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Консультация № 201803
03.12.2021, 14:43
0.00 руб.
05.12.2021, 05:56
1
7
2
Здравствуйте! Прошу помощи в следующем вопросе:
Найти указанные пределы. (не используя правилаЛопатияЛопиталя). Так как не получается написать пример прикладываю фото
Найти указанные пределы. (не используя правила
Прикрепленные файлы:
Обсуждение
03.12.2021, 16:01
общий
Хотелось бы знать что означает формулировка "правило Лопатия". Ни в поисковике Google, ни в Яндекс такого понятия не имеется. Вместо этого существует правило Лопиталя.
03.12.2021, 16:03
общий
это ответ
Дана функция f(x) = (1 - cos(m·x)) / x2
Вычислить предел x[$8594$]0Lim f(x) , не используя правила Лопиталя.
Решение: При попытке простой подстановки в предел конечного x-значения x = 0 , мы получаем
x[$8594$]0Lim f(x) = (1 - cos(m·0)) / 02 = (1 - 1) / 02 = 0 / 0 - неопределённость типа 0/0 .
Читаем учебную статью "Бесконечно малые функции. Замечательные эквивалентности в пределах" Ссылка
Заменим бесконечно малую функцию числителя эквивалентной функцией
1 - cos([$945$]) ~ [$945$]2 / 2 , где [$945$] = m·x . Тогда x = [$945$] / m , x2 = [$945$]2 / m2
В результате замены получим : x[$8594$]0Lim (1 - cos(m·x)) / x2 = ([$945$]2 / 2) / ([$945$]2 / m2) = m2 / 2
Ответ: x[$8594$]0Lim f(x) = m2 / 2
Вычислить предел x[$8594$]0Lim f(x) , не используя правила Лопиталя.
Решение: При попытке простой подстановки в предел конечного x-значения x = 0 , мы получаем
x[$8594$]0Lim f(x) = (1 - cos(m·0)) / 02 = (1 - 1) / 02 = 0 / 0 - неопределённость типа 0/0 .
Читаем учебную статью "Бесконечно малые функции. Замечательные эквивалентности в пределах" Ссылка
Заменим бесконечно малую функцию числителя эквивалентной функцией
1 - cos([$945$]) ~ [$945$]2 / 2 , где [$945$] = m·x . Тогда x = [$945$] / m , x2 = [$945$]2 / m2
В результате замены получим : x[$8594$]0Lim (1 - cos(m·x)) / x2 = ([$945$]2 / 2) / ([$945$]2 / m2) = m2 / 2
Ответ: x[$8594$]0Lim f(x) = m2 / 2
5
04.12.2021, 17:45
общий
это ответ
Здравствуйте, hipunova1512!
Предлагаю Вам другое решение задачи.
Предлагаю Вам другое решение задачи.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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