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Здравствуйте! Буду благодарна за помощь в следующем вопросе: Функция У задана различными аналитическими выражениями для различных областей изменения аргумента Х:1) найти точки разрыва функции, если они существуют; 2) найти односторонние пределы и скачок функции в точках разрыва; 3) сделать чертеж
= -3-x если x<-2 y = x^2-5 если -2=<x<3 =7-2x если x>=3
1) найти точки разрыва функции, если они существуют;
На каждом из трёх промежутков своей области определения функция непрерывна, потому что непрерывны линейная и квадратичная функции. Подозрительными на разрыв являются концы промежутков. Имеем
поэтому точка не является точкой разрыва заданной функции;
поэтому точка является точкой разрыва заданной функции.
2) найти односторонние пределы и скачок функции в точках разрыва;
Расчёт односторонних пределов был выполнен выше (см. также указание о непрерывности линейной и квадратичной функций). Скачок функции в точке разрыва составляет
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срдм1998 
не является точкой разрыва заданной функции;
является точкой разрыва заданной функции.
