Копія записника "Заняття 5. Похідні. Диференційні рівняння. Графіки функцій.ipynb"

-5-ipynb.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/gist/Krabaton/b379ba09c2d52fcada146a9027ab783f/-5-ipynb.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2nVX6jZdPp3S"
      },
      "source": [
        "# Вступ\n",
        "\n",
        "Ласкаво просимо до світу математичного аналізу!🌈\n",
        "\n",
        "Його вивчення є важливим для майбутніх програмістів, оскільки допомагає розвивати аналітичні та проблемно-розв'язувальні навички, які є необхідними в професійній діяльності. Розуміння математичних концепцій, таких як, наприклад, диференціальні рівняння та інтеграли, допомагає опанувати підходи до обробки великих обсягів даних, моделювання та прогнозування, розробляти більш ефективні та швидкодіючі алгоритми для розв'язання складних завдань.\n",
        "\n",
        "Давай подивимося, які теми чекають на тебе сьогодні:\n",
        "\n",
        "- почнемо вивчати **математичний аналіз** з фокусом на диференціальні рівняння та дізнаємося, як вони застосовуються для **моделювання реальних фізичних явищ**,\n",
        "- дізнаємося, що таке **функція** і як вона задається,\n",
        "- розберемося з поняттям **числових послідовностей** та їхніми **властивостями**,\n",
        "- розглянемо визначення та геометричний зміст **границі функції** та її властивостей,\n",
        "- навчимося **знаходити границі функції** аналітично та програмно, будувати **графік границі функції**,\n",
        "- дізнаємося, що таке **похідна та диференціал** і як їх визначати,\n",
        "- навчимося **досліджувати функцію** за допомогою похідних та екстремумів функцій.\n",
        "\n",
        "\n",
        "Ну як тобі наш план? Вирушаємо за новими знаннями та вміннями?\n",
        "\n",
        "Тоді полетіли! 🚀\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RFYyXVZJG_RI"
      },
      "source": [
        "## Функції, графіки функцій та послідовності\n",
        "### Функція однієї змінної\n",
        "\n",
        "**Функція** — це правило, яке кожному елементу з першої множини ставить у відповідність один і тільки один елемент з другої множини.\n",
        "\n",
        "Навколишній світ скрізь складається з функцій. Математика є потужним інструментом для розуміння природних процесів та допомагає нам зробити прогнози та раціональні рішення в різних галузях науки. Функції однієї змінної використовуються для опису різноманітних явищ у природі та навколишньому середовищі.\n",
        "\n",
        "Так, наприклад, температура повітря змінюється зі зміною висоти над рівнем моря. Ця залежність може бути описана функцією, де температура є змінною, а висота є параметром. Зазвичай при зростанні висоти температура знижується через зміну атмосферного тиску і проходження сонячної радіації через атмосферу.\n",
        "\n",
        "Інші приклади: швидкість руху води в річці зазвичай залежить від рівня води; коли тіло падає під дією земної гравітації, його швидкість змінюється з часом; освітленість довкілля, наприклад, падаючого сонячного світла, зазвичай залежить від відстані від джерела світла. Усі ці залежності може бути описані функціями.\n",
        "\n",
        "Функція може бути задана аналітично, графічно, таблицею й алгоритмом.\n",
        "\n",
        "\n",
        "1. **Аналітичний спосіб**. Функція задається формулою (формулами) або рівнянням, що зв’язує аргумент *x* та залежну змінну *y*. Під областю визначення мають на увазі сукупність значень аргументу, для яких аналітичний вираз має зміст і набуває дійсних значень.\n",
        "\n",
        "Наприклад,\n",
        "\n",
        "1) $y = x^2 + 2;$\n",
        "\n",
        "2)\n",
        "$y =  \\begin{cases}   2x - 1  &\\text {x => 3}\\\\   4 &\\text{x<3} \\end{cases} $\n",
        "\n",
        "\n",
        "3) $2x − 3y + 1 = 0$\n",
        "\n",
        "2. **Графічний спосіб**. Задається графік функції, тобто множина точок площини з координатами (х, f(x)).\n",
        "\n",
        "3. **Табличний спосіб**. Задається таблиця певних значень аргументу та відповідних їм значень функції.\n",
        "\n",
        "4. **Алгоритмічний спосіб**. Задається алгоритм − сукупність арифметичних і логічних операцій, які потрібно здійснити над аргументом, щоб одержати значення функції.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UqvyGBoRTv7T"
      },
      "source": [
        "## Графіки функцій\n",
        "**Графік функції** – це малюнок, на якому можна побачити, як змінюється значення Y залежно від значення Х.\n",
        "\n",
        "Точка з координатами ${\\displaystyle (0,0)}$ називається початком координат.\n",
        "\n",
        "Побудова графіків функцій виконується з використанням бібліотеки Matplotlib."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Розберемо приклад завдання графіка квадратичної функції в Python."
