mathanalysis_standardcalc209-215.ipynb

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    "%%html\n",
    "<style>\n",
    "@import url('https://fonts.googleapis.com/css?family=Roboto&effect=3d|brick-sign|');\n",
    "span {font-family:Roboto; color:black; text-shadow:4px 4px 4px #aaa;}  \n",
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    "</style> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math, sympy, numpy\n",
    "from sympy import *\n",
    "sympy.init_printing(use_unicode=True)\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[GeoGebra](https://www.geogebra.org/graphing?lang=en)\n",
    "\n",
    "[LaTeX/Mathematics](https://en.wikibooks.org/wiki/LaTeX/Mathematics)\n",
    "\n",
    "[ SymPy Modules Reference. Calculus](https://docs.sympy.org/latest/modules/calculus/index.html)\n",
    "\n",
    "[Sympy : Symbolic Mathematics in Python](https://www.scipy-lectures.org/advanced/sympy.html)\n",
    "\n",
    "[Math24.ru. Ряды Тейлора и Маклорена](http://www.math24.ru/%D1%80%D1%8F%D0%B4%D1%8B-%D1%82%D0%B5%D0%B9%D0%BB%D0%BE%D1%80%D0%B0-%D0%B8-%D0%BC%D0%B0%D0%BA%D0%BB%D0%BE%D1%80%D0%B5%D0%BD%D0%B0.html)\n",
    "\n",
    "[Math24.ru. Бесконечно малые функции](http://www.math24.ru/%D0%B1%D0%B5%D1%81%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D0%BE-%D0%BC%D0%B0%D0%BB%D1%8B%D0%B5-%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8.html)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Вариант 22\n",
    "\n",
    "# Дифференцирование и приложения"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №9\n",
    "\n",
    "Найти производную $n$-ого порядка.\n",
    "\n",
    "$\\large{\\displaystyle{y = \\frac{2x - 4}{8x + 3} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "$\\large{\\displaystyle{y ' = \\Bigg(\\frac{2x - 4}{8x + 3}\\Bigg) ' = \\frac{(2x - 4) ' (8x + 3) - (2x - 4) (8x + 3) '}{(8x + 3)^2} = }}$ \n",
    "\n",
    "\n",
    "$\\large{\\displaystyle{ = \\frac{2 (8x + 3) - 8(2x - 4)}{(8x + 3)^2} = \\frac{16x + 6 - 16x + 32}{(8x + 3)^2} = 38 * (8x + 3)^{-2} }}$ \n",
    "\n",
    "\n",
    "$\\large{\\displaystyle{y '' = \\Bigg(38 * (8x + 3)^{-2} \\Bigg) ' =  38 * (-2) * 8 * (8x + 3)^{-3} }}$\n",
    "\n",
    "\n",
    "$\\large{\\displaystyle{y ''' = \\Bigg(38 * (-2) * 8 * (8x + 3)^{-3} \\Bigg) ' =  38 * 6 * 8^2 * (8x + 3)^{-4} }}$\n",
    "\n",
    "$...$\n",
    "\n",
    "$\\large{\\displaystyle{y ^{(n)} = 38 * (-1)^{n-1} * n! * 8^{n - 1} *(8x + 3)^{-n - 1}   }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ответ\n",
    "\n",
    "$\\large{\\displaystyle{y ^{(n)} = 38 * (-1)^{n-1} * n! * 8^{n - 1} *(8x + 3)^{-n - 1}   }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = (2 * x - 4) / (8 * x + 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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      "text/latex": [
       "$$\\left ( - \\frac{8 \\left(2 x - 4\\right)}{\\left(8 x + 3\\right)^{2}} + \\frac{2}{8 x + 3}, \\quad \\frac{128 \\left(2 x - 4\\right)}{\\left(8 x + 3\\right)^{3}} - \\frac{32}{\\left(8 x + 3\\right)^{2}}, \\quad - \\frac{3072 \\left(2 x - 4\\right)}{\\left(8 x + 3\\right)^{4}} + \\frac{768}{\\left(8 x + 3\\right)^{3}}\\right )$$"
      ],
      "text/plain": [
       "⎛  8⋅(2⋅x - 4)      2     128⋅(2⋅x - 4)       32        3072⋅(2⋅x - 4)      76\n",
       "⎜- ─────────── + ───────, ───────────── - ──────────, - ────────────── + ─────\n",
       "⎜            2   8⋅x + 3             3             2               4          \n",
       "⎝   (8⋅x + 3)               (8⋅x + 3)     (8⋅x + 3)       (8⋅x + 3)      (8⋅x \n",
       "\n",
       "8    ⎞\n",
       "─────⎟\n",
       "    3⎟\n",
       "+ 3) ⎠"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(y, x), diff(diff(y, x), x), diff(diff(diff(y, x), x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(diff(y, x), 38 * (8 * x + 3) ** (-2), \n",
    "     diff(diff(y, x), x), 38 * (-2) * 8 * (8 * x + 3) ** (-3),\n",
    "     diff(diff(diff(y, x), x), x), 38 * 6 * 8 ** 2 * (8 * x + 3) ** (-4), \n",
    "     (x,0,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №10\n",
    "\n",
    "Вычислить предел функции.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to 0}  \\frac{4 \\ tg \\ 3 x - 3 \\ tg \\ 4x}{7x - sin \\ 7x} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "Числитель и знаменатель дроби стремятся к 0 при $x \\to 0$, \n",
    "\n",
    "значит дробь является неопределенным выражением вида $\\big[\\frac{0}{0}\\big]$ при $x \\to 0$.\n",
    "\n",
    "Заменить знаменатель на эквивалентную бесконечно малую функцию нельзя, поскольку:\n",
    "\n",
    "$7x - sin \\ 7x = 7x - 7x - \\overline{o}(7x) =  - \\overline{o}(7x)$ при $x \\to 0$.\n",
    "\n",
    "То же самое верно и в отношении числителя."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для раскрытия неопределенности $\\big[\\frac{0}{0}\\big]$ при $x \\to 0$ преобразуем функцию, \n",
    "\n",
    "используя разложение в ряды Маклорена:\n",
    "\n",
    "$\\large{\\displaystyle{ tg \\ 3x = 3x +  \\frac{(3x)^3}{3} + \\overline{o_1(x^3)} }}$\n",
    "\n",
    "$\\large{\\displaystyle{ tg \\ 4x = 4x +  \\frac{(4x)^3}{3} + \\overline{o_2(x^3)} }}$\n",
    "\n",
    "$\\large{\\displaystyle{sin \\ 7x = 7x - \\frac{(7x)^3}{3!} + \\overline{o_3(x^3)} }}$\n",
    "\n",
    "$\\large{\\displaystyle{ 4 \\ tg \\ 3x - 3 \\ tg\\ 4x = 12 x +  36 x^3 + 4 \\overline{o_1(x^3)} - 12 x - 64 x^3 - 3 \\overline{o_2(x^3)} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = -28x^3 + 4 \\overline{o_1(x^3)} - 3 \\overline{o_2(x^3)} }}$\n",
    "\n",
    "$\\large{\\displaystyle{7x - sin \\ 7x = 7x - 7x + \\frac{(7x)^3}{3!} - \\overline{o_3(x^3)} = \\frac{343}{6} x^3 - \\overline{o_3(x^3)} }}$\n",
    "\n",
    "Учитывая, что $4 \\overline{o_1(x^3)}  - 3 \\overline{o_2(x^3)}, \\overline{o_3(x^3)}$ - бесконечно малые величины более высокого порядка, чем $x^3$:\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to 0}  \\frac{4 \\ tg \\ 3 x - 3 \\ tg \\ 4x}{7x - sin \\ 7x}  = \\lim_{ x \\to 0}  \\frac{-28 x^3}{343 x^3 / 6 } = -\\frac{24}{49} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ответ\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to 0}  \\frac{4 \\ tg \\ 3 x - 3 \\ tg \\ 4x}{7x - sin \\ 7x} = -\\frac{24}{49} }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = (4 * tan(3 * x) - 3 * tan(4 * x)) / (7 * x - sin (7 * x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- \\frac{24}{49}$$"
      ],
      "text/plain": [
       "-24 \n",
       "────\n",
