vvedenie v matematicheskiy analiz

Министерство образования и науки рф
Волгоградский государственный технический университет
Кафедра «высшая математика»










введение в математический анализ

Методические указания
















Волгоград
2009
УДК 514.742.4(075)


Рецензент






Печатается по решению редакционно-издательского совета
Волгоградского государственного технического университета






Введение в математический анализ: метод. указания/ сост.
ВолгГТУ. – Волгоград, 2009 - с.

Работа содержит методические указания к выполнению типового расчета по теме «Введение в анализ», вопросы к зачету по теме, варианты заданий, приведены решения типовых задач.























© Волгоградский государственный
технический университет, 2009
Настоящие методические указания предназначены для студентов всех специальностей первого курса. По теме «Введение в математический анализ» необходимо выполнить индивидуальное задание и сдать теоретический зачет.

1. МЕТОДИЧЕСКИЕ УКАЗАНИЯ К ВЫПОЛНЕНИЮ ЗАДАНИЙ

Введение

Вычисление пределов функций начинают с непосредственной подстановки предельного значения основной переменной в выражении для функции, используя правила предельного перехода под знаком непрерывной функции, теоремы о пределах. Если получают неопределенности:
13 EMBED Equation.DSMT4 1415
используют различные приемы их «раскрытия».
Ниже приведенное правило дет некоторые свойства бесконечно малых и бесконечно больших функций, связь между ними.
Правило 1.
Если
13 EMBED Equation.DSMT4 1415 - (постоянная величина),
13 EMBED Equation.DSMT4 1415 - ограниченная функция,
13 EMBED Equation.DSMT4 1415 - бесконечно малая функция (или короче “0”),
13 EMBED Equation.DSMT4 1415- бесконечно большая функция, то
1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415 (13 EMBED Equation.DSMT4 1415 - одного знака);
3) 13 EMBED Equation.DSMT4 1415 4) 13 EMBED Equation.DSMT4 1415
5) 13 EMBED Equation.DSMT4 1415 6) 13 EMBED Equation.DSMT4 1415
7) 13 EMBED Equation.DSMT4 1415 8) 13 EMBED Equation.DSMT4 1415
9) 13 EMBED Equation.DSMT4 1415 10) 13 EMBED Equation.DSMT4 1415
11) 13 EMBED Equation.DSMT4 1415 12) 13 EMBED Equation.DSMT4 1415

Таблица эквивалентных бесконечно малых функций при 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

Примечание. Приближенными равенствами 6 и 8 пользуется в другой форме при 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

Правило 1.
При нахождении предела отношения бесконечно малых при бесконечно больших функций каждую из них (или одну) можно заменить другой функцией, ей эквивалентной. То есть:
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 (1.1)

Правило 2.
Алгебраическая сумма бесконечно малых функций разных порядков эквивалентна слагаемому низшего порядка.

Правило 3.
Алгебраическая сумма бесконечно больших функций разных поряд-ков эквивалентна слагаемому высшего порядка.


Правило 4.
При вычислении предела показательно-степенной функции 13 EMBED Equation.DSMT4 1415 где 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415
пользуются равенством:
13 EMBED Equation.DSMT4 1415 (1.2)

Правило 5.
Неопределенности вида 13 EMBED Equation.DSMT4 1415 или 13 EMBED Equation.DSMT4 1415 приводят к виду дроби, которая может дать новые – типа 13 EMBED Equation.DSMT4 1415 или 13 EMBED Equation.DSMT4 1415.
Часто используются при вычислении пределов следующие свойства показательной и степенной функции:
13 EMBED Equation.DSMT4 1415 (1.3)
13 EMBED Equation.DSMT4 1415 (1.4)
13 EMBED Equation.DSMT4 1415 (1.5)

