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Консультация № 118519
15.01.2008, 05:32
0.00 руб.
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Уважаемые эксперты, помогите, пожалуйста, решить задачу:
lim ((К.кв. 9+2x)-5)/ (x^1/3 -2)
x->8
Спасибо за рассмотрение.
Приложение:
К.кв.-корень квадратныйx->8 - x стремится к восьми
lim ((К.кв. 9+2x)-5)/ (x^1/3 -2)
x->8
Спасибо за рассмотрение.
Приложение:
К.кв.-корень квадратныйx->8 - x стремится к восьми
Обсуждение
Неизвестный
15.01.2008, 20:29
общий
это ответ
Здравствуйте, Котова Даша!
Для решения используем <a href=http://elib.ispu.ru/library/math/sem1/kiselev1/node53.html>правило Лопиталя</a>:
lim<sub>x→8</sub>(√(9+2x) - 5)/(³√x - 2) = lim<sub>x→8</sub>(√(9+2x) - 5)‘/(³√x - 2)‘ =
= lim<sub>x→8</sub>(1/√(9+2x))/(1/(3x<sup>2/3</sup>)) = lim<sub>x→8</sub>3x<sup>2/3</sup>/√(9+2x) = 3·8<sup>2/3</sup>/√(9+2·8) = 3·4/5 = 2.4
Good Luck!!!
Для решения используем <a href=http://elib.ispu.ru/library/math/sem1/kiselev1/node53.html>правило Лопиталя</a>:
lim<sub>x→8</sub>(√(9+2x) - 5)/(³√x - 2) = lim<sub>x→8</sub>(√(9+2x) - 5)‘/(³√x - 2)‘ =
= lim<sub>x→8</sub>(1/√(9+2x))/(1/(3x<sup>2/3</sup>)) = lim<sub>x→8</sub>3x<sup>2/3</sup>/√(9+2x) = 3·8<sup>2/3</sup>/√(9+2·8) = 3·4/5 = 2.4
Good Luck!!!
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