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Консультация № 72683
26.01.2007, 04:38
0.00 руб.
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2
2
Уважаемые эксперты, помогите в решении примеров по математическому анализу.
Я полностью забыл как решается!
найти пределы, непользуясь правилом лапиталя
lim(f) x->besk (4x^6-x^3+2x)/(2x^6-1)
x->-3 (√(x+10)-√(4-x))/2x^2-x-21
x->0 (cos(x)-cos^5(x))/x^2
x->besk (√(2-x)-√(x+6))/x^2-x-6
напишитие пожалуйста хотя бы по первому преобразованию к каждому примеру!
Заранее спасибо!!
Я полностью забыл как решается!
найти пределы, непользуясь правилом лапиталя
lim(f) x->besk (4x^6-x^3+2x)/(2x^6-1)
x->-3 (√(x+10)-√(4-x))/2x^2-x-21
x->0 (cos(x)-cos^5(x))/x^2
x->besk (√(2-x)-√(x+6))/x^2-x-6
напишитие пожалуйста хотя бы по первому преобразованию к каждому примеру!
Заранее спасибо!!
Обсуждение
Неизвестный
26.01.2007, 15:31
общий
это ответ
Здравствуйте, COMbat!
1) (4x^6 - x^3 + 2x)/(2x^6 - 1) = (4 - x^-3 + 2x^-5) / (2 - x^-6) -> 2. (при x->oo)
2) снизу (x+3)(2x-7), потом числитель и знаменатель умножаем и делим на
√(x+10)+√(4-x), сверху останется 2(x+3) и х+3 сократится и можно будет дальше просто подставить х=-3
3) сверху: cosx(1-cos^4(x)) = cosx *sin^2(x) * (1+cos^2(x)). Из замечательного предела sinx/x -> 1 получаем ответ cos0 * (1+cos^2(0)) = 2.
4) как решить этот номер не знаю.
1) (4x^6 - x^3 + 2x)/(2x^6 - 1) = (4 - x^-3 + 2x^-5) / (2 - x^-6) -> 2. (при x->oo)
2) снизу (x+3)(2x-7), потом числитель и знаменатель умножаем и делим на
√(x+10)+√(4-x), сверху останется 2(x+3) и х+3 сократится и можно будет дальше просто подставить х=-3
3) сверху: cosx(1-cos^4(x)) = cosx *sin^2(x) * (1+cos^2(x)). Из замечательного предела sinx/x -> 1 получаем ответ cos0 * (1+cos^2(0)) = 2.
4) как решить этот номер не знаю.
Неизвестный
27.01.2007, 12:12
общий
это ответ
Здравствуйте, COMbat!
Поскольку пример №4, не был решен - привожу его решение:
lim{x->∞} (√(2-x)-√(x+6))/(x^2-x-6)={домножаем числитель и знаменатель на √(2-x)+√(x+6)} =
=lim{x->∞} (2-x-x-6))/((x^2-x-6)(√(2-x)+√(x+6)))=
=lim{x->∞} -2/((x^2-x-6)(√(2-x)+√(x+6)))= -2/∞ = 0
Ответ:
lim{x->∞} (√(2-x)-√(x+6))/(x^2-x-6)=0.
Good Luck!!!
Поскольку пример №4, не был решен - привожу его решение:
lim{x->∞} (√(2-x)-√(x+6))/(x^2-x-6)={домножаем числитель и знаменатель на √(2-x)+√(x+6)} =
=lim{x->∞} (2-x-x-6))/((x^2-x-6)(√(2-x)+√(x+6)))=
=lim{x->∞} -2/((x^2-x-6)(√(2-x)+√(x+6)))= -2/∞ = 0
Ответ:
lim{x->∞} (√(2-x)-√(x+6))/(x^2-x-6)=0.
Good Luck!!!
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