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Консультация № 200290
18.02.2021, 09:37
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Помогите с решением лимита, подробно, просто не могу никак решить и понять, что не так:
lim┬(x → -1)〖(3x^2+4x-1)/(√(x+3)-√(5+3x))〗
lim┬(x → -1)〖(3x^2+4x-1)/(√(x+3)-√(5+3x))〗
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Обсуждение
18.02.2021, 18:11
общий
это ответ
Здравствуйте, Alex!
Вы писали : "не могу никак решить и понять, что не так" - Особенность Вашей функции - ограниченность области определения:
1) Значение x должно быть не менее -5/3 чтоб правый радикал знаменателя не выпал из области вещественных чисел в комплексные.
2) Значение x должно НЕ равняться -1 , потому что при x = -1 знаменатель дроби равен нулю, но числитель не равен нулю. А всем известно, что делить на ноль нельзя.
Когда функция имеет разрыв в какой-то точке, то вычислить значение функции в этой точке не удаётся, и поэтому придумали понятие "Лимит". Исследуя Лимит, можно увидеть и понять поведение функции при бесконечно близком приближении аргумента к запрещённому значению - к точке разрыва.
В подобных случаях очень помогает графо-построение.
Прилагаю график, построенный в приложении Маткад (ссылка) .
Ответ : Предел равен минус бесконечности, когда x --> -1 слева;
Предел равен плюс бесконечности, когда x --> -1 справа;
Учебная статья по теме Вашей Консультации : "Пределы функций. Примеры решений" Ссылка
Вы писали : "не могу никак решить и понять, что не так" - Особенность Вашей функции - ограниченность области определения:
1) Значение x должно быть не менее -5/3 чтоб правый радикал знаменателя не выпал из области вещественных чисел в комплексные.
2) Значение x должно НЕ равняться -1 , потому что при x = -1 знаменатель дроби равен нулю, но числитель не равен нулю. А всем известно, что делить на ноль нельзя.
Когда функция имеет разрыв в какой-то точке, то вычислить значение функции в этой точке не удаётся, и поэтому придумали понятие "Лимит". Исследуя Лимит, можно увидеть и понять поведение функции при бесконечно близком приближении аргумента к запрещённому значению - к точке разрыва.
В подобных случаях очень помогает графо-построение.
Прилагаю график, построенный в приложении Маткад (ссылка) .
Ответ : Предел равен минус бесконечности, когда x --> -1 слева;
Предел равен плюс бесконечности, когда x --> -1 справа;
Учебная статья по теме Вашей Консультации : "Пределы функций. Примеры решений" Ссылка
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