       " 49 "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(y, x, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y, -24/49, (x, -0.06, -0.01));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №11\n",
    "\n",
    "Вычислить предел функции.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -1}  \\frac{x^4 + x^3 - 3x^2 - 5x - 2}{x^4 + 2x^3 - 2x - 1} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "Числитель и знаменатель дроби стремятся к 0 при $x \\to 0$, \n",
    "\n",
    "значит дробь является неопределенным выражением вида $\\big[\\frac{0}{0}\\big]$ при $x \\to 0$.\n",
    "\n",
    "### I Способ\n",
    "\n",
    "Заменим переменную $t = x + 1, x \\to -1 \\implies x = t - 1, t \\to 0$.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -1}  \\frac{x^4 + x^3 - 3 x^2 - 5 x - 2}{x^4 + 2 x^3 - 2 x - 1} = \\lim_{ t \\to 0}  \\frac{(t - 1)^4 + (t - 1)^3 - 3 (t - 1)^2 - 5(t - 1) - 2}{(t - 1)^4 + 2 (t - 1)^3 - 2 (t - 1) - 1} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{ t \\to 0}  \\frac{t^4  - 4 t^3 + 6 t^2 - 4 t + 1 + t^3 - 3 t^2 + 3t - 1 - 3 (t^2 - 2 t + 1) - 5 t + 3}{t^4  - 4 t^3 + 6 t^2 - 4 t + 1 + 2 (t^3 - 3 t^2 + 3t - 1) - 2 t  + 1} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{ t \\to 0}  \\frac{t^4  - 3 t^3}{t^4  - 2 t^3} =  \\lim_{ t \\to 0}  \\frac{t - 3}{t - 2} = \\frac{-3}{-2} = 1.5}}$\n",
    "\n",
    "### II Способ\n",
    "\n",
    "Разложим на множители числитель и знаменатель дроби \n",
    "\n",
    "и поделим несколько раз на $x + 1 \\neq 0$ при $ x \\to - 1$:\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -1}  \\frac{x^4 + x^3 - 3 x^2 - 5 x - 2}{x^4 + 2 x^3 - 2 x - 1} = \\lim_{  x \\to -1}  \\frac{(x + 1)(x^3 - 3 x^2 - 2)}{(x + 1)(x^3 + x^2 - x - 1)} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{  x \\to -1}  \\frac{x^3 - 3 x^2 - 2}{x^3 + x^2 - x - 1} = \\lim_{  x \\to -1}  \\frac{(x + 1)(x^2 - x - 2)}{(x + 1)(x^2 - 1)} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{  x \\to -1}  \\frac{x^2 - x - 2}{x^2 - 1} = \\lim_{  x \\to -1}  \\frac{(x + 1)(x - 2)}{(x + 1)(x - 1)} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{  x \\to -1}  \\frac{x - 2}{x - 1} =  \\frac{-1 - 2}{-1 - 1} = 1.5}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ответ\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -1}  \\frac{x^4 + x^3 - 3x^2 - 5x - 2}{x^4 + 2x^3 - 2x - 1} = 1.5}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( t^{4} - 3 t^{3}, \\quad t^{4} - 2 t^{3}\\right )$$"
      ],
      "text/plain": [
       "⎛ 4      3   4      3⎞\n",
       "⎝t  - 3⋅t , t  - 2⋅t ⎠"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = Symbol('t')\n",
    "expand((t - 1)**4 + (t - 1)**3 - 3 * (t - 1)**2 - 5 * (t - 1) - 2), expand((t - 1)**4 + 2 * (t - 1)**3 - 2 * (t - 1) - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAqBAMAAACXcryGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIomZu0QQZlR2ze/dMqswxovtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAoElEQVQYGWNgEFJ2ZWBgYDNgqG9gYOD8wZC/gIGBdSsDP5ACgv4CEMl6HETyznsLooCCDWCK+xtQ7AIDyw8GhvxvYIr7AQNIkL0Aoi/YGGQ0ueA/CHwgSrewlS9QHeMDBv0ABga+BAbuDQwgh/B9BPIOMPD9BRvCAzHr/gQw7zCYZDYAU8VgkkOBQRDIuMTAMA1o2GFjuwMMDFxANyxgAAA2dCr7xqZ+QAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{3}{2}$$"
      ],
      "text/plain": [
       "3/2"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit((t ** 4 - 3 * t ** 3)/( t** 4 - 2 * t ** 3), t, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = (x ** 4 + x ** 3 - 3 * x ** 2 - 5 * x - 2) / (x ** 4 + 2 * x ** 3 - 2 * x - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left(x - 2\\right) \\left(x + 1\\right)^{3}, \\quad \\left(x - 1\\right) \\left(x + 1\\right)^{3}\\right )$$"
      ],
      "text/plain": [
       "⎛               3                 3⎞\n",
       "⎝(x - 2)⋅(x + 1) , (x - 1)⋅(x + 1) ⎠"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(x ** 4 + x ** 3 - 3 * x ** 2 - 5 * x - 2), factor(x ** 4 + 2 * x ** 3 - 2 * x - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASAAAAAaBAMAAADlO5zMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVESZEM27ZiLviTJ23asWSsTfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADSUlEQVRIDb2X22sTQRTGv022Ztuk26J/gPHRB2mgtCKoLPQCatH+ASoiqIiCEQUVRAJC8EFoHnwTbQR9KV4Cig+t0H1QRKhpoQUVCUSoF7RoWyoNVImzszmzu5NJEyJ0HzLf/M535hxmrwHoMF7nc6SbHW9e/aFK3f94XoVrsc1uwMzGMrUsjfLveKOyJrBHhatZ1kFawg1Ec23Drmr+dwIPVMnLGGls85872QNiifakkE2Ld6rMi402FLFZ+ilaInaYVPPjK1ud+0iNq+gcYGQEHbSF5MIY640HiTu73nNGhR2mn1VGoqxQvYN78kA4K5zRNSG56ENkKUj4zCjiSVzBOZpUXixpq5Zf8IM9K0wfstARr7B9OWNVhLmY7tR/BwmfmRZavW31G/TbGHGvw5A7VIJGMZry+5Q65jTUksSkVQm3W5FbQef2OFQNta7ALAWdNJvDFYtrzSbkjOmJp5Z/rtS8ofAxvKVo9GE+RZpGTdozzs0ZmNLJJf/41DdXBhsaLZfJUXvkDbFH4WdmGcofGOtUWXckoU/Nj9+TY+2LMpFs1JCERZaiIm8otIKTzJSILYRnhNkTL37mEEbernrOTtqeyVWSjRqSsMhSVOQNsfvqKBBJxUpm4CqkRG0JlzGd+kpzGmdJiFGyUUMSJruqIm/IWAZbO4pNw2SFfqTgHDkXjFo5nODSz8MJYSdBNmceLhQ+3CkUikz6MQb4yh8Zpor+RXlD+rKzQ0CH7fzKxwRwrhP4I3NcqCIMBGy0QxL28qorujvETxnQldItz1xRetlyGgqV0B+MaVncCBI2C9pEQ0HsZVVXdK+hEr4Ag/FfaPO8Qt0FRvuPm4vICsTFOPASVoDpkq3SkIwpR1WRN8TuMvYBs/XZLmwjr2+8BG1VW+vLhNh58x3GbPfeGekZLtsqDcmYVlFV5A1FMuiy0Del7QzWdBND3b1xfbe95Tyt444t5XJ5GAXLT2Ub7VB1Ns9SVDRP/11g90MRrXH/wo1rzVrPK66h9UyKGHuX+d72CkNtpLroPHfw5erxeoq97aOZeiZ1fEiN/5NeY/mfmlsj2Vxanaz3LO59U9cxb0CYf1PTv44NqFe3RJo7Kv/L6ro3wHAf+AdGGO7cmW/5zQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left ( x^{3} - 3 x - 2, \\quad x^{3} + x^{2} - x - 1\\right )$$"
      ],
      "text/plain": [
       "⎛ 3             3    2        ⎞\n",
       "⎝x  - 3⋅x - 2, x  + x  - x - 1⎠"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify((x ** 4 + x ** 3 - 3 * x ** 2 - 5 * x - 2) / (x + 1)), simplify((x ** 4 + 2 * x ** 3 - 2 * x - 1) / (x + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( x^{2} - x - 2, \\quad x^{2} - 1\\right )$$"
      ],
      "text/plain": [
       "⎛ 2           2    ⎞\n",
       "⎝x  - x - 2, x  - 1⎠"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify((x ** 3 - 3 * x - 2) / (x + 1)), simplify((x ** 3 +  x ** 2 - x - 1) / (x + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAqBAMAAACXcryGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIomZu0QQZlR2ze/dMqswxovtAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAoElEQVQYGWNgEFJ2ZWBgYDNgqG9gYOD8wZC/gIGBdSsDP5ACgv4CEMl6HETyznsLooCCDWCK+xtQ7AIDyw8GhvxvYIr7AQNIkL0Aoi/YGGQ0ueA/CHwgSrewlS9QHeMDBv0ABga+BAbuDQwgh/B9BPIOMPD9BRvCAzHr/gQw7zCYZDYAU8VgkkOBQRDIuMTAMA1o2GFjuwMMDFxANyxgAAA2dCr7xqZ+QAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{3}{2}$$"
      ],
      "text/plain": [
