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Консультация № 32400
29.12.2005, 20:23
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Доброе время суток, уважаемые эксперты.
Помогите, плиз, решить задачи по Матану. Горю, завтра зачет!!!
1) Найти все частичные пределы последовательности:
Xn = ( корень(n) / (5*корень(n) - 2) ) + cos (Pi*n / 5)
2) Привести примеры последовательностей Xn, Yn (n принадлежит N), таких, что
lim(Xn)=+бесконечность, n стремится к бесконечности,
lim(Yn)=+бесконечность, n стремится к бесконечности, а
а) lim(Xn - Yn) = 0, n стремится к бесконечности
б) lim(Xn - Yn) = бесконечность, n стремится к бесконечности
в) lim(Xn - Yn) = 24, n стремится к бесконечности
Помогите, плиз, решить задачи по Матану. Горю, завтра зачет!!!
1) Найти все частичные пределы последовательности:
Xn = ( корень(n) / (5*корень(n) - 2) ) + cos (Pi*n / 5)
2) Привести примеры последовательностей Xn, Yn (n принадлежит N), таких, что
lim(Xn)=+бесконечность, n стремится к бесконечности,
lim(Yn)=+бесконечность, n стремится к бесконечности, а
а) lim(Xn - Yn) = 0, n стремится к бесконечности
б) lim(Xn - Yn) = бесконечность, n стремится к бесконечности
в) lim(Xn - Yn) = 24, n стремится к бесконечности
Обсуждение
Неизвестный
30.12.2005, 11:33
общий
это ответ
Здравствуйте, Сажин Владимир Сергеевич!
1) что касается первого слагаемого, оно определено и стремиться к 1/5 для любых n, что касается cos, насколько я понимаю необходимо рассмотреть, например так
n делится на 10 - получим cos(2*pi*k)->1
n делится на 10 с остатком 1 cos(2*pi*(10*k+1)/10)= cos(2pi*k+pi/5)= cos(pi/5)
ну и т.д.
это первое, что пришло на ум, поэтому если есть более рациональное решение, то извините
2) а) Xn=корень(n+1) Yn = корень(n)
б) Xn=n Yn = корень(n)
в) Xn = n^2 +24 Yn = n^2
Так как матанализ был давно, не могу поручиться, что учла все, но вроде старалась не ошибиться. Будут вопросы, пишите по почте
Желаю удачи, с наступающим, надеюсь успела к зачету :)
1) что касается первого слагаемого, оно определено и стремиться к 1/5 для любых n, что касается cos, насколько я понимаю необходимо рассмотреть, например так
n делится на 10 - получим cos(2*pi*k)->1
n делится на 10 с остатком 1 cos(2*pi*(10*k+1)/10)= cos(2pi*k+pi/5)= cos(pi/5)
ну и т.д.
это первое, что пришло на ум, поэтому если есть более рациональное решение, то извините
2) а) Xn=корень(n+1) Yn = корень(n)
б) Xn=n Yn = корень(n)
в) Xn = n^2 +24 Yn = n^2
Так как матанализ был давно, не могу поручиться, что учла все, но вроде старалась не ошибиться. Будут вопросы, пишите по почте
Желаю удачи, с наступающим, надеюсь успела к зачету :)
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