Контрольная работа : Математический анализ (работа 7) 


Полнотекстовый поиск по базе:

Главная >> Контрольная работа >> Математика


Математический анализ (работа 7)




Оглавление

Задание 1

Задание 2

Задание 3

Задание 4

Задание 5

Задание 6

Литература

Задание 1.

Исследовать функцию и построить ее график: .

Решение:

y = 0, если х = 0 или х =

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

y(-1) = -2, y(1) = 2.

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

Задание 2

  1. ;

  2. ;

  3. ;

  4. ;

  1. Найти dy, если .

Решение:

  1. ,

Ответ: 1. ; 2. ; 3. ; 4. ; 5. .

Задание 3.

Вычислить объем тела, полученного вращением вокруг оси Ох фигуры, ограниченной линиями , х = 3 и осями координат.

Решение:

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

.

Ответ: .

Задание 4.

Для сжатия пружины на L см требуется сила 9,8 Н. Какую работу надо совершить, чтобы сжать пружину на 0,05 м.

Решение:

Работа , где F – сила, s – расстояние, пройденное под действием этой силы.

По закону Гука , где - абсолютное удлинение стержня, F – сила упругости, k – жесткость материала. Следовательно,

.

Ответ: .

Задание 5.

Найти интеграл:

а) ;б) .

Решение:

а)

б) .

Ответ: а) ; б) .

Задание 6.

Исследовать функцию и построить ее график:

  1. ;

  2. ;

  3. ;

  4. ;

Решение:

  1. - симметрична относительно оси Ох

y = 0, если , т.е. .

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

y(-2) = y(2) = -9/4

y(0) = 7/4

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

Область определения

y = 0, если , корней нет:

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

, если

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

Корень один, он близок к х = 1, находится между х = 1,05 и х = 1,06, это точка минимума.

y(1) = 2, y(2) = 3.2, y(3) = 4,95

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

y = 0, если х = 1,

область определения ,

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

, х = 0 – асимптота.

;

корней, принадлежащих области определения, нет.

;

корней, принадлежащих области определения, нет.

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

Уравнение y = 0 корней не имеет,

, , х = 1/5 – асимптота

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

y(0.007) = -0.3

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

y(0.4 + 4πk) = 4.9 + 48πk

y(-0.4 + 4πk) = -4.9 + 48πk

,

знак совпадает со знаком ctg(x/2)

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

Литература

  1. Зорич В.А. Математический анализ. Ч. 1, М., 2001. Ч. 2. 2001.

  2. Ильин В.А., Позняк Э.Г. Основы математического анализа. Ч. 1. М., 2001. Ч. 2, М., 2002.

  3. Кудрявцев Л.Д. Курс математического анализа: В 3 т. М., 1988-1989.

  4. Камынин Л.И. Курс математического анализа. Т. 1. М., 1993. Т. 2. М., 1995.

  5. Демидович Б.П. Сборник задач и упражнений по математическому анализу. М., 2003.

Похожие работы:

  • Математический анализ

    Шпаргалка >> Математика
    Математический анализ (шпаргалка) Определение функции нескольких переменных. ...
  • Математический анализ. Практикум

    Учебное пособие >> Математика
    Математический анализ. Практикум. Для студентов ВУЗов ... полезности при заданном бюджетном ограничении. Математическая модель этой задачи: В случае ... , подробное решение и вывод. 1. Введение в математический анализ Задача 1. Найти область определения функции ...
  • Математический анализ

    Реферат >> Математика
    ... понятия предела определяются важнейшие понятия математического анализа – производная и интеграл. Предел последовательности ... является основным инструментом исследования функций в математическом анализе, в частности, используется для отыскания ...
  • Математический анализ

    Реферат >> Математика
    ГЛАВА#1.МАТЕМАТИЧЕСКИЙ АНАЛИЗ. §1 ПОНЯТИЕ ОКРЕСТНОСТИ,БЕСКОНЕЧНО МАЛОГО,ПРЕДЕЛА, ...
  • Математическое моделирование как философская проблема

    Реферат >> Математика
    ... управления. Это сделало доступным их математический анализ».12 Кибернетическое моделирование используется и как ... . Бурное развитие математического анализа, исследования операций, теории вероятностей и математической статистики способствовало формированию ...
  • Математическая интуиция

    Реферат >> Математика
    ... механики стимулировало теорию вероятностей и математическую статистику, функциональный анализ и теорию меры. Интересно то ... этого взаимодействия. Так, Риман, применив математический анализ к алгебраической геометрии, создал новую теорию ...
  • Билеты по математическому анализу

    Реферат >> Математика
    ... -------------------------------------------------- Экзаменационный билет по предмету МАТЕМАТИЧЕСКИЙ АНАЛИЗ Билет № 3 Докажите правило ... примерный перечень экзаменационных вопросов Математический анализ Какими десятичными дробями представляются ...
  • Вклад Л.Эйлера в развитие математического анализа

    Реферат >> Математика
    ... математического анализа. Цель реферата – изучить историю развития математического анализа в XVIII веке. 1 Понятие математического анализа. Исторический очерк Математический анализ ...
  • Анализ медико-биологических данных с помощью Microsoft Excel и СПП STADIA 6.2

    Реферат >> Информатика, программирование
    ... , охватывающая планирование и анализ результатов количественных биологических экспериментов и наблюдений методами математической статистики. Современный ... : Изд-во КГУ, 2001. – 89 с. Математический анализ биологических данных / Г.Н. Зайцев, М.: “Наука”, 1991 ...