      ],
      "metadata": {
        "id": "hMrWEJ8N09-z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Приклад програмного розв'язання"
      ],
      "metadata": {
        "id": "Rnc1ho72FVrw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Приклад 1"
      ],
      "metadata": {
        "id": "I8HDBDcTGT76"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        " $y = x^2 + 2$"
      ],
      "metadata": {
        "id": "7-T9ugJZhhLA"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
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          "base_uri": "https://localhost:8080/",
          "height": 417
        },
        "id": "3WWdOdvjWY4F",
        "outputId": "45b2fcae-02b5-477a-e4c7-d5041c545f3b"
      },
      "outputs": [
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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "# Перемістимо лівий і нижній стовпчики до x = 0 і y = 0 відповідно.\n",
        "ax.spines[[\"left\", \"bottom\"]].set_position((\"data\", 0))\n",
        "\n",
        "# Сховаємо верхню та праву лінію\n",
        "ax.spines[[\"top\", \"right\"]].set_visible(False)\n",
        "\n",
        "# Намалюємо стрілки (як чорні трикутники: \">k\"/\"^k\") на кінцях осей.\n",
        "# Також вимкнемо відсікання (clip_on=False) стрілок.\n",
        "ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n",
        "ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n",
        "\n",
        "# Сформуємо ряд значень x. 100 елементів від -10 до 10.\n",
        "x = np.linspace(-10, 10., 100)\n",
        "\n",
        "# Додамо проміжні лінії\n",
        "ax.grid(True, linestyle='-.')\n",
        "\n",
        "# Сформуємо функцію y = x**2+2\n",
        "ax.plot(x, x**2+2)\n",
        "\n",
        "# Запускаємо малювання графіка\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "> Першу частину коду можна використовувати як основу, а далі задавати власні значення елементів та функцію і будувати її графік.\n",
        "\n",
        "\n",
        "> Тепер, коли ти подивився/-лася, як виглядає код, і розумієш значення кожного рядка, ти можеш власними руками його торкнутися 🤩. Для цього зайди за [посиланням](https://colab.research.google.com/drive/195oMejBSOlQbYS_SCJaDanpoEt6147hr#scrollTo=3WWdOdvjWY4F) у Google Colab, самостійно запусти код у комірці, спробуй змінити функцію та знову запустити код. Сміливіше!!\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "qWJkTsmae7a8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Тепер подивимось, як реалізувати графік лінійної функції, але в нас є дві частини функціональної залежності."
      ],
      "metadata": {
        "id": "W6mBl-Ki1jxy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "[Приклад 2](https://colab.research.google.com/drive/195oMejBSOlQbYS_SCJaDanpoEt6147hr#scrollTo=XR4A65LpnBif)"
      ],
      "metadata": {
        "id": "HUpZA4gW3nq8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$y =  \\begin{cases}   2x - 1  &\\text {x => 3}\\\\   4 &\\text{x<3} \\end{cases} $"
      ],
      "metadata": {
        "id": "6FAFHQMmhiJK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "# Перемістимо лівий і нижній стовпчики до x = 0 і y = 0 відповідно.\n",
        "ax.spines[[\"left\", \"bottom\"]].set_position((\"data\", 0))\n",
        "\n",
        "# Сховаємо верхню та праву лінію\n",
        "ax.spines[[\"top\", \"right\"]].set_visible(False)\n",
        "\n",
        "# Намалюємо стрілки (як чорні трикутники: \">k\"/\"^k\") на кінцях осей.\n",
        "# Також вимкнемо відсікання (clip_on=False) стрілок.\n",
        "ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n",
        "ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n",
        "\n",
        "# Додамо проміжні лінії\n",
        "ax.grid(True, linestyle='-.')\n",
        "\n",
        "# Сформуємо ряд значень x. 100 елементів від -5 до 5.\n",
        "x = np.linspace(-5, 5, 100, False)\n",
        "\n",
        "# Задаємо 2 частини функціональної залежності\n",
        "a = np.where(x>3, 2*x-1, np.nan)\n",
        "b = np.where((x<=3), 4, np.nan)\n",
        "\n",
        "# Генеруємо 2 графіки однакового кольору\n",
        "ax.plot(x,a,color='blue')\n",
        "ax.plot(x,b,color='blue')\n",
        "\n",
        "# Запускаємо малювання графіка\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "ULy3Ln4ohieW",
        "outputId": "1ca28132-2445-4891-a010-a94cb5d5b23c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 417
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Тепер намалюємо графік для системи рівнянь."
