mathanalysis_practice102.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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",
       "h1,h2 {font-family:Roboto; color:slategray; text-shadow:4px 4px 4px #aaa;} \n",
       "div.output_subarea, div.output_area pre{font-family:Roboto; font_size:120%; color:darkblue;}\n",
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       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "%%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",
    "h1,h2 {font-family:Roboto; color:slategray; text-shadow:4px 4px 4px #aaa;} \n",
    "div.output_subarea, div.output_area pre{font-family:Roboto; font_size:120%; color:darkblue;}\n",
    "</style> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задачи / Problems\n",
    "[Сборник задач по математике для втузов. В 4-х частях. Под ред. Ефимова А.В., Поспелова А.С. (Часть 2)](https://drive.google.com/file/d/1qUN5t1IQdWvlRf0gdVYZ87MznWUaHq2x/view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math, sympy\n",
    "from sympy import *\n",
    "sympy.init_printing(use_unicode=True)\n",
    "import pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x 1 =  2\n",
      "x 2 =  0\n",
      "x 3 =  6\n",
      "x 4 =  0\n",
      "x 5 =  10\n"
     ]
    }
   ],
   "source": [
    "# 5.214 \n",
    "# Напишите первые пять членов последовательности / Write the first five terms of the sequence\n",
    "def x(n): return n * (1 -  (-1) ** n)\n",
    "for n in range(1,6):  print ('x',n,'= ',x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x 1 =  0\n",
      "x 2 =  2\n",
      "x 3 =  0\n",
      "x 4 =  2\n",
      "x 5 =  0\n"
     ]
    }
   ],
   "source": [
    "# 5.218\n",
    "# Напишите формулу общего члена последовательности / Write the formula for the general term of the sequence\n",
    "def x(n): return 1 -  (-1) **( n + 1)\n",
    "for n in range(1,6):  print ('x',n,'= ',x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x_{n} = 1 - (-1)^{n + 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$x_{n} = 1 - (-1)^{n + 1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x 1 =  2.0\n",
      "x 2 =  1.3333333333333333\n",
      "x 3 =  1.2\n",
      "x 4 =  1.1428571428571428\n",
      "x 5 =  1.1111111111111112\n"
     ]
    }
   ],
   "source": [
    "# 5.219\n",
    "# Напишите формулу общего члена последовательности / Write the formula for the general term of the sequence\n",
    "def x(n): return 2 * n / (1 + 2 * (n - 1))\n",
    "for n in range(1,6):  print ('x',n,'= ',x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x_{n} = \\frac{2 * n} {1 + 2 * (n - 1)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$x_{n} = \\frac{2 * n} {1 + 2 * (n - 1)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "xn = [2, 4/3, 6/5, 8/7, 10/9]\n",
    "for n in range(1,6):  print (xn[n-1] == x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x 1 =  2.0\n",
      "x 2 =  1.3333333333333333\n",
      "x 3 =  1.2\n",
      "x 4 =  1.1428571428571428\n",
      "x 5 =  1.1111111111111112\n"
     ]
    }
   ],
   "source": [
    "def x(n): return 2 * n / (2 * n - 1)\n",
    "for n in range(1,6):  print ('x',n,'= ',x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x_{n} = \\frac{2 * n} {2 * n - 1}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$x_{n} = \\frac{2 * n} {2 * n - 1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x 1 =  1\n",
      "x 2 =  0\n",
      "x 3 =  -3\n",
      "x 4 =  0\n",
      "x 5 =  5\n"
     ]
    }
   ],
   "source": [
    "# 5.220\n",
    "# Напишите формулу общего члена последовательности / Write the formula for the general term of the sequence\n",
    "def x(n): return  int(n  * math.sin(math.pi * n/2 ))\n",
