{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ff7534ba",
   "metadata": {},
   "source": [
    "## Подготовка к КР по теме \"Циклы\" (задания, выполняемые без использование компьютера).  Вариант X\n",
    "\n",
    "### Внимание!! \n",
    "Тренировочная работа была сделана под влиянием высокой температуры. Предупреждаю заранее, что могут быть нерешаемые или бредовые задания. Прошу понять. ;("
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f34b4a7c",
   "metadata": {},
   "source": [
    "***№ 1.*** Для каких начальных значений переменной $x$ завершится выполнение оператора цикла (указать интервал(ы) или пустое множество {∅}):\n",
    "\n",
    "1) `while x < 10: x = x * x - 90`      \n",
    "\n",
    "**Ответ 1:**\n",
    "\n",
    "2) `while x >= 0: x = abs(math.cos(x))` \n",
    "\n",
    "**Ответ 2:**\n",
    "\n",
    "3) `while x // 3 < 0: x = x + 2` \n",
    "\n",
    "**Ответ 3:**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2998bb33",
   "metadata": {},
   "source": [
    "-----\n",
    "***№ 2а).*** Дан фрагмент программы для получения значений $y$. Переписать программу, заменив цикл `while` циклом `for`. Дополнительные переменные не использовать.\n",
    "\n",
    "```python\n",
    "y = 150\n",
    "i = 5\n",
    "while i < 11:\n",
    "    y = y // i\n",
    "    i = i + 2\n",
    "print(y)\n",
    "```\n",
    "\n",
    "Используйте шаблон:\n",
    "\n",
    "```python\n",
    "y = 150\n",
    "for i in range(____, ____):\n",
    "    y =\n",
    "print(y)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2342fe01",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Решение задание № 2а\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a82fcc8f",
   "metadata": {},
   "source": [
    "-----\n",
    "***№ 2б).*** Дан фрагмент программы для получения значений $y$. Переписать программу, заменив цикл `while` циклом `for`. Дополнительные переменные не использовать.\n",
    "\n",
    "```python\n",
    "y = 3\n",
    "i = 15\n",
    "while i >= 7:\n",
    "    y = y + i\n",
    "    i = i - 2\n",
    "print(y)\n",
    "```\n",
    "\n",
    "Используйте шаблон:\n",
    "\n",
    "```python\n",
    "y = 3\n",
    "for i in range(____, ____, -1):\n",
    "    y =\n",
    "print(y)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "70c34f12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Решение задание № 2б\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06263230",
   "metadata": {},
   "source": [
    "----\n",
    "***№ 3.***\n",
    "Записать соотношения для вычисления всех членов последовательности $y_i$:\n",
    "$$    \n",
    "1, \\quad  \\frac{x^2}{2!}, \\quad  \\frac{x^4}{4!}, \\quad  \n",
    "\\frac{x^6}{6!},\\quad  ... \n",
    "$$\n",
    "\n",
    "*Указание.* При записи формул используйте только традиционные математические символы (не знаки операций из ЯП). \n",
    "\n",
    "**Начальное значение $y_i$ с конкретным указанием $i$**: ____ ____    (пример вида ответа: $y_0=x$)\n",
    "    \n",
    "**Рек. соотношение для $y_i$**: ____ ____      (пример вида ответа: $y_i=-y_{i-1}\\frac{i+1}{i}$)\n",
    "\n",
    "**Интервал изменения $i$ для рек. соотношения**: ____ ____    (пример вида ответа: $i=1,2,...$)\n",
    "\n",
    "*Внимание!* примеры носят иллюстративный характер.\n",
    "\n",
    "----\n",
    "Ниже приведены окошки для вставки ваших ответов. Это рисунок, который можно скопировать, исправить в Paint (например) и вставить обратно в jupyter. "
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "9cb270a8",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "954895fc",
   "metadata": {},
   "source": [
    "----\n",
    "***№ 4.*** **Полностью** написать программу, которая решает следующую задачу: дано $b ∈ R$.\n",
    "Найти первый член последовательности $a_i$ ($i = 1,2, ...$), меньший $b$. Последовательность $a_1$,\n",
    "$a_2$,... образована по закону:\n",
    "$$\n",
    "  a_1 = 1, \\ \\  a_i = a_{i−1}\\cdot \\frac{i-1}{i+1}\\ \\ \\ (i = 2, 3,...).\n",
    "$$\n",
    "\n",
    "**Что значит «полностью» написать программу:** в программе должны присутствовать операторы ввода данного и вывода ответа."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d1564345",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Решение задание № 4\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d268a7f",
   "metadata": {},
   "source": [
    "----\n",
    "***№ 5.*** Полностью написать программу, которая решает следующую задачу: дано $n ∈ N$.\n",
    "Вычислить сумму:\n",
    "$$    \n",
    "\\sum_{i=1}^n \\frac{(−1)^{i-1}}{2i + 1}.\n",
    "$$\n",
