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Консультация № 161730
01.03.2009, 18:55
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Здравствуйте! Помоги пожалуйста вот с такими заданиями: Исследовать функцию на непрерывность, установить характер точек разрыва и сделать схематический чертеж: а) f(x) = 1/ln(x-3) б)f(x) = 1-x2/x+1. заранее большое спасибо!!
Обсуждение
04.03.2009, 07:31
общий
Мне кажется, рассуждать можно следующим образом:
а) Функция непрерывна на х э (3; 4)U(4; +infinity). В точке 3 разрыв 1-го рода справа (предел справа равен 0), если считать ее непрерывность на отрезке [3;а], 3<a<4, формально же разрыв второго рода,т.к. нет предела слева. В точке 4 разрыв 2-го рода (пределов слева и справа нет);
б) Функция непрерывна на х э (-infinity;-1)U(-1; +infinity). В точке -1 разрыв 1-го рода (пределы справа и слева равны 2).
а) Функция непрерывна на х э (3; 4)U(4; +infinity). В точке 3 разрыв 1-го рода справа (предел справа равен 0), если считать ее непрерывность на отрезке [3;а], 3<a<4, формально же разрыв второго рода,т.к. нет предела слева. В точке 4 разрыв 2-го рода (пределов слева и справа нет);
б) Функция непрерывна на х э (-infinity;-1)U(-1; +infinity). В точке -1 разрыв 1-го рода (пределы справа и слева равны 2).
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