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Консультация № 175396
17.12.2009, 21:17
45.00 руб.
0
6
1
Здравствуйте,уважаемые эксперты!Помогите,пожалуйста,вычислить lim(x стремится к а) (2-(x/a)) в степени tg(пx/2a).Заранее благодарен.
Обсуждение
Неизвестный
17.12.2009, 22:10
общий
Тимофеев Алексей Валентинович:
lim(2-(x/a)) ^tg(пx/2a) = lim exp{tg(пx/2a)*ln(2-(x/a))} = exp{lim(ln(2-x/a)/ctg(пx/2a)}.
Последний предел легко вычисляется по правилу Лопиталя
lim(2-(x/a)) ^tg(пx/2a) = lim exp{tg(пx/2a)*ln(2-(x/a))} = exp{lim(ln(2-x/a)/ctg(пx/2a)}.
Последний предел легко вычисляется по правилу Лопиталя
18.12.2009, 11:04
общий
Ответ № 257868 от Nicolacha, 5-й класс
Здравствуйте, Тимофеев Алексей Валентинович.
i*l*m*(-(x-2*a)/a)^(sin(пи*x/(2*a))/cos(пи*x/(2*a)))*xa
Более подробней можете посмотреть в поисковой системе NIGMA.
Ответил: Nicolacha, 5-й класс
Дата отправки: 17.12.2009, 21:17
1)кому нужен голый ответ без решения?
2)вы его сами проверяли?
Судя по ответу lim=l*i*m 
18.12.2009, 21:11
общий
Химик CH:
У меня получился ответ е в степени 2/п,но не знаю,правильно это или нет.
У меня получился ответ е в степени 2/п,но не знаю,правильно это или нет.
21.12.2009, 17:15
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович.
Найдем логарифм выражения, предел которого нужно найти.
ln lim(2-(x/a)) ^tg(пx/2a) = lim tg(пx/2a)*ln(2-(x/a)= lim(ln(2-x/a)/ctg(пx/2a).
Этот предел можно найти по первому правилу Лопиталя.
lim(x[$8594$]a) ln(2-x/a)'=lim(-1/(2a-x))=-1/a
lim(x[$8594$]a) ctg(пx/2a)'=-п/2asin2(пx/2a)=-п/2a (x[$8594$]a)
-1/a : -п/2a=2/п
lim(x [$8594$]а) (2-(x/a))tg(пx/2a)=e2/п
Найдем логарифм выражения, предел которого нужно найти.
ln lim(2-(x/a)) ^tg(пx/2a) = lim tg(пx/2a)*ln(2-(x/a)= lim(ln(2-x/a)/ctg(пx/2a).
Этот предел можно найти по первому правилу Лопиталя.
lim(x[$8594$]a) ln(2-x/a)'=lim(-1/(2a-x))=-1/a
lim(x[$8594$]a) ctg(пx/2a)'=-п/2asin2(пx/2a)=-п/2a (x[$8594$]a)
-1/a : -п/2a=2/п
lim(x [$8594$]а) (2-(x/a))tg(пx/2a)=e2/п
5
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