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
>
>;
>
>;
>
>;
>
>;
Найти dy, если >
>.
Решение:
>
>
>
>
>
>
>
>
>
>,
>
>
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:
>
>;
>
>;
>
>;
>
>;
>
>
Решение:
>>
- 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
Зорич В.А. Математический анализ. Ч. 1, М., 2001. Ч. 2. 2001.
Ильин В.А., Позняк Э.Г. Основы математического анализа. Ч. 1. М., 2001. Ч. 2, М., 2002.
Кудрявцев Л.Д. Курс математического анализа: В 3 т. М., 1988-1989.
Камынин Л.И. Курс математического анализа. Т. 1. М., 1993. Т. 2. М., 1995.
Демидович Б.П. Сборник задач и упражнений по математическому анализу. М., 2003.