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Консультация № 176431
01.02.2010, 18:16
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11
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Здравствуйте уважаемые эксперты, помогите решить премер
Вычислить предел
lim((x-1+cosx)*(sinx/2)^2)/(e^(3)-1)^3
x[$8594$]0
Вычислить предел
lim((x-1+cosx)*(sinx/2)^2)/(e^(3)-1)^3
x[$8594$]0
Обсуждение
Неизвестный
01.02.2010, 18:32
общий
это ответ
Здравствуйте, Верещака Андрей Павлович.
lim{x[$8594$]0}(x-1+cosx)*sin2(x/2)/(e^(3)-1)^3 = 1/(e^(3)-1)^3)*(0-1+cos0)*(sin0/2) = 0.
По крайней мере вы сами записали пример в таком виде.
Может все-таки имелось ввиду
lim((x-1+cosx)/(sinx/2)^2)*(e^(3)-1)^3
x→0
или что-то в этом роде?
lim{x[$8594$]0}(x-1+cosx)*sin2(x/2)/(e^(3)-1)^3 = 1/(e^(3)-1)^3)*(0-1+cos0)*(sin0/2) = 0.
По крайней мере вы сами записали пример в таком виде.
Может все-таки имелось ввиду
lim((x-1+cosx)/(sinx/2)^2)*(e^(3)-1)^3
x→0
или что-то в этом роде?
5
Неизвестный
01.02.2010, 19:08
общий
Верещака Андрей Павлович:
Тогда все правильно. Обошлось без раскрытия неопределенностей.
Тогда все правильно. Обошлось без раскрытия неопределенностей.
Неизвестный
01.02.2010, 19:53
общий
скажите пожалуйста а почему (0-1+cos0)*(sin0/2) оказалось в знаменателе?
Неизвестный
01.02.2010, 20:02
общий
скажите пожалуйста а почему (0-1+cos0)*(sin0/2) оказалось в знаменателе?
Не в знаменателе, а в числителе. Как положено.
01.02.2010, 20:12
общий
Верещака Андрей Павлович:
По правилам арифметических действий
a/b*c=(a/b)*c=(a*c)/b
По правилам арифметических действий
a/b*c=(a/b)*c=(a*c)/b
01.02.2010, 20:14
общий
Верещака Андрей Павлович:
Советую все же повнимательнее посмотреть условие задачи. Скорее всего там опечатка.
Советую все же повнимательнее посмотреть условие задачи. Скорее всего там опечатка.
02.02.2010, 14:13
общий
Быстров Сергей Владимирович:
Опечатка скорее всего в другом: вместо (e^(3)-1)^3 должно быть (e^(x)-1)^3
Это ж очевидно! Автор примера составил его так, чтобы было ноль в кубе делёное на ноль в кубе. Так что не будет тут никаких уловок -- надо раскрывать неопределённость и всё.
Опечатка скорее всего в другом: вместо (e^(3)-1)^3 должно быть (e^(x)-1)^3Это ж очевидно! Автор примера составил его так, чтобы было ноль в кубе делёное на ноль в кубе. Так что не будет тут никаких уловок -- надо раскрывать неопределённость и всё.
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