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Консультация № 181571
23.12.2010, 11:58
55.00 руб.
0
5
2
Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Обсуждение
23.12.2010, 19:20
общий
Остается только применить правило Лопиталя 2 раза.
В числителе
->20-50=-30
В знаменателе 2
lim=-15
В числителе
->20-50=-30В знаменателе 2
lim=-15
23.12.2010, 21:46
общий
Здравствуйте! Если решать данный предел по правилу Лопиталя, полное решение будет иметь вид:
24.12.2010, 00:18
общий
Адресаты:
Почему опять не помещаете в ответ? Не уверены в правильности? 
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
24.12.2010, 09:19
общий
это ответ
Здравствуйте, Посетитель - 351942!
Если решать данный предел по правилу Лопиталя, полное решение будет иметь вид:
Если решать данный предел по правилу Лопиталя, полное решение будет иметь вид:
24.12.2010, 10:19
общий
это ответ
Здравствуйте, Посетитель - 351942!
Так как нахождение вторых производных сложно, попробуем разложить функцию в ряд Тейлора до второго члена.
-4+5e^2x=1+5(e^2x-1)=1+5[$8721$](2x)^n/n!=1+5(2x+2x^2+...)
(1+y)^(-1/5)=1-1/5y+3/25y^2+...=1-(2x+2x^2+...)+3(2x+2x^2+...)^2=1-2x-(2-12)x^2+...=1-2x+10x^2+o(x^2)
ln(1+x)=x-x^2/2+..
ln(1+5x)=5x-25/2x^2+..
1-2x+10x^2+10x-25x^2-1-8x+o(x^2)=-15x^2+o(x^2)
lim(-15x^2+o(x^2))/x^2=-15
Так как нахождение вторых производных сложно, попробуем разложить функцию в ряд Тейлора до второго члена.
-4+5e^2x=1+5(e^2x-1)=1+5[$8721$](2x)^n/n!=1+5(2x+2x^2+...)
(1+y)^(-1/5)=1-1/5y+3/25y^2+...=1-(2x+2x^2+...)+3(2x+2x^2+...)^2=1-2x-(2-12)x^2+...=1-2x+10x^2+o(x^2)
ln(1+x)=x-x^2/2+..
ln(1+5x)=5x-25/2x^2+..
1-2x+10x^2+10x-25x^2-1-8x+o(x^2)=-15x^2+o(x^2)
lim(-15x^2+o(x^2))/x^2=-15
Форма ответа
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