math3_hw2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 1\n",
    "- Предложить пример функции,  не имеющей предела в нуле и в бесконечностях\n",
    "    - $sin(x)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 3\n",
    "#### Исследовать функцию $f(x) = x^3 - x^2$ по плану\n",
    "- Область задания и область значений\n",
    "    $$(-\\infty, +\\infty), (-\\infty, +\\infty)$$\n",
    "- Нули функции и их кратность\n",
    "    x = 1, x = 0, один из корней кратный\n",
    "- Отрезки знакопостоянства\n",
    "    $$(-\\infty, 1), (1, +\\infty)$$\n",
    "- Интервалы монотонности\n",
    "    \n",
    "    Возьмем производную: \n",
    "    $f`(x)=3x^2 - 2x$\n",
    "     Корни производной $x_1=0$, $x_2=2/3$\n",
    "     Функция является возрастающей на $(-\\infty, 0)$ и $(2/3, -\\infty)$, убывающей на $(0, 2/3)$\n",
    "- Четность функции\n",
    "    Ни чётная, ни нечётная функция (функция общего вида)\n",
    "- Ограниченность\n",
    "    Функция не ограничена\n",
    "- Периодичность\n",
    "    Не периодична"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11781a9e8>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.linspace(-100, 100, 300)\n",
    "y = x**3 - x**2\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "#plt.ylim((-0.5, 0.5))\n",
    "#plt.xlim((-1, 1))\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание\n",
    "Найти предел:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lim_{x\\to 0}\\frac{3x^3-2x^2}{4x^2}$\n",
    "$\\frac{3x^3-2x^2}{4x^2}  \\Rightarrow \\frac{x^2(3x-2)}{4x^2}  \\Rightarrow \\frac{(3x-2)}{4} $\n",
    "$\\lim_{x\\to 0}\\frac{(3x-2)}{4} = -\\frac{1}{2} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lim_{x\\to 0}\\frac{\\sin(2x)}{4x} \\Rightarrow \\lim_{x\\to 0}\\frac{2\\sin(x)*\\cos(x)}{4x} \\Rightarrow \\lim_{x\\to 0}\\frac{\\sin(x)}{x} * \\lim_{x\\to 0}\\cos(x) * \\lim_{x\\to 0}\\frac{1}{4} \\Rightarrow 1 * 1 * 1/4 = 1/4 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lim_{x\\to 0}\\frac{x}{\\sin(x)} \\Rightarrow \\lim_{x\\to 0}\\frac{x * \\sin(x)}{\\sin(x) * x} = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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