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Консультация № 67558
18.12.2006, 17:55
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Здравствуйте!!! Уважаемые Эксперты, прошу, пожалуйста, помогите решить это задание!
Найти пределы функции, заданных в:
1)lim при x-->8 (√(2x+9)-5) /( ^3√(x^2)-4)
2) lim при x-->0 (7^(3x) -3^(2x)) / (tgx+x)
3) lim при x-->0 (2-e^(x^2))^(1/ln(1+tg^(2) pi x/3)
4) lim при x-->0 (2^(2x) -1/x)^(x+1)
5) lim при x-->0 (2 tg^(2)x + 7sin^(3)x)/(4x^(2)-9x^(5)
Найти пределы функции, заданных в:
1)lim при x-->8 (√(2x+9)-5) /( ^3√(x^2)-4)
2) lim при x-->0 (7^(3x) -3^(2x)) / (tgx+x)
3) lim при x-->0 (2-e^(x^2))^(1/ln(1+tg^(2) pi x/3)
4) lim при x-->0 (2^(2x) -1/x)^(x+1)
5) lim при x-->0 (2 tg^(2)x + 7sin^(3)x)/(4x^(2)-9x^(5)
Обсуждение
Неизвестный
19.12.2006, 13:42
общий
это ответ
Здравствуйте, XDRIVE!
1)
lim(x->8) (√(2x+9)-5) /( ^3√(x^2)-4) = (Правило Лопиталя)
lim(x->8) (3*x^(4/3)/((2*x)*(2*x+9)^1/2)) =
=3*16/(16*5)=3/5
2)
(Правило Лопиталя)
lim(x->0) (7^(3x) -3^(2x)) / (tgx+x)
(7^(3x) -3^(2x))‘ = 3*7^(3x)*ln7 - 2*3^(2x)*ln3
(tgx+x)‘ = 1/cos^2 x + 1
при x->0 3*7^(3x)*ln7 - 2*3^(2x)*ln3 -> 3*ln7 - 2*ln3
1/cos^2 x + 1 -> 2
=> lim = 3*ln7/2 - ln3
3, 4, 5 - аналогично.
1)
lim(x->8) (√(2x+9)-5) /( ^3√(x^2)-4) = (Правило Лопиталя)
lim(x->8) (3*x^(4/3)/((2*x)*(2*x+9)^1/2)) =
=3*16/(16*5)=3/5
2)
(Правило Лопиталя)
lim(x->0) (7^(3x) -3^(2x)) / (tgx+x)
(7^(3x) -3^(2x))‘ = 3*7^(3x)*ln7 - 2*3^(2x)*ln3
(tgx+x)‘ = 1/cos^2 x + 1
при x->0 3*7^(3x)*ln7 - 2*3^(2x)*ln3 -> 3*ln7 - 2*ln3
1/cos^2 x + 1 -> 2
=> lim = 3*ln7/2 - ln3
3, 4, 5 - аналогично.
Форма ответа
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