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Консультация № 192524
04.02.2018, 20:25
0.00 руб.
0
2
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Пусть задана функция f(x)=x+3, x<>2 и f(x)=1, x=2
а) Имеет ли функция y = f (x) предел в точке x = 2 ?
б) Является ли y = f (x) непрерывной в точке x = 2 ?
Ответы обоснуйте.
Пусть задана функция f(x)=x+3, x<>2 и f(x)=1, x=2
а) Имеет ли функция y = f (x) предел в точке x = 2 ?
б) Является ли y = f (x) непрерывной в точке x = 2 ?
Ответы обоснуйте.
Обсуждение
04.02.2018, 22:20
общий
это ответ
Здравствуйте, CTEKLO!
Так как функция равна f(x)=x+3, когда x<>2, то ее предел равен 5 в точке 2. В то же время значение функции в точке 2 не совпадает с этим пределом. Значит, функция имеет разрыв в точке 2 и не является непрерывной. Это разрыв первого рода.
Так как функция равна f(x)=x+3, когда x<>2, то ее предел равен 5 в точке 2. В то же время значение функции в точке 2 не совпадает с этим пределом. Значит, функция имеет разрыв в точке 2 и не является непрерывной. Это разрыв первого рода.
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