       "3/2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(y, x, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y, 1.5, (x, -1.5, -0.5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №12\n",
    "\n",
    "Составить уравнение нормали и касательной к кривой, заданной параметрически, \n",
    "\n",
    "в точке, соответствующей значению параметра $t_0$.\n",
    "\n",
    "$\\large{\\displaystyle{\\begin {cases}\n",
    "x = \\ln tg \\ t, \\\\\n",
    "y = \\frac{1}{sin^2 t},\n",
    "\\end {cases}, \\ t_0 = \\frac{\\pi}{4} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "Уравнение касательной в точке $x_0$:\n",
    "\n",
    "$\\large{\\displaystyle{y - f(x_0) = f'(x_0)(x - x_0)}}$.\n",
    "\n",
    "Уравнение нормали в точке $x_0$:\n",
    "\n",
    "$\\large{\\displaystyle{y - f(x_0) = -\\frac{1}{f'(x_0)}(x - x_0)}}$.\n",
    "\n",
    "$\\large{\\displaystyle{ x_0 = \\ln tg \\ t_0 = \\ln tg \\bigg(\\frac{\\pi}{4}\\bigg) = 0 }}$\n",
    "\n",
    "$\\large{\\displaystyle{ f(x_0) = y_0 =  \\frac{1}{sin^2 t_0} =  \\frac{1}{sin^2 \\frac{\\pi}{4}} = \\frac{1}{(\\sqrt{2}/2)^2} = 2 }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\large{\\displaystyle{ f ' (x) = \\frac{y ' (t)}{x ' (t)}  = \\frac{\\big(\\frac{1}{sin^2 t}\\big) '}{(\\ln tg \\ t) ' } = \\frac{-\\frac{2 \\ cos \\ t}{sin^3 t} }{\\frac{1}{tg \\ t \\ cos^2 t}} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{= \\frac{-2 \\ cos^3 \\ t \\ tg \\ t}{sin^3 t}  = -2 \\ ctg^2 t}}$\n",
    "\n",
    "$\\large{\\displaystyle{ f ' (x_0) = \\frac{y ' (t_0)}{x ' (t_0)} = -2 \\ ctg^2(t_0) =  -2 \\ ctg^2 \\bigg(\\frac{\\pi}{4}\\bigg) = -2}}$\n",
    "\n",
    "Уравнение касательной в точке $x_0$:\n",
    "\n",
    "$\\large{\\displaystyle{y - 2 = -2 \\ (x - 0) \\iff   y = -2 \\ x + 2}}$.\n",
    "\n",
    "Уравнение нормали в точке $x_0$:\n",
    "\n",
    "$\\large{\\displaystyle{y - 2 = -\\frac{1}{-2}(x - 0) \\iff   y = 0.5 \\ x + 2}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ответ\n",
    "\n",
    "Уравнение касательной в точке $t_0 = \\frac{\\pi}{4}: y = -2x + 2$.\n",
    "\n",
    "Уравнение нормали в точке $t_0 = \\frac{\\pi}{4}: y = 0.5x + 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = Symbol('t')\n",
    "x = log(tan(t))\n",
    "y = 1 / sin(t) ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 2.0\\right )$$"
      ],
      "text/plain": [
       "(0, 2.0)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.evalf(subs={t:pi/4}), y.evalf(subs={t:pi/4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\frac{\\tan^{2}{\\left (t \\right )} + 1}{\\tan{\\left (t \\right )}}, \\quad - \\frac{2 \\cos{\\left (t \\right )}}{\\sin^{3}{\\left (t \\right )}}\\right )$$"
      ],
      "text/plain": [
       "⎛   2                   ⎞\n",
       "⎜tan (t) + 1  -2⋅cos(t) ⎟\n",
       "⎜───────────, ──────────⎟\n",
       "⎜   tan(t)        3     ⎟\n",
       "⎝              sin (t)  ⎠"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x, t), diff(y, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAAOBAMAAABA5yhLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMiKZu6uJRO92ZlRfaCDxAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvklEQVQYGWNggALWNHUHMHPmsQCYGANDBAPnLxCP6QGjKUK0kYFhN4h3mYFhOkJ0vwBDP0hrBQPDewG4cDMDQ78DkPeNgWH9A7gokGEPxIwg0QtIoix/gBzWnwwM/geQRJkTgByw6AQGIWMQMAEKpAExAyNQ7foDIBYE8CaAaaC57x9AREDkSwZWkMvKGRjuI1zGMoGBB8S7zcCQBFIEAcFpac0M8goMzA8Yt8DEGBj0////xMCcwMA454QDAwCc1SsQiBMAKwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$-2.0$$"
      ],
      "text/plain": [
       "-2.00000000000000"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(y, t).evalf(subs={t:pi/4}) / diff(x, t).evalf(subs={t:pi/4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,y, (t, 0.1,0.9)); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = numpy.linspace(0.49, 0.99)\n",
    "\n",
    "x =  lambda k: numpy.log(numpy.tan(k))\n",
    "y = lambda k: 1 / numpy.sin(k) ** 2\n",
    "\n",
    "plt.figure(figsize=(10,10)) ; plt.grid(c='steelblue',ls='--',lw=0.5)\n",
    "plt.plot(x(t), y(t), c='steelblue', lw=4, label=r'$x = ln \\ tg \\ t, y = \\frac{1}{sin^2 t}$')\n",
    "plt.plot(x(t), -2 * x(t) + 2, c='darkred',ls='--',lw=2, label=r'$y = -2x + 2$')\n",
    "plt.plot(x(t), 0.5 * x(t) + 2, c='darkorange',ls='--',lw=2, label=r'$y = 0.5x + 2$')\n",
    "plt.scatter(0,2, s=100)\n",
    "\n",
    "plt.xlabel(r'$x$', fontsize=15); plt.ylabel(r'$y$', fontsize=15); plt.ylim(1.5, 2.7)\n",
    "plt.legend(fontsize=15, shadow=True, bbox_to_anchor=(1.5,0.5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №13\n",
    "\n",
    "Найти наибольшее и наименьшее значения функции на заданном отрезке.\n",
    "\n",
    "$\\large{\\displaystyle{ y = \\frac{x - 1}{1 + x}, \\ x \\in \\big[0; 4\\big] }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "Областью определения данной функции является объединение интервалов $(-\\infty; -1) \\cup (-1; +\\infty)$.\n",
    "\n",
    "Значит, на отрезке $\\big[0; 4\\big]$ она непрерывна и достигает наименьшего и наибольшего значений.\n",
    "\n",
    "Точки, в которых функция достигает на отрезке этих значений, являются \n",
    "\n",
    "- или точками локального экстремума, принадлежащими этому интервалу,\n",
    "\n",
    "- или концами отрезка.\n",
    "\n",
    "В точках локального экстремума производная функции равна нулю или не существует.\n",
    "\n",
    "$\\large{\\displaystyle{ y ' = \\bigg(\\frac{x - 1}{1 + x}\\bigg) ' = \\frac{(x - 1)' \\ ( x + 1) - (x - 1) \\ ( x+ 1)'}{(x + 1)^2} =  \\frac{2}{(x + 1)^2} }}$\n",
    "\n",
    "$\\large{\\displaystyle{\\forall x \\in \\big[0; 4\\big]: \\exists y ' (x) \\land   y ' (x) \\neq 0}}$.\n",
    "\n",
    "На заданном интервале функция локальных экстремумов не имеет.\n",
    "\n",
    "Вычислим значение функции на концах отрезка.\n",
    "\n",
    "$y(0) = (0 - 1) / (0 + 1) = -1$ - наименьшее значение.\n",
    "\n",
    "$y(4) = (4 - 1) / (4 + 1) = 0.6$ - наибольшее."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ответ:\n",
    "    \n",
    "$\\large{\\displaystyle{ \\max_{ x \\in [0; 4]}  \\frac{x - 1}{1 + x} = 0.6 }}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\min_{ x \\in [0; 4]}  \\frac{x - 1}{1 + x} = -1 }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = (x - 1) / (1 + x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( - \\frac{x - 1}{\\left(x + 1\\right)^{2}} + \\frac{1}{x + 1}, \\quad \\frac{2 \\left(x - 1\\right)}{\\left(x + 1\\right)^{3}} - \\frac{2}{\\left(x + 1\\right)^{2}}\\right )$$"
      ],
      "text/plain": [
