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Консультация № 199513
04.11.2020, 21:42
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Здравствуйте! Прошу помощи в следующем вопросе:
Найти предел, используя эквивалентные бесконечно малые функции
Найти предел, используя эквивалентные бесконечно малые функции
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Обсуждение
10.11.2020, 04:22
общий
это ответ
Здравствуйте, svrvsvrv!
Условие : Дана функция y(x) = (x2 - x - 6) / arcsin2[tg(x + 2)]
Вычислить предел Lim y(x) при x [$8594$] -2 , используя эквивалентные бесконечно малые функции.
Решение : При попытке вычислить предел простой подстановкой предельного значения x = -2 получаем неопределённость вида 0/0 .
Используем правила эквивалентности "Если [$945$] [$8594$] 0 , то arcsin([$945$]) ~ [$945$]" и tg([$945$]) ~ [$945$]" .
Функция arcsin([$945$]) задана в квадрате. Поэтому и заменяем её на [$945$]2 .
После сокращения числителя и знаменателя большой дроби на множитель (x+2) получаем
Ответ : Предел заданной функции равен минус бесконечности.
Скриншот с формулами прилагаю ниже.
Учебно-методическая статья по Вашей теме : "Бесконечно малые функции. Замечательные эквивалентности в пределах" Ссылка1 .
Решение похожих задач rfpro.ru/question/199511 ; rfpro.ru/question/199512 .
Условие : Дана функция y(x) = (x2 - x - 6) / arcsin2[tg(x + 2)]
Вычислить предел Lim y(x) при x [$8594$] -2 , используя эквивалентные бесконечно малые функции.
Решение : При попытке вычислить предел простой подстановкой предельного значения x = -2 получаем неопределённость вида 0/0 .
Используем правила эквивалентности "Если [$945$] [$8594$] 0 , то arcsin([$945$]) ~ [$945$]" и tg([$945$]) ~ [$945$]" .
Функция arcsin([$945$]) задана в квадрате. Поэтому и заменяем её на [$945$]2 .
После сокращения числителя и знаменателя большой дроби на множитель (x+2) получаем
Ответ : Предел заданной функции равен минус бесконечности.
Скриншот с формулами прилагаю ниже.
Учебно-методическая статья по Вашей теме : "Бесконечно малые функции. Замечательные эквивалентности в пределах" Ссылка1 .
Решение похожих задач rfpro.ru/question/199511 ; rfpro.ru/question/199512 .
5
Огромное Вам спасибо!
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