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Консультация № 194595
04.02.2019, 20:20
0.00 руб.
0
2
2
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Будет ли функция
cos(2x)+cos((sqrt3)x)=y
периодической?
Будет ли функция
cos(2x)+cos((sqrt3)x)=y
периодической?
Обсуждение
04.02.2019, 21:01
общий
это ответ
Здравствуйте, alina.poroshina124564!
Нет, не будет: она принимает значение 2 только в одной точке х=0, а больше нигде. Значит периода быть не может
Нет, не будет: она принимает значение 2 только в одной точке х=0, а больше нигде. Значит периода быть не может
07.02.2019, 20:48
общий
это ответ
Здравствуйте, alina.poroshina124564!
Известно, что главным периодом функции
является число 
При этом в соответствии с известной теоремой главным периодом функции 
является число 
а главным периодом функции 
является число 
Обе функции непрерывны, поэтому, как известно, период их суммы, если он существует, равен наименьшему общему кратному периодов этих функций. Но у чисел 
и 
нет общих кратных, поэтому сумма функций 
и 
не является периодической функцией.
Известно, что главным периодом функции
является число При этом в соответствии с известной теоремой главным периодом функции является число а главным периодом функции является число Обе функции непрерывны, поэтому, как известно, период их суммы, если он существует, равен наименьшему общему кратному периодов этих функций. Но у чисел и нет общих кратных, поэтому сумма функций и не является периодической функцией.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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