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Значит, контрольную Вам не зачтут, пока не выполните задание.
Вы правильно заметили: нужно продолжить функцию и исследовать на чётность-нечётность. Чтобы было проще, предлагаю построить график функции на заданном промежутке, а затем этот график транслировать на промежуток, симметричный заданному относительно оси ординат. Посмотреть, какое из соотношений выполняется: 1) - тогда функция чётная; 2) - тогда функция нечётная; 3) ни первое, ни второе соотношения не выполняются - тогда функция ни чётная, ни нечётная. Исходя из полученного результата можно будет выбрать ряд Фурье из перечисленных в задании.
А сейчас я должен покинуть портал, чтобы разобраться и со своими задачами.
Учитывая, что попыток продолжить обсуждение задачи с Вашей стороны не последовало, ограничусь повторением своего последнего сообщения.
Вы правильно заметили: нужно продолжить функцию и исследовать на чётность-нечётность. Чтобы было проще, предлагаю построить график функции на заданном промежутке, а затем этот график транслировать на промежуток, симметричный заданному относительно оси ординат. Посмотреть, какое из соотношений выполняется: 1) - тогда функция чётная; 2) - тогда функция нечётная; 3) ни первое, ни второе соотношения не выполняются - тогда функция ни чётная, ни нечётная. Исходя из полученного результата можно будет выбрать ряд Фурье из перечисленных в задании.
Об авторе:
Facta loquuntur.
Форма ответа
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bill1091989 
- тогда функция чётная;
- тогда функция нечётная;