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Консультация № 178015
24.04.2010, 20:01
0.00 руб.
0
4
1
Здравствуйте! Уважаемые эксперты помогите найти предел Lim [$8747$]c(x^n)d(x^n) при n стремящимся к [$8734$]
Обсуждение
25.04.2010, 08:04
общий
это ответ
Здравствуйте, Лиза Кошкина.
Полагаю, что дело обстоит следующим образом:
d(xn) = nxn – 1dx,
xnd(xn) = nxn + n – 1dx = nx2n – 1dx,
∫cxnd(xn) = c∫xnd(xn) = cn∫x2n - 1dx = cnx2n/(2n) = cx2n/2,
при n → ∞ ∫cxnd(xn) = cx2n/2 → cx∞/2 =
= 0, если |x| < 1,
= ∞, если |x| > 1,
= c/2, если |x| = 1.
С уважением.
Полагаю, что дело обстоит следующим образом:
d(xn) = nxn – 1dx,
xnd(xn) = nxn + n – 1dx = nx2n – 1dx,
∫cxnd(xn) = c∫xnd(xn) = cn∫x2n - 1dx = cnx2n/(2n) = cx2n/2,
при n → ∞ ∫cxnd(xn) = cx2n/2 → cx∞/2 =
= 0, если |x| < 1,
= ∞, если |x| > 1,
= c/2, если |x| = 1.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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