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Консультация № 200097
16.01.2021, 00:15
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Здравствуйте! У меня возникли сложности с таким вопросом: определить по Гейне и по Коши lim f(x)=+бесконечность при х стремящемся к а+0. нарисовать иллюстрацию. если можно, определить и показать на рисунке при х стремящемся к а-0. никак не пойму, в чем у них различие
Обсуждение
16.01.2021, 02:45
общий
Адресаты:
Хорошая учебная статья по Вашей теме "Предел последовательности и предел функции по Коши" Ссылка
"при х стремящемся к а-0. никак не пойму, в чем у них различие" - вспомните школьную гиперболу y = 1/x , начертите график (не обязательно точный)
И тогда Вы легко сообразите, что в окрестности точки x=0 предел функции равен:
+Бесконечности когда x стремится к нулю справа x[$8594$]+0
-Бесконечности когда x стремится к нулю слева x[$8594$]-0
=Разрыв второго рода.
"при х стремящемся к а-0. никак не пойму, в чем у них различие" - вспомните школьную гиперболу y = 1/x , начертите график (не обязательно точный)
И тогда Вы легко сообразите, что в окрестности точки x=0 предел функции равен:
+Бесконечности когда x стремится к нулю справа x[$8594$]+0
-Бесконечности когда x стремится к нулю слева x[$8594$]-0
=Разрыв второго рода.
17.01.2021, 10:22
общий
Адресаты:
В статье по моей выше-сылке есть абзац "Предел функции по Гейне: число называется пределом функции f(x) в точке x0, если для любой последовательности…"
Слово "Гейне" 4 раза упоминается в статье. Если Вы не владеете приёмами производительной работы, то показываю скриншот из моего браузера Mozilla FireFox . Клав-сочетанием Ctrl+F открываем панель поиска внизу страницы, вводим запрос
гейне
Браузер находит и выделяет первую находку напоказ. Жмём F3 перечислить все находки в цикле.
Слово "Гейне" 4 раза упоминается в статье. Если Вы не владеете приёмами производительной работы, то показываю скриншот из моего браузера Mozilla FireFox . Клав-сочетанием Ctrl+F открываем панель поиска внизу страницы, вводим запрос
гейне
Браузер находит и выделяет первую находку напоказ. Жмём F3 перечислить все находки в цикле.
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