       "⎛   x - 1       1    2⋅(x - 1)      2    ⎞\n",
       "⎜- ──────── + ─────, ───────── - ────────⎟\n",
       "⎜         2   x + 1          3          2⎟\n",
       "⎝  (x + 1)            (x + 1)    (x + 1) ⎠"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(y, x), diff(diff(y, x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\frac{2}{\\left(x + 1\\right)^{2}}, \\quad - \\frac{4}{\\left(x + 1\\right)^{3}}\\right )$$"
      ],
      "text/plain": [
       "⎛   2        -4    ⎞\n",
       "⎜────────, ────────⎟\n",
       "⎜       2         3⎟\n",
       "⎝(x + 1)   (x + 1) ⎠"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(y, x)), simplify(diff(diff(y, x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAVBAMAAACJabL9AAAAGFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAABcYkG9AAAAB3RSTlMAdt0yiUTv6RzaoQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABdJREFUCB1jEFIWUmZwZQAi2hFOykKpAEaYC4V1fTYsAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ \\right ]$$"
      ],
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(y, x), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( -1.0, \\quad 0.6\\right )$$"
      ],
      "text/plain": [
       "(-1.0, 0.6)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:0}), y.evalf(subs={x:4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y, diff(y, x), (x, 0, 4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №14\n",
    "\n",
    "Провести полное исследование функции и построить ее график.\n",
    "\n",
    "$\\large{\\displaystyle{ y = \\frac{4}{x^2 + 2 x - 3} }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = 4 / (x ** 2 + 2 * x - 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "1) Найдем область определения функции и точки разрыва.\n",
    "\n",
    "$\\large{\\displaystyle{ y = \\frac{4}{x^2 + 2 x - 3} = \\frac{4}{(x - 1) \\ (x + 3)} }}$\n",
    "\n",
    "$\\large{\\displaystyle{ D(y)= (-\\infty; -3) \\cup (-3; 1) \\cup (1; +\\infty) }}$\n",
    "\n",
    "$\\large{\\displaystyle{ x = -3; x = 1 }}$ - точки разрыва.\n",
    "\n",
    "2) Вычислим односторонние пределы функции\n",
    "\n",
    "- в граничных точках области определения, \n",
    "\n",
    "- в точках разрыва. \n",
    "\n",
    "Найдем вертикальные асимптоты.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to +\\infty}  \\frac{4}{x^2 + 2 x - 3} = \\lim_{ x \\to +\\infty}  \\frac{4}{x^2} = 0}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -\\infty}  \\frac{4}{x^2 + 2 x - 3} = \\lim_{ x \\to -\\infty}  \\frac{4}{x^2} = 0}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -3+0}  \\frac{4}{x^2 + 2 x - 3} = \\frac{4}{(-3 + 0 - 1) \\ (-3 + 0 + 3)} = \\frac{4}{+ 0 \\ (-4 + 0)} = -\\infty }}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -3-0}  \\frac{4}{x^2 + 2 x - 3} = \\frac{4}{(-3 - 0 - 1) \\ (-3 - 0 + 3)} = \\frac{4}{- 0 \\ (-4 - 0)} = +\\infty}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to 1+0}  \\frac{4}{x^2 + 2 x - 3} = \\frac{4}{(1 + 0 - 1) \\ (1+ 0 + 3)} = \\frac{4}{+ 0 \\ (4 + 0)} = +\\infty}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to 1-0}  \\frac{4}{x^2 + 2 x - 3} = \\frac{4}{(1 - 0 - 1) \\ (1- 0 + 3)} = \\frac{4}{- 0 \\ (4 - 0)} = -\\infty}}$\n",
    "\n",
    "Прямые $x = -3, \\ x = 1$ являются вертикальными асимптотами."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left(x - 1\\right) \\left(x + 3\\right)$$"
      ],
      "text/plain": [
       "(x - 1)⋅(x + 3)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor(x ** 2 + 2 * x - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(4 / (x ** 2 + 2 * x - 3), x, -oo), limit(4 / (x ** 2 + 2 * x - 3), x, +oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAVBAMAAABCslYDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInZUiRDNmWbvRN27qzJGkhbKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABgElEQVQ4EZWSP0gCYRjGn9P71JREaHBpOChqdSiXKFwaGqxriSIpoSUqUKLA8RZrcW3IpVsKoqEimhoioTEKWiOOaGppCEKEqOcz7490Q/fAfT7v730ffO8PgBQCSJGzoUyABOIap0eCJIABQBSDRSI6okawSKyMnmAJYA9HnkhymH8pdqse1LEvFZr5is5zFVuefm1w30T28NXysLaNNabqCK8tTbPKM+RIKWOuFX4Acg7qmDREyRwHVNY7uHDbBOIgy/rNZb8uByx8FIGkCYyhzrn1KykrxP5pi0eMV5c0IP5tEhnAu4zYkhH1i4c0XdJYzXBj0BxjhaYjORm5N4A+m9i/Gs1GE1AycrGGjYGwBTxGuNkkhEulmwB6MyUTqg7U+MxcbaOgietq2sBy0aV0UV00sNiclW9nEyeenvr0zBspcdfEpQfT5u8sYOiTe+EcCXofjfqwNlLOwM/MTzk/KFnUAG78mkLzo5L18yr4Nf+8TGfolk4xnPIfJpbCD7XtSFWo9PZwAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( -\\infty, \\quad \\infty\\right )$$"
      ],
      "text/plain": [
       "(-∞, ∞)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(4 / (x ** 2 + 2 * x - 3), x, -3, '+'), limit(4 / (x ** 2 + 2 * x - 3), x, -3, '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\infty, \\quad -\\infty\\right )$$"
      ],
      "text/plain": [
       "(∞, -∞)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(4 / (x ** 2 + 2 * x - 3), x, 1, '+'), limit(4 / (x ** 2 + 2 * x - 3), x, 1, '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Проверим, является ли функция четной, нечетной, периодической.\n",
    "\n",
    "$\\large{\\displaystyle{y(-x) = \\frac{4}{(-x)^2 + 2 (-x) - 3} = \\frac{4}{x^2 - 2x - 3} \\implies y(-x) \\neq y(x) \\land y(-x) \\neq -y(x) }}$\n",
    "\n",
    "Функция не является четной или нечетной.\n",
    "\n",
    "Обозначим $ t \\neq 0$ предполагаемый период функции.\n",
    "\n",
    "$\\large{\\displaystyle{y(x + t) = y(x) \\iff \\frac{4}{(x + t)^2 + 2 (x + t) - 3} = \\frac{4}{x^2 + 2x - 3} \\iff }}$ \n",
    "\n",
    "$\\large{\\displaystyle{\\iff  (x + t)^2 + 2 (x + t) = x^2 + 2x \\iff 2 x t + t^2 + 2 t= 0 \\iff}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\iff t \\ (t + 2 x + 2) = 0 \\iff t = 0 \\lor t = -2x - 2}}$\n",
    "\n",
    "$\\large{\\displaystyle{ t \\neq const \\land t = t(x) }}$\n",
    "\n",
    "Функция не является периодической.\n",
    "\n",
    "4) Найдем точки пересечения графика функции с осями координат.\n",
    "\n",
    "$\\large{\\displaystyle{x = 0 \\implies y = \\frac{4}{0 ^2+ 2 * 0 - 3} \\approx -1.33 }}$\n",
    "\n",
    "$\\large{\\displaystyle{\\forall x \\in \\mathbb{R}: y(x) \\neq 0}}$\n",
    "\n",
    "График функции пересекает ось $Oy$ в точке $(0; -1\\frac{1}{3})$ и не пересекает ось $Ox$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4 / (x ** 2 + 2 * x - 3) == 4 / ((-x )** 2 + 2 * (-x) - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-4 / (x ** 2 + 2 * x - 3) == 4 / ((-x )** 2 + 2 * (-x) - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$-1.33333333333333$$"
      ],
      "text/plain": [
