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Консультация № 199516
05.11.2020, 10:59
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Раздел I, задание: №1 и 2 (Исследовать функцию на непрерывность) 
Обсуждение
10.11.2020, 07:10
общий
это ответ
Здравствуйте, alekseyslobodyanyuk20003!
1. Показательная функция 10[sup]x[/sup] непрерывна при любом конечном аргументе x, поэтому функцию
исследуем лишь для тех x, при которых показатель стремится к бесконечности, то есть при x [$8594$] 7. Найдём пределы слева и справа:
Так пределы не совпадают, то x = 7 - точка разрыва (второго рода, поскольку один из пределов равен бесконечности) и функция непрерывна везде, кроме x = 7.
2. Функции -x, sin x и x-2 непрерывны при любых x, поэтому исследуем функцию лишь в точках "стыковки":
В точке x = 0 значения пределов слева и справа совпадают друг с другом и со значением функции в точке (y(0) = 0), поэтому разрыва нет. В точке x = [$960$] левый и правый предел не совпадают, поэтому это точка разрыва (первого рода, так как оба предела конечны). Функция непрерывна везде, кроме x = [$960$].
1. Показательная функция 10[sup]x[/sup] непрерывна при любом конечном аргументе x, поэтому функцию
исследуем лишь для тех x, при которых показатель стремится к бесконечности, то есть при x [$8594$] 7. Найдём пределы слева и справа:
Так пределы не совпадают, то x = 7 - точка разрыва (второго рода, поскольку один из пределов равен бесконечности) и функция непрерывна везде, кроме x = 7.
2. Функции -x, sin x и x-2 непрерывны при любых x, поэтому исследуем функцию лишь в точках "стыковки":
В точке x = 0 значения пределов слева и справа совпадают друг с другом и со значением функции в точке (y(0) = 0), поэтому разрыва нет. В точке x = [$960$] левый и правый предел не совпадают, поэтому это точка разрыва (первого рода, так как оба предела конечны). Функция непрерывна везде, кроме x = [$960$].
5
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