    "for n in range(1,6):  print ('x',n,'= ',x(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x_{n} = n * sin(\\frac{\\pi * n} {2 })$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$x_{n} = n * sin(\\frac{\\pi * n} {2 })$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### # 5.225\n",
    "Найдите наибольший (или наименьший) член ограниченной сверху (или снизу) последовательности.\n",
    "\n",
    "Find the largest (or smallest) term in a sequence bounded above (or below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def x(n): return  math.sqrt(n)/ (9 + n)\n",
    "n = range(100)\n",
    "x = [x(i) for i in n]\n",
    "plt.axhline(1/6, c='r', ls='--')\n",
    "plt.plot(n,x); plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = symbols('n')\n",
    "x = sqrt(n)/ (9 + n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- \\frac{\\sqrt{n}}{\\left(n + 9\\right)^{2}} + \\frac{1}{2 \\sqrt{n} \\left(n + 9\\right)}$$"
      ],
      "text/plain": [
       "     √n           1      \n",
       "- ──────── + ────────────\n",
       "         2   2⋅√n⋅(n + 9)\n",
       "  (n + 9)                "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(x,n) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAVBAMAAAC55aPcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt0yiUSZqxDvIrvNZlQeUJ4CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAc0lEQVQIHWMQUmYAASDlCmYwAGkgiy2tAsLiUGSwXAAWY5/AwJ0AZvEfYGD5AGb1b2Bg/AwX+wpX9xfM4pjKYP4PzGJoE3kIUQe0hO0HRIyBgWcDmMU3g2G9AZjFqMGwF+oCF7cAKAvsLrCr8LCcoP6YCgDPHx85DbRtdwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left [ 9\\right ]$$"
      ],
      "text/plain": [
       "[9]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(diff(x,n) ,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAqBAMAAACXcryGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMt0Qq5nNdrvviSJEVGY9pkAUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAdklEQVQYGWNgYBAyYGBgYHbNB1EMDPVUpDzmqxSADSWL+A8CH4jTumqVAFDhpgMsCkAqlYGjgYGB9zOQycDANgFM8ScujwEy7PMYOC8AqQ8MrJMZGPgVGPj+MDAwJTDw/WNg4IDweIByID1dDJZAlQxcoY4MDAAgYyHviJQ6LgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{1}{6}$$"
      ],
      "text/plain": [
       "1/6"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.subs(n,9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x_9 = \\frac{1}{6}$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$x_9 = \\frac{1}{6}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### # 5.229 (б)\n",
    "\n",
    "Последовательность монотонно возрастает / The sequence increases monotonically\n",
    "\n",
    "$ \\forall n \\in \\mathbb{N} \\ (x_n < x_{n + 1}) $\n",
    "\n",
    "Отрицание логического высказывания / Negation of a logical statement\n",
    "\n",
    "$ \\exists n \\in \\mathbb{N} \\ (x_n \\geq x_{n + 1}) $\n",
    "\n",
    "#### # 5.229 (г)\n",
    "\n",
    "Последовательность $ (x_n)_{n \\in \\mathbb{N}}$ бесконечно большая / The sequence $ (x_n)_{n  \\in \\mathbb {N}} $ is infinitely large\n",
    "\n",
    "$ \\forall E > 0 \\ \\exists N \\in \\mathbb{N} \\ \\forall n \\in \\mathbb{N} \\ (n > N \\implies |x_n| > E) $ \n",
    "\n",
    "Отрицание логического высказывания / Negation of a logical statement\n",
    "\n",
    "$ \\exists E > 0 \\ \\forall N \\in \\mathbb{N} \\ \\exists n \\in \\mathbb{N} \\ (n > N \\land |x_n| \\leq E) $ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### # 5.230\n",
    "\n",
    "Найдите / Find \n",
    "\n",
    "$a: \\displaystyle{a = \\lim_{x \\to \\infty} x_n} \\ \\& \\ N(\\varepsilon): |x_n - a| < \\varepsilon , \\ \\forall n > N(\\varepsilon)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOBAMAAADgeEClAAAAIVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADdcGRXAAAACnRSTlMAMt0Qq5nNdrvvxbMB0AAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABtJREFUCB1jYGBUZmAwCVvMwMDAThbB0rnIHQBAqQoWQ8kakgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$1$$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5.230(б)\n",