       "-1.33333333333333"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAVBAMAAACJabL9AAAAGFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAABcYkG9AAAAB3RSTlMAdt0yiUTv6RzaoQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABdJREFUCB1jEFIWUmZwZQAi2hFOykKpAEaYC4V1fTYsAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ \\right ]$$"
      ],
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(4 / (x ** 2 + 2 * x - 3), 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5) Найдем наклонные асимпоты графика функции.\n",
    "\n",
    "Вычислим коэффициенты для прямой $y = kx + b$, являющейся наклонной асимптотой.\n",
    "\n",
    "$\\large{\\displaystyle{k =  \\lim_{ x \\to +\\infty}  \\frac{\\frac{4}{x^2 + 2 x - 3}}{x} = \\lim_{ x \\to +\\infty}  \\frac{4}{x^3 + 2x^2 - 3 x} = 0}}$\n",
    "\n",
    "$\\large{\\displaystyle{k= \\lim_{ x \\to -\\infty}  \\frac{\\frac{4}{x^2 + 2 x - 3}}{x} = \\lim_{ x \\to -\\infty}  \\frac{4}{x^3 + 2x^2 - 3 x} = 0}}$\n",
    "\n",
    "$\\large{\\displaystyle{b =  \\lim_{ x \\to +\\infty}  \\frac{4}{x^2 + 2 x - 3} - kx = \\lim_{ x \\to +\\infty}  \\frac{4}{x^2 + 2 x - 3} - 0= 0}}$\n",
    "\n",
    "$\\large{\\displaystyle{b =  \\lim_{ x \\to -\\infty}  \\frac{4}{x^2 + 2 x - 3} - kx = \\lim_{ x \\to -\\infty}  \\frac{4}{x^2 + 2 x - 3} - 0= 0}}$\n",
    "\n",
    "$y = 0$ - уравнение наклонной асимптоты.\n",
    "\n",
    "6) Вычислим первую производную. Найдем точки локального экстремума и промежутки монотонности.\n",
    "\n",
    "$\\large{\\displaystyle{ y ' = \\bigg(\\frac{4}{x^2 + 2 x - 3}\\bigg) ' =  \\frac{(4)' \\ (x^2 + 2 x - 3) - 4 \\ (x^2 + 2 x - 3)'}{(x^2 + 2 x - 3)^2} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{= \\frac{0 \\ (x^2 + 2 x - 3) - 4 \\ (2 x + 2 x)}{(x^2 + 2 x - 3)^2} = \\frac{ - 8 \\ (x + 1)}{(x + 3)^2 (x - 1)^2} }}$\n",
    "\n",
    "Функция может иметь локальный экстремум в критических точках, если:\n",
    "\n",
    "- функция определена и непрерывна в этих точках,\n",
    "\n",
    "- значение производной в них равно нулю или не существует.\n",
    "\n",
    "В данном случае производная функции определена на всей $ D(y)= (-\\infty; -3) \\cup (-3; 1) \\cup (1; +\\infty)$,\n",
    "\n",
    "поэтому нужно найти только стационарные точки $x$, для которых $y ' (x) = 0$\n",
    "\n",
    "$\\large{\\displaystyle{ \\frac{ - 8 \\ (x + 1)}{(x + 3)^2 (x - 1)^2} = 0 \\iff x = -1 }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Промежутки монотонности:\n",
    "\n",
    "| $x$ |  $(-\\infty; -3)$ | $-3$ | $(-3; -1)$ |$ -1$ | $(-1; 1)$ | $1$ | $(1; +\\infty)$ |\n",
    "| :-: | :-: | :-: |  :-: | :-: |  :-: | :-: |  :-: |\n",
    "|  $y ' (x)$  | $+$  | $\\nexists$ | $+$ | $0$  | $-$  | $\\nexists$ | $-$ |\n",
    "|  $y (x)$  | $\\nearrow$  | $\\nexists$  | $\\nearrow$   |  $-1$  | $\\searrow$  | $\\nexists$ | $\\searrow$ |\n",
    "\n",
    "$x = -1$ является точкой локального максимума, $y ( -1 ) = -1$.\n",
    "\n",
    "$x = -3$, $x = 1$ не являются точками локального экстремума.\n",
    "\n",
    "$(-\\infty; -3), \\ (-3; -1)$ - функция возрастает.\n",
    "\n",
    "$(-1; 1), \\ (1; +\\infty)$ - функция убывает."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(y / x, x, oo, '+'), limit(y / x, x, oo, '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 0, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(y - 0 *x, x, oo, '+'), limit(y - 0 * x, x, oo, '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- \\frac{8 x + 8}{\\left(x^{2} + 2 x - 3\\right)^{2}}$$"
      ],
      "text/plain": [
       "  -(8⋅x + 8)   \n",
       "───────────────\n",
       "              2\n",
       "⎛ 2          ⎞ \n",
       "⎝x  + 2⋅x - 3⎠ "
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(y, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAVBAMAAAA6IZrnAAAAJ1BMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAilU6eAAAADHRSTlMAdt0yiUQQzauZu+/yYRgwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAQ0lEQVQYGWMQUmZAAoxKBgyuSHwgkyUAWYRZDU0kY/oxNBEGRtqLpCuBANDpNLOLY/WhRjS/g8IFNTRIEHFCDWftAADtFhpqaNL7fAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ -1\\right ]$$"
      ],
      "text/plain": [
       "[-1]"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(y, x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAAOBAMAAABA5yhLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMquZdrvviSJUZkSudLgOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAh0lEQVQYGWNggAEWQwhrVdkGmBADg2jSRzCH6QCjNUKUgR0iepmBYQWmaCsDw3kBhDBU7TcGhvcH0EUZQaIX0EW5fzEw+BdgFV3AIGQMAiYMUDcwAtW+x1DLADT3PIZtDB0MDPcxXXaTgSEJYRnYXHkFBuYDjFMQoqydn8MZmBMYGJeXOjAAAPp6KQt/Z3OHAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$-1.0$$"
      ],
      "text/plain": [
       "-1.00000000000000"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:-1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left(-\\infty < x \\wedge x < -3\\right) \\vee \\left(-3 < x \\wedge x < -1\\right), \\quad \\left(-1 < x \\wedge x < 1\\right) \\vee \\left(1 < x \\wedge x < \\infty\\right)\\right )$$"
      ],
      "text/plain": [
       "((-∞ < x ∧ x < -3) ∨ (-3 < x ∧ x < -1), (-1 < x ∧ x < 1) ∨ (1 < x ∧ x < ∞))"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(y, x) > 0, x), solve(diff(y, x) < 0, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7) Вычислим вторую производную. Найдем точки перегиба графика функции и промежутки выпуклости.\n",
    "\n",
    "$\\large{\\displaystyle{y '' = \\Bigg(\\frac{ - 8 \\ (x + 1)}{(x^2 + 2 x - 3)^2}\\Bigg)' = }}$  \n",
    "\n",
    "$\\large{\\displaystyle{= -8 * \\frac{(x + 1)' \\ (x^2 + 2 x - 3)^2 - (x + 1) \\ ((x^2 + 2 x - 3)^2)'}{(x^2 + 2 x - 3)^4} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{=  -8 * \\frac{(x^2 + 2 x - 3)^2 - 2 \\ (x + 1) \\ (x^2 + 2 x - 3) \\ (2x + 2)}{(x^2 + 2 x - 3)^4} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{=  -8 * \\frac{x^2 + 2 x - 3 - 2 \\ (2x^2 + 4 x + 2)}{(x^2 + 2 x - 3)^3} =  \\frac{8 \\ (3 x^2 + 6 x + 7)}{(x^2 + 2 x - 3)^3} }}$\n",
    "\n",
    "$\\large{\\displaystyle{y '' = \\frac{8 \\ (3 x^2 + 6 x + 7)}{(x + 3)^3 (x- 1)^3} }}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция может иметь точки перегиба, если:\n",
    "\n",
    "- функция определена и непрерывна в этих точках,\n",
    "\n",
    "- значение второй производной в них равно нулю или не существует.\n",
    "\n",
    "В данном случае \n",
    "\n",
    "- $y '' (x)$ определена на всей $ D(y)= (-\\infty; -3) \\cup (-3; 1) \\cup (1; +\\infty)$,\n",
    "\n",
    "- $\\nexists x \\in \\mathbb{R}: y '' (x) = 0$\n",