      ],
      "metadata": {
        "id": "qqkVx2VU4aXZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "[Приклад 3](https://colab.research.google.com/drive/195oMejBSOlQbYS_SCJaDanpoEt6147hr#scrollTo=u9NPK62PsvYP&line=1&uniqifier=1)"
      ],
      "metadata": {
        "id": "zNtvNa3X4mxJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$2x − 3y + 1 = 0$  \n",
        "$y= -\\frac{2}{3}x - \\frac{1}{3} $"
      ],
      "metadata": {
        "id": "sx9NWV53iDRn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "# Перемістимо лівий і нижній стовпчики до x = 0 і y = 0 відповідно.\n",
        "ax.spines[[\"left\", \"bottom\"]].set_position((\"data\", 0))\n",
        "\n",
        "# Сховаємо верхню та праву лінію\n",
        "ax.spines[[\"top\", \"right\"]].set_visible(False)\n",
        "\n",
        "# Намалюємо стрілки (як чорні трикутники: \">k\"/\"^k\") на кінцях осей.\n",
        "# Також вимкнемо відсікання (clip_on=False) стрілок.\n",
        "ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n",
        "ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n",
        "\n",
        "# Додамо проміжні лінії\n",
        "ax.grid(True, linestyle='-.')\n",
        "\n",
        "# Сформуємо ряд значень x. 100 елементів від -5 до 5.\n",
        "x = np.linspace(-5, 5, 100, False)\n",
        "\n",
        "# Функціональну залежність\n",
        "ax.plot(x, -(2/3)*x-1/3)\n",
        "\n",
        "# Запускаємо малювання графіка\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "nxcDyfErkNRg",
        "outputId": "b9e73b35-9227-4321-bd4c-7a174a38b674",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Завдання\n",
        "\n",
        "1. Побудуй такі графіки функцій:\n",
        "- $y = \\cfrac{1}{x^2+2x+3}$\n",
        "- $y = \\cfrac{1}{x^2-2x+3}$\n",
        "- $y = sin (x) + 2$\n",
        "- $y = sin (x) +-1$\n",
        "- $y = -x^2$\n",
        "- $y = \\sqrt {x+1}$\n",
        "- $y =  \\cfrac{6}{x-3}$\n",
        "\n",
        "2. Побудуй графіки функцій, що відповідають наступній жартівливій картинці (рис.1):"
      ],
      "metadata": {
        "id": "yATyaBeRqYxK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)\n",
        "\n",
        "Рис. 1"
      ],
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      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "### Числові послідовності\n",
        "**Числова послідовність** — це функція, визначена на множині натуральних чисел, яка набуває значення на числових об'єктах.\n",
        "\n",
        "\n",
        "Нехай дана певна множина $X$.  \n",
        "Задамо кожному натуральному числу $n \\in N$ якийсь певний елемент\n",
        "$x_n \\in X$.\n",
        "\n",
        "Вийде функція: $x_n=f(n):N \\to X$\n",
        "\n",
        "Така функція називається **нескінченною послідовністю** елементів із $X$.\n",
        "Для стислості ми будемо надалі казати просто послідовність.\n",
        "\n",
        "Щоб знати послідовність, достатньо знати всі елементи: $x_1,x_2,x_3,\\ldots$ (члени послідовності для всіх номерів $1, 2, 3, \\ldots, n, \\ldots$).   \n",
        "Тому послідовність часто визначають як **упорядкований** (тобто\n",
        "пронумерований послідовними натуральними числами) **набір елементів** з множини $X$.\n",
        "\n",
        "Послідовності, всі члени яких є числами, називаються **числовими послідовностями**.\n",
        "\n",
        "Прикладами числових послідовностей є **арифметична та геометрична прогресії**. Арифметичні прогресії застосовуються у фінансах для розрахунків амортизації, у фізиці для моделювання руху з рівномірною швидкістю та в багатьох інших сферах. Геометричні прогресії широко використовуються у фінансах, дослідженні популяцій, екології, комп'ютерних науках та інших галузях.\n",
