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Консультация № 175944
09.01.2010, 13:59
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Здравствуйте очередной раз, снова требуется помощь и потом еще не раз наверное будет)
Исследовать данные функции на непрерывность, найти точки разрыва и установить их характер. Построить графики функций.
/x+3, x<_0
f(x)=|1, 0<x<_2 f(x)=1/e(в степени x-2)
\x2-2, x>2
Огробное спасибо заранее))
Исследовать данные функции на непрерывность, найти точки разрыва и установить их характер. Построить графики функций.
/x+3, x<_0
f(x)=|1, 0<x<_2 f(x)=1/e(в степени x-2)
\x2-2, x>2
Огробное спасибо заранее))
Обсуждение
10.01.2010, 13:36
общий
это ответ
Здравствуйте, Владимир1601.
Пусть
1/(x + 3), если x ≤ 0,
f(x) = 1/e, если 0 < x ≤ 2,
1/(x2 – 2), если x > 2.
Функция непрерывна на интервале (-∞, 0).При x → 0- f(x) = 1/(x + 3) → 1/(0 + 3) = 1/3 ≈ 0,333 = f(0). При x → 0+ f(x) = 1/e ≈ 0,368. То есть в точке x = 0 значение предела функции слева не совпадает со значением предела справа. В этой точке функция претерпевает конечный разрыв (разрыв первого рода).
Функция непрерывна на интервале (0, 2). При x → 2- f(x) f(x) = 1/e ≈ 0,368 = f(2). При x → 2+ f(x) = 1/(x2 – 2) → 1/(22 – 2) = 1/2. То есть в точке x = 2 значение предела функции слева не совпадает со значением предела справа. В этой точке функция также претерпевает конечный разрыв (разрыв первого рода).
Функция непрерывна на интервале (2, +∞).
С уважением.
Пусть
1/(x + 3), если x ≤ 0,
f(x) = 1/e, если 0 < x ≤ 2,
1/(x2 – 2), если x > 2.
Функция непрерывна на интервале (-∞, 0).При x → 0- f(x) = 1/(x + 3) → 1/(0 + 3) = 1/3 ≈ 0,333 = f(0). При x → 0+ f(x) = 1/e ≈ 0,368. То есть в точке x = 0 значение предела функции слева не совпадает со значением предела справа. В этой точке функция претерпевает конечный разрыв (разрыв первого рода).
Функция непрерывна на интервале (0, 2). При x → 2- f(x) f(x) = 1/e ≈ 0,368 = f(2). При x → 2+ f(x) = 1/(x2 – 2) → 1/(22 – 2) = 1/2. То есть в точке x = 2 значение предела функции слева не совпадает со значением предела справа. В этой точке функция также претерпевает конечный разрыв (разрыв первого рода).
Функция непрерывна на интервале (2, +∞).
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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