    "\n",
    "Промежутки выпуклости:\n",
    "\n",
    "| $x$ |  $(-\\infty; -3)$ | $-3$ | $(-3; 1)$ | $1$ | $(1; +\\infty)$ |\n",
    "| :-: | :-: | :-: |  :-: | :-: |  :-: |\n",
    "|  $y '' (x)$  | $+$  | $\\nexists$ | $-$ | $\\nexists$ | $+$ |\n",
    "|  $y (x)$  | $\\cup$  | $\\nexists$  | $\\cap$  | $\\nexists$ | $\\cup$ |\n",
    "\n",
    "Функция не имеет точек перегиба. \n",
    "\n",
    "$(-\\infty; -3), \\ (1; +\\infty)$ - график функции является выпуклым вниз.\n",
    "\n",
    "$(-3; 1)$ - график функции является выпуклым вверх."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{4 \\left(- 4 x - 4\\right) \\left(- 2 x - 2\\right)}{\\left(x^{2} + 2 x - 3\\right)^{3}} - \\frac{8}{\\left(x^{2} + 2 x - 3\\right)^{2}}$$"
      ],
      "text/plain": [
       "4⋅(-4⋅x - 4)⋅(-2⋅x - 2)          8       \n",
       "─────────────────────── - ───────────────\n",
       "                  3                     2\n",
       "    ⎛ 2          ⎞        ⎛ 2          ⎞ \n",
       "    ⎝x  + 2⋅x - 3⎠        ⎝x  + 2⋅x - 3⎠ "
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(diff(y,x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{8 \\left(3 x^{2} + 6 x + 7\\right)}{x^{6} + 6 x^{5} + 3 x^{4} - 28 x^{3} - 9 x^{2} + 54 x - 27}$$"
      ],
      "text/plain": [
       "               ⎛   2          ⎞            \n",
       "             8⋅⎝3⋅x  + 6⋅x + 7⎠            \n",
       "───────────────────────────────────────────\n",
       " 6      5      4       3      2            \n",
       "x  + 6⋅x  + 3⋅x  - 28⋅x  - 9⋅x  + 54⋅x - 27"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(expand(diff(diff(y,x), x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ -1 - \\frac{2 i}{3} \\sqrt{3}, \\quad -1 + \\frac{2 i}{3} \\sqrt{3}\\right ]$$"
      ],
      "text/plain": [
       "⎡     2⋅√3⋅ⅈ       2⋅√3⋅ⅈ⎤\n",
       "⎢-1 - ──────, -1 + ──────⎥\n",
       "⎣       3            3   ⎦"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(diff(y,x), x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left(-\\infty < x \\wedge x < -3\\right) \\vee \\left(1 < x \\wedge x < \\infty\\right), \\quad -3 < x \\wedge x < 1\\right )$$"
      ],
      "text/plain": [
       "((-∞ < x ∧ x < -3) ∨ (1 < x ∧ x < ∞), -3 < x ∧ x < 1)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(diff(y, x), x) > 0, x), solve(diff(diff(y, x), x) < 0, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8) Построим график функции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y, (x, -5.1, -3.1)); plot(y, (x, -2.9, 0.9)); plot(y, (x, 1.1, 3.1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = numpy.linspace(-5.1, -3.1); x2 = numpy.linspace(-2.9, 0.9); x3 = numpy.linspace(1.1, 3.1)\n",
    "y = lambda x: 4 / (x ** 2 + 2 * x - 3)\n",
    "dy = lambda x: -8 * (x + 1) / (x ** 2 + 2 * x - 3) ** 2\n",
    "d2y = lambda x: 8 * (3 * x ** 2 + 6 * x + 7) / (x ** 2 + 2 * x - 3) ** 3\n",
    "\n",
    "plt.figure(figsize=(10,10)) ; plt.grid(c='steelblue',ls='--',lw=0.5)\n",
    "plt.plot(x1, y(x1), c='steelblue', lw=3, label=r'$y = \\frac{4}{x^2 + 2 x - 3}, x \\in (-4.1; -3.1)$')\n",
    "plt.plot(x2, y(x2), c='steelblue', lw=3, label=r'$y = \\frac{4}{x^2 + 2 x - 3}, x \\in (-2.9; 0.9)$')\n",
    "plt.plot(x3, y(x3), c='steelblue', lw=3, label=r'$y = \\frac{4}{x^2 + 2 x - 3}, x \\in (1.1; 2.1)$')\n",
    "\n",
    "plt.plot(x1, dy(x1), c='darkblue', lw=1, \n",
    "         label=r'$y =  \\frac{ - 8 \\ (x + 1)}{(x + 3)^2 (x - 1)^2}, x \\in (-4.1; -3.1)$')\n",
    "plt.plot(x2, dy(x2), c='darkblue', lw=1, \n",
    "         label=r'$y =  \\frac{ - 8 \\ (x + 1)}{(x + 3)^2 (x - 1)^2} , x \\in (-2.9; 0.9)$')\n",
    "plt.plot(x3, dy(x3), c='darkblue', lw=1, \n",
    "         label=r'$y =  \\frac{ - 8 \\ (x + 1)}{(x + 3)^2 (x - 1)^2} , x \\in (1.1; 2.1)$')\n",
    "\n",
    "plt.plot(x1, d2y(x1), c='magenta', lw=1, \n",
    "         label=r'$y =  \\frac{ 8 \\ (3 x^2 + 6x + 7)}{(x + 3)^3 (x - 1)^3}, x \\in (-4.1; -3.1)$')\n",
    "plt.plot(x2, d2y(x2), c='magenta', lw=1, \n",
    "         label=r'$y =  \\frac{ 8 \\ (3 x^2 + 6x + 7)}{(x + 3)^3 (x - 1)^3} , x \\in (-2.9; 0.9)$')\n",
    "plt.plot(x3, d2y(x3), c='magenta', lw=1, \n",
    "         label=r'$y =  \\frac{ 8 \\ (3 x^2 + 6x + 7)}{(x + 3)^3 (x - 1)^3} , x \\in (1.1; 2.1)$')\n",
    "\n",
    "plt.axvline(-3, c='darkred',ls='--',lw=2, label=r'$x = - 3$')\n",
    "plt.axvline(1, c='red',ls='--',lw=2, label=r'$x = 1$')\n",
    "plt.axhline(0, c='darkorange',ls='--',lw=2, label=r'$y = 0$')\n",
    "\n",
    "plt.scatter([-4, -1, 2], [y(-4), y(-1), y(2)], s=50)\n",
    "\n",
    "plt.xlabel(r'$x$', fontsize=15); plt.ylabel(r'$y$', fontsize=15); plt.ylim(-10, 10)\n",
    "plt.legend(fontsize=15, shadow=True, bbox_to_anchor=(1.6,1.0));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Типовой расчет №15\n",
    "\n",
    "Провести полное исследование функции и построить ее график.\n",
    "\n",
    "$\\large{\\displaystyle{ y = (2 + x) \\ e^{x - 4} }}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x')\n",
    "y = (2 + x) * E ** (x - 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение\n",
    "\n",
    "1) Найдем область определения функции и точки разрыва.\n",
    "\n",
    "$\\large{\\displaystyle{ \\forall x \\in \\mathbb{R}: \\exists y(x); D(y)= (-\\infty;  +\\infty) }}$\n",
    "\n",
    "Функция определена и непрерывна для всех значений аргумента из множества действительных чисел.\n",
    "\n",
    "Точек разрыва нет.\n",
    "\n",
    "2) Вычислим односторонние пределы функции\n",
    "\n",
    "- в граничных точках области определения, \n",
    "\n",
    "- в точках разрыва. \n",
    "\n",
    "Найдем вертикальные асимптоты.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to +\\infty}  (2 + x) \\ e^{x - 4}  =  \\lim_{ x \\to +\\infty}  (2 + x)  \\lim_{ x \\to +\\infty}  e^{x - 4} = +\\infty \\cdot +\\infty = +\\infty }}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -\\infty}   (2 + x) \\ e^{x - 4} = \\lim_{ x \\to -\\infty}   (2 + x) \\lim_{ x \\to -\\infty}  e^{x - 4} = [-\\infty \\cdot 0] }}$\n",
    "\n",
    "Для раскрытия неопределенности используем правило Лопиталя.\n",
    "\n",
    "$\\large{\\displaystyle{ \\lim_{ x \\to -\\infty}   (2 + x) \\ e^{x - 4} = \\lim_{ x \\to -\\infty} \\frac{x + 2}{e^{4 - x}} = \\lim_{ x \\to -\\infty} \\frac{(x + 2)'}{(e^{4 - x}) '} = }}$\n",
    "\n",
    "$\\large{\\displaystyle{ = \\lim_{ x \\to -\\infty}  \\frac{1}{ -e^{4 - x}} = 0}}$\n",
    "\n",