        "\n",
        "Також відома числова послідовність — послідовність Фібоначчі. Вона починається з 0 і 1, а кожний наступний член послідовності дорівнює сумі двох попередніх. Наприклад, 0, 1, 1, 2, 3, 5, 8, 13 і т.д. Цю послідовність можна побачити в природі, наприклад, у розміщенні листя на стеблі соняшника або сосни.\n",
        "\n",
        "Числова послідовність називається **обмеженою** (обмеженою знизу, обмеженою зверху), якщо обмежено\n",
        "(знизу / зверху) множину значень цієї послідовності.\n",
        "\n",
        "Множина $M$ точок числової осі називається обмеженою зверху (обмеженою знизу), якщо всі числа, що належать\n",
        "множині $M$, менше або рівні (більше або рівні) деякого фіксованого числа $C$. Множена $M$ називається просто\n",
        "обмеженою, якщо вона обмежена зверху і знизу.\n",
        "\n",
        "Будь-яка скінченна числова послідовність обмежена.\n",
        "\n",
        "Числова послідовність $x_n$ називається **збіжною до числа $a$**, якщо різниця між $x_n$ і $a$ зі зростанням номера $n$ стає як завгодно малою. Іншими словами: якщо для будь-якого заданого числа $ ɛ > 0$ знайдеться номер $N(\\varepsilon)$ такий, що при\n",
        "$n \\ge N(\\varepsilon)$ виконується співвідношення $|x_n - a| \\le \\varepsilon$. При цьому число $a$ називається **границею\n",
        "послідовності** $x_n$.\n",
        "\n",
        "\n",
        "Це визначення можна сформулювати ще й так: послідовність $x_n$ сходить (збігає) до $a$, якщо для будь-якого\n",
        "$\\varepsilon > 0$ усі її члени, починаючи з деякого номера, лежать у $\\varepsilon$-околиці точки $a$.\n",
        "\n",
        "Факт збіжності $x_n$ до $a$ записується так:\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$\\lim\\limits_{n \\to \\infty} x_n = a$\n",
        "\n",
        "</Formula>\n",
        "\n",
        "\n",
        "**Основні теореми числових послідовностей**:\n",
        "\n",
        "1. Послідовність може сходитися (збігатися) лише до однієї границі.\n",
        "2. Збіжна послідовність обмежена.\n",
        "3. Для двох числових послідовностей $x_n$ і $y_n$, якщо є $\\lim\\limits_{n \\to \\infty} x_n , \\lim\\limits_{n \\to \\infty} y_n$:\n",
        "- існує границя послідовності $x_n+y_n$ (суми даних послідовностей), причому\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$\\lim\\limits_{n \\to \\infty} (x_n+y_n) = \\lim\\limits_{n \\to \\infty} x_n + \\lim\\limits_{n \\to \\infty} y_n$;\n",
        "\n",
        "</Formula>\n",
        "\n",
        "- існує границя послідовності $x_n \\cdot y_n$ (добутку даних послідовностей), причому\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$\\lim\\limits_{n \\to \\infty} (x_n \\cdot y_n) = \\lim\\limits_{n \\to \\infty} x_n \\cdot \\lim\\limits_{n \\to \\infty} y_n$;\n",
        "\n",
        "</Formula>\n",
        "\n",
        "- якщо до того ж $\\lim\\limits_{n \\to \\infty} y_n \\ne 0$ , то, починаючи з деякого номера, визначена\n",
        "   послідовність $\\frac{x_n}{y_n}$ (відношення даних послідовностей) збігається, причому\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$\\lim\\limits_{n \\to \\infty} \\cfrac{x_n}{y_n} = \\cfrac{\\lim\\limits_{n \\to \\infty} x_n}{\\lim\\limits_{n \\to \\infty} y_n }$.\n",
        "\n",
        "</Formula>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nolQXArHIRtV"
      },
      "source": [
        "## Границя функції\n",
        "\n",
