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Консультация № 73005
28.01.2007, 14:40
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Уважаемые эксперты помогите решить задачу
Установить является ли функция 6^(1/(х-5)) непрерывной или разрывной в точках х1= и х2=3
в случае разрыва найти ее пределы
Установить является ли функция 6^(1/(х-5)) непрерывной или разрывной в точках х1= и х2=3
в случае разрыва найти ее пределы
Обсуждение
Неизвестный
29.01.2007, 09:26
общий
это ответ
Здравствуйте, COMbat!
f(x)=6<sup>(1/(х-5))</sup>
Т.к. в вопросе отсутствует значение х1, смею предположить, что имелось ввиду х1=5
В этой точке функция разрывна и ее пределы справа и слева от х1=5 будут равны
lim(x->5+)(f(x)) = ∞
lim(x->5-)(f(x)) = 0
Что касается х2=3, то в этой точке функция непрерывна и f(x2)=6<sup>1/2</sup>=√6
Удачи!
f(x)=6<sup>(1/(х-5))</sup>
Т.к. в вопросе отсутствует значение х1, смею предположить, что имелось ввиду х1=5
В этой точке функция разрывна и ее пределы справа и слева от х1=5 будут равны
lim(x->5+)(f(x)) = ∞
lim(x->5-)(f(x)) = 0
Что касается х2=3, то в этой точке функция непрерывна и f(x2)=6<sup>1/2</sup>=√6
Удачи!
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