1.1. Пределы рациональных функций
Пример 1. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 (Пр.4); Пр.2 13 EMBED Equation.DSMT4 1415Пр. 1.813 EMBED Equation.DSMT4 1415
Пример 2. 13 EMBED Equation.DSMT4 1415Пр. 1.1113 EMBED Equation.DSMT4 1415Пр. 613 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр. 1.1113 EMBED Equation.DSMT4 1415
Пример 3. 13 EMBED Equation.DSMT4 1415Пр. 4, Пр.213 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
Пример4. 13 EMBED Equation.DSMT4 1415Пр.613 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр.4,Пр.213 EMBED Equation.DSMT4 1415
Примечание. Если бы мы воспользовались вначале последовательно правилами 4 и 2, то получили бы:
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
что неверно, так как разность эквивалентных бесконечно больших функций есть функция более низкого порядка, чем каждая из них (бесконечно большая, постоянная) как в рассмотренном примере, или, в крайнем случае, предел их разности может быть бесконечно малой функцией (см. пример 2 пункта. 2.4.2).
Пример 5. 13 EMBED Equation.DSMT4 1415/разложим многочлены на множители/=13 EMBED Equation.DSMT4 1415

1.2. Пределы иррациональных выражений
Пример 1. 13 EMBED Equation.DSMT4 1415Пр. 4, Пр. 213 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
Примечание. При вычислении пределов иррациональных выражений, дающих неопределенности типа 13 EMBED Equation.DSMT4 1415 или 13 EMBED Equation.DSMT4 1415 используют введение новой переменной, освобождающей от иррациональности, или преобразование выражения с помощью сопряженного ему. Например, парами взаимно сопряженных выражений будут:
1) 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415
3) 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415 которые при вычислении пределов используются в формах:
13 EMBED Equation.DSMT4 1415 (1.6)
13 EMBED Equation.DSMT4 1415 (1.7)
13 EMBED Equation.DSMT4 1415 (1.8)
Пример 2. 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр.613 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
Пример 3. 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
Пример 4. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
Примечание. Обратите внимание на то, что при вычислении предела 5 из пункта 2.4.I и 3,4 настоящего пункта, при раскрытии неопределенности 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415 стараются так преобразовать выражение, чтобы дробь можно было сократить на множители 13 EMBED Equation.DSMT4 1415 стремящийся к нулю.

1.3. Вычисление пределов с использованием таблицы эквивалентных бесконечно малых функций.
Пример 1. 13 EMBED Equation.DSMT4 1415Пр.213 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр. 313 EMBED Equation.DSMT4 1415
Пример 2. 13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1413 EMBED Equation.DSMT4 14151513 EMBED Equation.DSMT4 1415
Пример 3. 13 EMBED Equation.DSMT4 1415 Пр. 213 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
Пример 4. 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
Пример5. 13 EMBED Equation.DSMT4 1415Пр.4,Пр.613 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр.613 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
Пример 6. 13 EMBED Equation.DSMT4 1415 (Пр.5)= 13 EMBED Equation.DSMT4 1415
Пример 7. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
Пример 8. 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
Пример 9. 13 EMBED Equation.DSMT4 1415 не определен из-за знака 13 EMBED Equation.DSMT4 1415
1) 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415Пр.413 EMBED Equation.DSMT4 1415
Таким образом, существуют различные односторонние на 13 EMBED Equation.DSMT4 1415 и на 13 EMBED Equation.DSMT4 1415 пределы.


1.4. Указания к заданию 5.
Пример. Докажите, что
13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415
бесконечно малые функции одного порядка при 13 EMBED Equation.DSMT4 1415 Найдите значение постоянной “C”, при котором они будут эквивалентны.
Решение.
13 EMBED Equation.DSMT4 1415Пр. 13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415Пр. 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415Пр.313 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415 при 13 EMBED Equation.DSMT4 1415

1.5. Пример выполнения задания 5.
Определите порядок относительно “x” функции
13 EMBED Equation.DSMT4 1415
бесконечно малой при 13 EMBED Equation.DSMT4 1415
Решение.
13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415при 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 - бесконечно малая одного порядка по отношению к 13 EMBED Equation.DSMT4 1415, то сеть второго порядка относительно “x”.

1.6. Указания к выполнению задания 7.
При исследовании функции на непрерывность пользуются теоремой о непрерывности элементарных функций там, где они определены; признаком непрерывности фуки в точке 13 EMBED Equation.DSMT4 1415 когда
13 EMBED Equation.DSMT4 1415 (2.19)
При наличии точек разрывов исследуют функции в их окрестности и соответствующим образом классифицируют.