    "Точек разрыва нет, значит и вертикальных асимптот нет."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( 0, \\quad \\infty\\right )$$"
      ],
      "text/plain": [
       "(0, ∞)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(y, x, -oo), limit(y, x, +oo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Проверим, является ли функция четной, нечетной, периодической.\n",
    "\n",
    "$\\large{\\displaystyle{ y (-x) = (2 + (-x)) \\ e^{-x - 4}  = \\frac{2 - x}{e^{x + 4}} }}$\n",
    "\n",
    "$\\large{\\displaystyle{ y (-x) \\neq y(x) \\land y (-x) \\neq -y(x) }}$\n",
    "\n",
    "Функция не является четной или нечетной.\n",
    "\n",
    "Обозначим $ t \\neq 0$ предполагаемый период функции.\n",
    "\n",
    "$\\large{\\displaystyle{y(x + t) = y(x) \\iff (2 + x + t) \\ e^{x + t - 4} = (2 + x) \\ e^{x  - 4} \\iff }}$ \n",
    "\n",
    "$\\large{\\displaystyle{\\iff ( 2 + x + t) \\ e^{x + t - 4} - (2 + x) \\ e^{x  - 4} = 0 \\iff }}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\iff (t \\ e^t + x \\ e^t - x + 2 \\ e^t - 2) \\ e^{x-4} = 0 \\iff }}$\n",
    "\n",
    "$\\large{\\displaystyle{\\iff t \\ e^t + x \\ e^t - x + 2 \\ e^t - 2 = 0 \\iff}}$\n",
    "\n",
    "$\\large{\\displaystyle{ \\iff  e^t \\ (t + x + 2 ) = x + 2 \\iff e^t = \\frac{x + 2}{t + x + 2} }}$\n",
    "\n",
    "$\\large{\\displaystyle{ t \\neq const \\land t = t(x) }}$\n",
    "\n",
    "Функция не является периодической.\n",
    "\n",
    "4) Найдем точки пересечения графика функции с осями координат.\n",
    "\n",
    "$\\large{\\displaystyle{x = 0 \\implies y = \\frac{2}{e^4} \\approx 0.04 }}$\n",
    "\n",
    "$\\large{\\displaystyle{y = 0 \\iff (2 + x) \\ e^{x  - 4} = 0 \\iff x + 2 = 0 \\iff x = -2 }}$\n",
    "\n",
    "График функции пересекает ось $Oy$ в точке $(0; \\frac{2}{e^4})$ и пересекает ось $Ox$ в точке $(-2; 0)$ ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2 + x) * E ** (x - 4) == (2 + (-x)) * E ** ((-x) - 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-(2 + x) * E ** (x - 4) == (2 + (-x)) * E ** ((-x) - 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ - x + \\operatorname{LambertW}{\\left (\\left(x + 2\\right) e^{x + 2} \\right )} - 2\\right ]$$"
      ],
      "text/plain": [
       "⎡             ⎛         x + 2⎞    ⎤\n",
       "⎣-x + LambertW⎝(x + 2)⋅ℯ     ⎠ - 2⎦"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = Symbol(' t')\n",
    "solve(((2 + x + t) * E ** (x + t - 4) - (2 + x) * E ** (x - 4))/ E ** (x - 4), t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.0366312777774684$$"
      ],
      "text/plain": [
       "0.0366312777774684"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ -2, \\quad \\tilde{\\infty}\\right ]$$"
      ],
      "text/plain": [
       "[-2, zoo]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve((2 + x) * E ** (x - 4), x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5) Найдем наклонные асимпоты графика функции.\n",
    "\n",
    "$\\large{\\displaystyle{\\lim_{ x \\to +\\infty}  \\frac{(2 + x) \\ e^{x - 4}}{x}  =  \\lim_{ x \\to +\\infty}  \\frac{2 + x}{x}  \\lim_{ x \\to +\\infty}  e^{x - 4} = }}$ \n",
    "\n",
    "$\\large{\\displaystyle{= \\lim_{ x \\to +\\infty}  \\bigg(\\frac{2}{x} + 1\\bigg)  \\lim_{ x \\to +\\infty}  e^{x - 4} = 1 \\cdot +\\infty = +\\infty }}$\n",
    "\n",
    "$\\large{\\displaystyle{\\lim_{ x \\to -\\infty}  \\frac{(2 + x) \\ e^{x - 4}}{x}  =  \\lim_{ x \\to -\\infty}  \\frac{2 + x}{x}  \\lim_{ x \\to -\\infty}  e^{x - 4} = }}$ \n",
    "\n",
    "$\\large{\\displaystyle{=  \\lim_{ x \\to -\\infty}  \\bigg(\\frac{2}{x} + 1\\bigg)  \\lim_{ x \\to -\\infty}  e^{x - 4} = 1 \\cdot 0 = 0 }}$\n",
    "\n",
    "Наклонная асимптота отсутствует.\n",
    "\n",
    "6) Вычислим первую производную. Найдем точки локального экстремума и промежутки монотонности.\n",
    "\n",
    "$\\large{\\displaystyle{y ' = ((2 + x) \\ e^{x - 4}) ' = (2 + x)' \\ e^{x - 4} + (2 + x) \\ (e^{x - 4})' = e^{x - 4} + (2 + x) \\ e^{x - 4} }}$ \n",
    "\n",
    "$\\large{\\displaystyle{y ' = (3 + x) \\ e^{x - 4} }}$\n",
    "\n",
    "Производная определена и непрерывна для всех значений аргумента из множества действительных чисел.\n",
    "\n",
    "Точками локального экстремума могут быть только стационарные точки, для которых $y ' = 0$.\n",
    "\n",
    "$\\large{\\displaystyle{y ' = 0 \\iff (3 + x) \\ e^{x - 4} = 0 \\iff x + 3 = 0 \\iff x = -3 }}$\n",
    "\n",
    "$\\large{\\displaystyle{y (-3) = (2 - 3) \\ e^{-3 - 4} = -\\frac{1}{e^7} \\approx -0.001}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Промежутки монотонности:\n",
    "\n",
    "| $x$ | $(-\\infty; -3)$ | $-3$ | $(-3; +\\infty)$ |\n",
    "| :-: | :-: | :-: | :-: | \n",
    "|  $y ' (x)$  | $-$ | $0$ | $+$ |\n",
    "|  $y (x)$  | $\\searrow$  | $-\\frac{1}{e^7}$ | $\\nearrow$ |\n",
    "\n",
    "$x = -3$ является точкой локального максимума, $y ( -3 ) = -\\frac{1}{e^7}$.\n",
    "\n",
    "$(-\\infty; -3)$ - функция убывает.\n",
    "\n",
    "$(-3; +\\infty)$ - функция возрастает."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\infty, \\quad 0\\right )$$"
      ],
      "text/plain": [
       "(∞, 0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit((2 + x) * E ** (x - 4) / x, x, oo), limit((2 + x) * E ** (x - 4) / x, x, -oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left(x + 3\\right) e^{x - 4}$$"
      ],
      "text/plain": [
       "         x - 4\n",
       "(x + 3)⋅ℯ     "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(y, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAVBAMAAAA6IZrnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt0yiUQQzSKZu2ZU76sdDLBYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAe0lEQVQYGWMQUmZAAoxKBgyuSHwgkyUASYTDZVYAqkgmA/cfVBH5A2zfUUViAxjQRBgYeH6jqmFgCNqAJmL4zgBNhIEHale6EgiAnX4/AcWFxgwM6w8gi7D9T0ATYbjHwICmazeGe1hnovsUHCzIJkPCiUgRJ9Rw1g0AADBAI52rblRZAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ -3\\right ]$$"
      ],
      "text/plain": [
       "[-3]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(y, x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$-0.000911881965554516$$"
      ],
      "text/plain": [