        "Розглянемо функцію виду\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$y=f(x):X \\to R$,\n",
        "\n",
        "</Formula>\n",
        "\n",
        "де $ X ⊂  R $, тобто множина, в якоій незалежна змінна може змінюватися безперервним чином.\n",
        "\n",
        "Функція називається **обмеженою** (обмеженою зверху, обмеженою знизу) на множині $A \\subset X$, якщо\n",
        "відповідну властивість має множина $f(A)$ її значень на множині $A$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9wi_svpUimRv"
      },
      "source": [
        "В природі також багато прикладів границь функцій, які впливають на різні процеси і явища. Наприклад, кожна рослина має свою границю росту, яка залежить від доступних ресурсів, таких як світло, вода, поживні речовини та простір. Коли рослина досягає своєї максимальної величини, її ріст зазвичай зупиняється або стає дуже повільним. Інший приклад - границі температур, які обмежують життєдіяльність багатьох організмів (деякі організми не можуть вижити при надто високих або низьких температурах)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1CbWYLmV_96E"
      },
      "source": [
        "Одним із головних завдань дослідження функції є визначення її поведінки при наближенні аргументу $x$ \"впритул\"\n",
        "(як завгодно близько) до фіксованого числа $x_0$.   \n",
        "Властивості функції, що виявляються при такому наближенні, називають її\n",
        "_локальними_, або _асимптотичними_ властивостями при $x \\to x_0$ (кажуть, при $x$, що прагне до $x_0$).\n",
        "\n",
        "Нехай функція $y=f(x)$ визначена на деякому інтервалі, що містить точку $x_0$ всередині себе, за винятком, можливо, самої точки $ x_0 $.\n",
        "\n",
        "Ця функція називається обмеженою при $x \\to x_0$, якщо вона обмежена на деякій множині виду\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$(x_0-\\delta,x_0) \\cup (x_0,x_0+\\delta), \\delta > 0$,\n",
        "\n",
        "</Formula>\n",
        "\n",
        "тобто, як кажуть іноді, на виколоті $\\delta$-околиці точки $x_0$.\n",
        "\n",
        "Аналогічні визначення даються обмеженості $f(x)$ зверху чи знизу при $x \\to x_0$.\n",
        "\n",
        "\n",
        "Нехай, як і раніше, $y=f(x)$ функція визначена в деякій околиці точки $x_0$. Число $a$ називається\n",
        "**границею функції** $f(x)$ при $x$, що прагне $x_0$, якщо різниця між $f(x)$ і $a$, з наближенням $x$ до $x_0$,\n",
        "стає як завгодно малою, точніще якщо для будь-якого заданого числа $\\varepsilon > 0$ знайдеться число $\\delta(\\varepsilon)$ таке, що при\n",
        "$ | x - x_0 | < \\delta(\\varepsilon)$ виконується співвідношення $|f(x) - a| < \\varepsilon$.\n",
        "\n",
        "Якщо це визначення виконується, то пишуть\n",
        "\n",
        "<Formula description=\"\">\n",
        "\n",
        "$\\lim\\limits_{x \\to x_0} f(x) = a$.\n",
        "\n",
        "</Formula>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CZql0bT7B1fs"
      },
      "source": [
        "### Геометричний зміст границі функції\n",
        "\n",
        "Розберемо, у чому полягає геометричний зміст границі функції у точці. Побудуємо графік функції $y = f (x) $ і відзначимо на\n",
        "ньому точки $x = a $ і $ y = A $ (рис 1).\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lJLZbxJaB2MS"
      },
      "source": [
        "![limit01.png](data:image/png;base64,\n",
        "\n",
        "1.   Новый пункт\n",
        "\n",
        "1.   Новый пункт\n",
        "2.   Новый пункт\n",
        "\n",
        "\n",
        "2.   Новый пункт\n",
        "\n",
        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