    "\n",
    "*Указание.* В программе запрещено использовать выбирающие операторы; операцию `**`; функцию\n",
    "`pow()`; экспоненциально-логарифмическую запись; рекуррентную формулу для вычисления отдельного \n",
    "слагаемого $y_i$ в сумме $\\sum\\limits_{i=1}^n y_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5d9b0d95",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Решение задание № 5\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01559b97",
   "metadata": {},
   "source": [
    "-------------\n",
    "## II часть (с использованием компьютера)\n",
    "\n",
    "Перед началом работы обязательно переименуйте данный файл. Для этого выберите пункт меню File, затем Rename... В открывшемся окне, замените имя файла на свои фамилию и имя (без пробела), записанные латинскими символами. Затем замените цифру 0 после gr на номер своей группы (1, 2, 3, 4, 5 или 6).\n",
    "\n",
    "Например, этот файл студента Иванова Петра из 1 группы должен называться IvanovPetr_gr1_varX\n",
    "\n",
    "------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eb16091",
   "metadata": {},
   "source": [
    "***№ 6.*** Проверить, верно ли, что в записи введенного натурального числа все цифры принадлежат кратны трём. Как только условие будет нарушено, работу цикла прекратить.\n",
    "\n",
    "**№ 6A (while).** Напишите программу для решения задания 6, выполнив следующие указания:\n",
    "\n",
    "6А.1. В программе запрещено использовать ЛЮБЫЕ выбирающие операторы или конструкции, а также оператор `break`.\n",
    "\n",
    "6А.2. В программе обязательно должны присутствовать операторы для построения трассировочной таблицы и вывода ответа --- `True` или `False`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2e4829ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "# решение задания 6A\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "853947a2",
   "metadata": {},
   "source": [
    "---- \n",
    "**№ 6B (while, break).** Напишите программу для решения задания 6, выполнив следующие *указания*:\n",
    "\n",
    "6B.1. В программе используйте по ОДНОМУ разу: `while`, `if`, `break`, `print()`.\n",
    "\n",
    "6B.2. Не использовать булевские переменные.\n",
    "\n",
    "6B.3. В программе обязательно должен присутствовать оператор для вывода ответа --- `True` или \n",
    "`False`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "126cae03",
   "metadata": {},
   "outputs": [],
   "source": [
    "# решение задания 6B\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c9f149",
   "metadata": {},
   "source": [
    "----\n",
    "***№ 7.*** Дано $x \\in R$. \n",
    "Написать программу для получения и вывода на печать всех членов последовательности\n",
    "$$    \n",
    "1, \\quad  \\frac{x^2}{2!}, \\quad  \\frac{x^4}{4!}, \\quad  \n",
    "\\frac{x^6}{6!},\\quad  ...\n",
    "$$\n",
    "больших, либо равных по модулю $\\varepsilon =10^{-5}$, а также их номеров.\n",
    "\n",
    "*Указания.* 1) Используйте соотношения, полученные в задании 3. 2) Неоправданное использование дополнительных переменных и лишних операций понижает оценку учащегося."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "98d6a699",
   "metadata": {},
   "outputs": [],
   "source": [
    "# решение задания 7\n",
    "# ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ddcc4b1",
   "metadata": {},
   "source": [
    "----\n",
    "***№ 8.*** Даны $n\\in N$, $x\\in R$.\n",
    "Оформить в виде двух подпрограмм с параметрами вычисление следующих выражений\n",
    "$$\n",
    "  f_1 =\\sin x + \\frac{1}{2}\\sin^2 x + {\\dots} + \\frac{1}{n}\\sin^n x,\\quad   f_2 = \\frac{1}{x^2}.\n",
    "$$\n",
    "\n",
    "Вычислить:\n",
    "$$\n",
    "  y =\n",
    "  \\left\\{\n",
    "    \\begin{array}{ll}\n",
    "      f_1,  & \\text{если $-1<x<0$}, \\\\\n",
    "      f_2, & \\text{в противном случае}.\n",
    "    \\end{array}\n",
    "  \\right.\n",
    "$$\n",
    "\n",
    "Для случая **не**выполнения условия $-1<x<0$ дополнительно нарисовать фрагмент графика функции $f_2$ с помощью функции `plot` пакета `sympy` на $[0.25; 2.25]$.\n",
    "\n",
    "*Указания и примечания.* 1) Вложенные циклы не использовать.\n",
    "2) Программа в любом случае должна выдавать ответ (числовой, графический или строковый)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b3d1756e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# решение задания 8\n",
    "# ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9baa8d7b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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