       "-0.000911881965554516"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:-3})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWUAAAAVBAMAAABs/uL9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInZUiRDNmWbvRN27qzJGkhbKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADmElEQVRIDdVWXUgUURT+dmdnd3bVbaHAh14W6Q9C2oewp1LIiAhrk9JCqYUIoiKXSNywh7Ewg4J6TQiXoiJ8UKwoEMqEehAqKYqIfoawl6iopAih7Jw7M3d2d3Zj0IQ64L3n57vffHPn3OsCiOF/MqHWn/ifJOMCq13pSF6wfswJ/j3PV380C95iNSXFqWmcKb3pgdIlyTALxwN9M7RJYA8Q0uWD/JPYlZJRodNSulQInUnsgX5FQv0O9ABh5wGRXsxzhCkHnQp7y17kxyIqBBWBlEjVGPkFD/RXsyDN4SQu5y2t1e1Qu5m0XXMe/JAfc2SD3mYo2J4pWJGDjy7VqQ17umXqVLt0TedP9BKq/ACCOg7LBDmRW3bkv24KaKzeWS8aWakLxrioVj2dWGuhbJA2uqEXyr6dm+zVrvn0onNZ1FyaMKzK8nWm44neYevXgcA49joZRKtfW9HWIctJ+x+HBtkPxpQ0zyFUxzvZASSoEmpbdjXRmXn36EujaUoZB+pETd0YtzCe6C0s8PaVQd82hWsyw05tQoSV9n5rMf+XCp1zH4EbPHdhRew5O5AgVrJjMgVEs5QuZvQyal8NVd5z1dep80Tmjd7E8qjQvaEMopfo9g+zGZQMf+NSxW4e2aIoTwkH9AWq2DNw30w4IMSpq6azlNbpL9dsZj8lB6Zo0Lj6zNwY8rzRNwl5t3lpXxLRz6zZtqiBcnqRXM3AvLgo8zXeIjx8Nad8zdhMX57FFzXWHPhJAzs5mr3R8xq2T8CjBCJnIbcU2PXN0pzz2TEQU5OE5ys/JPYn8gXbBIXTG3GKD9CR9gmAKOYPLDX4SAfmc97pDdp9D/S8hkydTrJm6o1RM8FjeNzqDed4tWbfmCerjOq+FC0cq/iMOgrI5BlcQ58m0ZZFIAl+P7cpBvAkSM1hXhfyDHqjt/nOi97QRtBgZ6jZdMj7uXFIPL323RFcZMQxHh7SCfjVfDZib6cFQiipjqLlx5YM+B9VMWtHa1y9012pm0V1+WLheKO3CU+C7+dQHP12huYrHc5vJE1c0M1VSkYovMewCdrnQ/FVx+USEwQ0PDCAJd8JOSxeVQJsJ/CSzrC/zWnEU2LHPdJbLJEO+o2EshjKDJu3YNYOFiSKhS6QUlyze+0Jw51zZVz0hFhIDZF2IWeToJt4ji1D/Hf/6jMa/ypbETLfCCVbixRmntJnvtTbynJuPt+cP8abGI+oLuA3RBXvjKMR+04AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( -3 < x \\wedge x < \\infty, \\quad -\\infty < x \\wedge x < -3\\right )$$"
      ],
      "text/plain": [
       "(-3 < x ∧ x < ∞, -∞ < x ∧ x < -3)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(y, x) > 0, x), solve(diff(y, x) < 0, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7) Вычислим вторую производную. Найдем точки перегиба графика функции и промежутки выпуклости.\n",
    "\n",
    "$\\large{\\displaystyle{y '' = ((3 + x) \\ e^{x - 4}) ' = (3 + x)' \\ e^{x - 4} + (3 + x) \\ (e^{x - 4})' = e^{x - 4} + (3 + x) \\ e^{x - 4} }}$ \n",
    "\n",
    "$\\large{\\displaystyle{y '' = (4 + x) \\ e^{x - 4} }}$\n",
    "\n",
    "Вторая производная определена и непрерывна для всех значений аргумента из множества действительных чисел.\n",
    "\n",
    "Точками перегиба могут быть только те, для которых $y '' = 0$.\n",
    "\n",
    "$\\large{\\displaystyle{y '' = 0 \\iff (4 + x) \\ e^{x - 4} = 0 \\iff x + 4 = 0 \\iff x = -4 }}$\n",
    "\n",
    "$\\large{\\displaystyle{y (-4) = (2 - 4) \\ e^{-4 - 4} = -\\frac{2}{e^8} \\approx -0.0007}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Промежутки выпуклости:\n",
    "\n",
    "| $x$ |  $(-\\infty; -4)$ | $-4$ | $(-4; +\\infty)$ |\n",
    "| :-: | :-: | :-: | :-: | \n",
    "| $y '' (x)$ | $-$ | 0 | $+$ |\n",
    "| $y (x)$ | $\\cap$ | $ -\\frac{2}{e^8}$ | $\\cup$ |\n",
    "\n",
    "Функция имеет одну точку перегиба $(-4;  -\\frac{2}{e^8})$. \n",
    "\n",
    "$(-4; +\\infty)$ - график функции является выпуклым вниз.\n",
    "\n",
    "$(-\\infty; -4)$ - график функции является выпуклым вверх."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left(x + 4\\right) e^{x - 4}$$"
      ],
      "text/plain": [
       "         x - 4\n",
       "(x + 4)⋅ℯ     "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(diff(diff(y,x), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAVBAMAAAA6IZrnAAAALVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAdt0yiUQQzZmrZiLvu9e84gsAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABpSURBVBgZYxBSZkACjEoGDK5IfCCTJQBFhLkBXYRpArqIELoI83J0ERZ2dBFpdBHuBegiLAwwkXQlEFBmWA0XgTqaWwBdhHXmzHknHdB8wYNuOwPfBTRfcNS9FUDThRkaxIs4oYazTgAAigAb5G8vYC4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ -4\\right ]$$"
      ],
      "text/plain": [
       "[-4]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(diff(y,x), x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAAAPBAMAAACb93d3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMol2mSJUZrurRO9iHDTAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAADZElEQVQ4EY2UwWtcVRTGfy8zr/Nm5s3kNUVwlRlUEK3QkVRqcdG3ce0oJlZcZEqh6ULasYhPJKUDXcSFkNm4tVOFVlzo1CouFDpSoSjFDP4DSdFFRbFpmsa0NR3POfclk0oXXobv3HPe953v3XfvHfgfIzj7EFIWHk3LMV6LbbmVrfgQnStNzrRsYnEITE7G+cFgcB9/6l0hJLMRQbI7przy+LMwd+IruPHYRORyb+q1PpjaiqYxDmSbzkhxpO09vxUtcZXT/bDmP5Mk+3mKXS12NbLX+QB/g8yB58S3x3SfiVsv4/Ic/Ji2sqJqHEcIPe3vxifwhs4sDoEnKXalR9As1PC7/Azf8D38RajsUNa0RM+mCp/BmGthRdM4Dhw2mrLgOzgTbUZLDPI3pZaXthR7SLIC09yIWGiZW/km4fo2N3nhsbRVT4SmcRyyH2slHX/DYlvmFocwsuSev8pok9Id7x4cjy/DQuzWViNc3ea2eIH3XAsrmiY0Dv5Iz7US9NSgk8azmhh0Rp+YOimPgy4Vcbtra5NzwAHCczOxTMgs89ORt2X1moeDmXbaSotOYxyObnMLbsNLDWmr8egWNCpPU5Ylh33m62TXdN8udeR8rVGMgg11E9UF5vtpPr3SSltp0WmME3T+61ZP3Q6qm0G9skzuGszLT9xuM97PLoh7pqlGFxX2KRRrihfJH7y0YW7SSopOYxwfdRub0LHXE4PFhnxJjYe2oDFaoyBLeAUqdUpreO+8fjyWWyfN4FQLcuabW3f5efL3d6atyK07jXE+NTdl6ZCtOtPejJYYZKoU7sIL6CnJ31HmqYiCWHwpsxjOyxqq5FZdrp+hbUIrphrhBI0H3L6FLyLpZXEI8olkbd4/0rNLQa8Du+FDgtavcjDlctR5vyyHbhnNvWXZ4o6preg0yildvbrwZ13lNj6HEzqxOISS7NsSJXndwhK5Kh9FwSrZOjsikf4BL8IhH8pdLL8ub9UytRWdRjnSudwTSEem7f1GpYrFIfA1423yshXsZzzmcFTscDpJLjPHjmsE+5LZWtDkWOTyXyLOuRauqBrjiH60u+klx2PqzViPmsUh4Cc/yFf/XYiPHJGZPynXb89gsCJ/zVciRuT/usrc7FvC0Tx7Jem7Fq6oGscht+de418hmV2nGkx1ygAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$-0.000670925255805024$$"
      ],
      "text/plain": [
       "-0.000670925255805024"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.evalf(subs={x:-4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( -4 < x \\wedge x < \\infty, \\quad -\\infty < x \\wedge x < -4\\right )$$"
      ],
      "text/plain": [
       "(-4 < x ∧ x < ∞, -∞ < x ∧ x < -4)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(diff(y, x), x) > 0, x), solve(diff(diff(y, x), x) < 0, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8) Построим график функции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(y, (x, -4.1, 0.1)); plot(diff(y,x), (x, -4.1, 0.1)); plot(diff(diff(y,x), x), (x, -4.1, 0.1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.linspace(-4.1, 0.1)\n",
    "y = lambda x: (2 + x) * numpy.exp(x - 4)\n",
    "dy = lambda x: (3 + x) * numpy.exp(x - 4)\n",
    "d2y = lambda x: (4 + x) * numpy.exp(x - 4)\n",
    "\n",
    "plt.figure(figsize=(10,10)) ; plt.grid(c='steelblue',ls='--',lw=0.5)\n",
    "\n",
    "plt.plot(x, y(x), c='steelblue', lw=3, label=r'$ y = (2 + x) \\ e^{x - 4}$')\n",
    "plt.plot(x, dy(x), c='darkblue', lw=1, label=r'$ y = (3 + x) \\ e^{x - 4}$')\n",
    "plt.plot(x, d2y(x), c='magenta', lw=1, label=r'$ y = (4 + x) \\ e^{x - 4}$')\n",
    "\n",
    "plt.scatter([-4, -3, -2, -1, 0], [y(-4), y(-3), y(-2), y(-1), y(0)], s=50)\n",
    "\n",
    "plt.xlabel(r'$x$', fontsize=15); plt.ylabel(r'$y$', fontsize=15); plt.ylim(-0.01, 0.04)\n",
    "plt.legend(fontsize=15, shadow=True, bbox_to_anchor=(1.6,0.5));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}