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Консультация № 200968
26.05.2021, 13:32
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Обсуждение
26.05.2021, 14:19
общий
это ответ
Здравствуйте, ushatalal!
Я предполагаю, что можно воспользоваться тем, что
Тогда
Я предполагаю, что можно воспользоваться тем, что
Тогда
Об авторе:
Facta loquuntur.
Facta loquuntur.
26.05.2021, 21:42
общий
это ответ
Проблемы (неопределенность вида 0/0) только с y. Поэтому воспользуемся правилом Лопиталя и продифференцируем числитель и знаменатель по y. Тогда при y, стремящемся к 0
lim [ tg (2*x*y)/(x2*y) ] = lim [ d/dy { tg (2*x*y)} /d/dy (x2*y) ] = lim [ 2*x/cos2(2*x*y )/x2 ] =lim [ 2/(x*cos2(2*x*y ) ],
который при х стремящемся к 1 и при y стремящемся к 0 равен 2/(1*cos2(2*1*0) = 2/(1*1) =2
ОТВЕТ: 2
lim [ tg (2*x*y)/(x2*y) ] = lim [ d/dy { tg (2*x*y)} /d/dy (x2*y) ] = lim [ 2*x/cos2(2*x*y )/x2 ] =lim [ 2/(x*cos2(2*x*y ) ],
который при х стремящемся к 1 и при y стремящемся к 0 равен 2/(1*cos2(2*1*0) = 2/(1*1) =2
ОТВЕТ: 2
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