Пример 1. Исследовать функцию на непрерывность и построить её схематический график, если
13 EMBED Equation.DSMT4 1415
Решение. Сначала найдем область определения функции
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415 13 SHAPE \* MERGEFORMAT 1415
Область определения симметрична относительно начала координат, следует исследовать функцию на признак четности.
13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415функция нечетная и её график симметричен относительно начала координат. Таким образом, достаточно исследовать функцию на промежутке 13 EMBED Equation.DSMT4 1415построить график, а затем отобразить его симметрию начала координат.
В точке 13 EMBED Equation.DSMT4 1415 функция определена справа, поэтому найдем лишь правосторонний предел в ней:
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 - точка бесконечного разрыва (П-рода), не входит в 13 EMBED Equation.DSMT4 1415
На 13 EMBED Equation.DSMT4 1415 получим
13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415график приближается к оси OX ( =0) снизу при 13 EMBED Equation.DSMT4 1415
Для уточнения графика найдем дополнительную точку 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
Заданная функция элементарная, и область её непрерывности совпадает с областью определения
13 EMBED Equation.DSMT4 1415 - область непрерывности.
Строим график для 13 EMBED Equation.DSMT4 1415 а затем достраиваем для 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415
13 SHAPE \* MERGEFORMAT 1415






2. ИНДИВИДУАЛЬНЫЕ ЗАДАНИЯ

2.1. Найти и изобразить на числовой оси области определения функций:
ВАРИАНТ 1.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 5.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 8.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 14.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 16.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 18.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415


ВАРИАНТ 23.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 28.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30.
1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415




2.2. Исследовать заданные функции на четность и нечетность, найти интервалы законопостоянства:
ВАРИАНТ 1. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 8. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 14. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 16. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 18. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 23. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 28. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29. 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30, 1) 13 EMBED Equation.DSMT4 1415 2) 13 EMBED Equation.DSMT4 1415

2.3. Построить замкнутые области, ограниченные заданными линиями и удовлетворяющие приведенным ограничениям:
ВАРИАНТ 1. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3, 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equatio
·n.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 8. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11. 1) 13 EMBED Equation.DSMT4 1415
2) 13 EMBED Equation.DSMT4 1415 3) 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 14. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 16. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 18. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 21. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 23. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ28. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30. 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

2.4. Найти указанные пределы:
ВАРИАНТ 1.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415


ВАРИАНТ 3.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 141513 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 8.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 14.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 16.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 18.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 23.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 28.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

2.5. Доказать, что при 13 EMBED Equation.DSMT4 1415 функции 13 EMBED Equation.DSMT4 1415 и 13 EMBED Equation.DSMT4 1415 являются бесконечно малыми одного порядка 13 EMBED Equation.DSMT4 1415 Найти значение 13 EMBED Equation.DSMT4 1415 при котором они будут эквивалентными:
ВАРИАНТ 1.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 8.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 14.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 16.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 18.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 23.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 28.
13 EMBED Equation.DSMT4 1415


ВАРИАНТ 29.
13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30.
13 EMBED Equation.DSMT4 1415

2.6. Определить порядок относительно 13 EMBED Equation.DSMT4 1415 функции 13 EMBED Equation.DSMT4 1415 бесконечно малой при 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 1. ВАРИАНТ 2.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3. ВАРИАНТ 4.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5. ВАРИАНТ 6.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7. ВАРИАНТ 8.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9. ВАРИАНТ 10.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11. ВАРИАНТ 12.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13. ВАРИАНТ 14.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15. ВАРИАНТ 16.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17. ВАРИАНТ 18.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19. ВАРИАНТ 20.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21. ВАРИАНТ 22.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 23. ВАРИАНТ 24.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25. ВАРИАНТ 26.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 27. ВАРИАНТ 28.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29. ВАРИАНТ 30.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

2.7. Исследовать на непрерывность, классифицировать точки разрыва функций, построить схематические графики:
ВАРИАНТ 1.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 2.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 3.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 4.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 5.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 6.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 7.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 8.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 9.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 10.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 11.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 12.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 13.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 14.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 15.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 16.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 17.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415

ВАРИАНТ 18.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 19.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 20.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 21.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 22.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415



ВАРИАНТ 23.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 24.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 25.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 26.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 27.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 28.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 29.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
ВАРИАНТ 30.
13 EMBED Equation.DSMT4 1415 13 EMBED Equation.DSMT4 1415
+

+

-

2

-2

y

x

0

2

3

-2

-3

y

x

0

-2

-4

1

5

13 EMBED Equation.DSMT4 1415

13 EMBED Equation.DSMT4 1415

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