    "from sympy.abc import n\n",
    "limit_seq(sqrt(n ** 2 + 1) / n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\large{| \\frac{\\sqrt{n ^ 2 + 1}}{n}  - 1 | }$$ < 0.005$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$\\large{| \\frac{\\sqrt{n ^ 2 + 1}}{n}  - 1 | }$$ < 0.005$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.00615390423749074$$"
      ],
      "text/plain": [
       "0.00615390423749074"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = abs(sqrt(n ** 2 + 1) / n - 1)\n",
    "N(f.subs(n,9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.00498756211208903$$"
      ],
      "text/plain": [
       "0.00498756211208903"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(f.subs(n,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# N = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAArBAMAAABcLm8jAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMhAi783diatmdpm7RFShYZRwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAl0lEQVQYGWNgEGBgMmBgYPAPTVMAUmnfioAkQwOIQKc6V20ECR5isL8Aohl4EsAU92cgM4CB+yMDA0sCA8cHBgZ2IOsAAwPzBoYlCkAl1js2gRWSR/wHAaCheADzJLAkH1DhF6DtEbt35zEwcIMdwMDHwMAB0VoIppgPgCkOiBfsIVKlECoHTDH9AFO8v8EU33cwxewHpABkciSPOqo32wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{5}{7}$$"
      ],
      "text/plain": [
       "5/7"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5.230(г)\n",
    "from sympy.abc import n\n",
    "limit_seq((5 * n ** 2 + 1) / (7 * n ** 2 - 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\large {| \\frac{5 * n ^ 2 + 1}{7 * n^2 - 3}  - \\frac{5}{7} | }$$< 0.005$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$\\large {| \\frac{5 * n ^ 2 + 1}{7 * n^2 - 3}  - \\frac{5}{7} | }$$< 0.005$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.00557244174265448$$"
      ],
      "text/plain": [
       "0.00557244174265448"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g= abs((5 * n ** 2 + 1) / (7 * n ** 2 - 3) -  5/7)\n",
    "N(g.subs(n,9))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.00450912072145926$$"
      ],
      "text/plain": [
       "0.00450912072145926"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(g.subs(n,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    " # N = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### # 5.249\n",
    "\n",
    "$x_n = n * sin(\\frac{\\pi n}{2})$\n",
    "\n",
    "$ \\exists E > 0 \\ \\forall N \\in \\mathbb{N} \\ \\exists n \\in \\mathbb{N} \\ (n > N \\land |x_n| \\leq E) $ \n",
    "\n",
    "не является бесконечно большой / is not infinitely large"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = range(100)\n",
    "b = [i * math.sin(math.pi * i / 2) for i in a]\n",
    "plt.axhline(50, c='r', ls='--'); plt.text(20,55, '  E', color='r')\n",
    "plt.axhline(-50, c='r', ls='--'); plt.text(20,-60, '- E', color='r') \n",
    "plt.plot(a,b,c='b');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### # 5.250\n",
    "\n",
    "$x_n = \\lg(\\lg{n}), \\ n \\geq 2$\n",
    "\n",
    "$ \\forall E > 0 \\ \\exists N \\in \\mathbb{N} \\ \\forall n \\in \\mathbb{N} \\ (n > N \\implies |x_n| > E) $\n",
    "\n",
    "является бесконечно большой / is infinitely large"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = range(2,500)\n",
    "b = [math.log2(math.log2(i)) for i in a]\n",
    "plt.axhline(3, c='r', ls='--'); plt.text(50,2.7, ' E', color='r')\n",
    "plt.plot(a,b,c='b'); plt.text(30,1.8, 'lg(lg n)', color='b');"
   ]
  }
 ],
 "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",
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