2), x, 2, dir='+')\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -\\infty$"
      ],
      "text/plain": [
       "-oo"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = Limit(x/(x-2), x, 2, dir='-')\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.110  $\\displaystyle \\lim_{x \\to -\\infty} 2^x$ &emsp; $\\displaystyle \\lim_{x \\to \\infty} \\log _{2}\\dfrac{1}{x}$ の極限を求めよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Limit, Symbol, S, log\n",
    "\n",
    "x = Symbol('x')\n",
    "l = Limit(2**x, x, -S.Infinity)\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -\\infty$"
      ],
      "text/plain": [
       "-oo"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = Limit(log(1/x, 2), x, S.Infinity)\n",
    "l.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.130 $y = (x+1)(2x-1)$ を微分せよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 x + 1$"
      ],
      "text/plain": [
       "4*x + 1"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Derivative\n",
    "\n",
    "x = Symbol('x')\n",
    "y = (x + 1)*(2*x - 1)\n",
    "d = Derivative(y, x)\n",
    "d.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.140 $y = \\log(3x + 2)$ を微分せよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3}{3 x + 2}$"
      ],
      "text/plain": [
       "3/(3*x + 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Derivative, log\n",
    "\n",
    "x = Symbol('x')\n",
    "y = log(3*x + 2)\n",
    "d = Derivative(y, x)\n",
    "d.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.143  $y = e^{2x}$  &emsp;  $y = 3^{-x}$ を微分せよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 e^{2 x}$"
      ],
      "text/plain": [
       "2*exp(2*x)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Derivative, exp\n",
    "\n",
    "x = Symbol('x')\n",
    "y = exp(2*x)\n",
    "d = Derivative(y, x)\n",
    "d.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - 3^{- x} \\log{\\left(3 \\right)}$"
      ],
      "text/plain": [
       "-3**(-x)*log(3)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 3 ** (-x)\n",
    "d = Derivative(y, x)\n",
    "d.doit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p.148  曲線 $ y = x + \\dfrac{2}{x}$ 上の点 $(1, 3)$ における、接線と法線の方程式を求めよ。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 4 - x\n"
     ]
    }
   ],
   "source": [
    "from sympy import Symbol, Derivative, expand\n",
    "\n",
    "x = Symbol('x')\n",
    "fx = x + 2/x\n",
    "t = 1\n",
    "d = Derivative(fx, x)\n",
    "fdt = d.doit().subs({x: t})\n",
    "ft = fx.subs({x: t})\n",
    "expr = fdt*(x - t) + fx.subs({x: t})\n",
    "\n",
    "print(f'y = {expand(expr)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = x + 2\n"
     ]
    }
   ],
   "source": [
    "expr = -1/fdt*(x - t) + fx.subs({x: t})\n",
    "print(f'y = {expand(expr)}')"
   ]
  }
 ],
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