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Консультация № 180335
16.10.2010, 17:46
44.86 руб.
16.10.2010, 17:54
0
3
1
Уважаемые эксперты, здравствуйте! нужна помощь в решении задачи. Заранее спасибо!
Обсуждение
.
Неизвестный
17.10.2010, 13:14
общий
это ответ
Здравствуйте, залесский женя!
На языке
(по Коши) число 
называется пределом функции в точке 
(т.е. при 
), если для любого положительного 
найдётся такое положительное 
, что для всех 
, удовлетворяющих неравенству 
, выполняется неравенство 
.
Таким образом, возьмём произвольное
и найдём такую зависимость 
, что для всех 
, удовлетворяющих неравенству 
, выполняется неравенство 
.
Для этого преобразуем выражение в левой части последнего неравенства следующим образом:
. Т.е. неравенство можно представить как 
, а это значит, что нам достаточно взять 
, чтобы для любого , удовлетворяющему неравенству 
, выполнялось неравенство . Что и требовалось доказать.
Теперь таблица.
[table][row][col][/col][col]0.1[/col][col]0.01[/col][col]0.001[/col][col]0.0001[/col][/row][row][col][/col][col]0.05[/col][col]0.005[/col][col]0.0005[/col][col]0.00005[/col][/row][/table]
Удачи Вам!
На языке
(по Коши) число называется пределом функции в точке (т.е. при ), если для любого положительного найдётся такое положительное , что для всех , удовлетворяющих неравенству , выполняется неравенство .Таким образом, возьмём произвольное
и найдём такую зависимость , что для всех , удовлетворяющих неравенству , выполняется неравенство .Для этого преобразуем выражение в левой части последнего неравенства следующим образом:
. Т.е. неравенство можно представить как , а это значит, что нам достаточно взять , чтобы для любого , удовлетворяющему неравенству , выполнялось неравенство . Что и требовалось доказать.Теперь таблица.
[table][row][col]
[/col][col]0.1[/col][col]0.01[/col][col]0.001[/col][col]0.0001[/col][/row][row][col][/col][col]0.05[/col][col]0.005[/col][col]0.0005[/col][col]0.00005[/col][/row][/table]Удачи Вам!
5
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