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Консультация № 187273
12.04.2013, 13:34
98.13 руб.
0
4
4
Здравствуйте! Прошу помощи в следующем вопросе:
Желательно с подробным решением. Заранее ОГРОМНОЕ СПАСИБО! 
Обсуждение
12.04.2013, 15:02
общий
это ответ
Здравствуйте, Алекс!
3.
.
Легко видеть, что это неопределённость вида
.
Слева всё дифференцируемо. Вот и продифференцируем числитель и знаменатель.
.
Знаменатель дифференцируем в окрестности нуля. Поищем предел выражения, при стремлении x к 0.
.
А значит и искомое выражение стремится к 0.
3.
.Легко видеть, что это неопределённость вида
.Слева всё дифференцируемо. Вот и продифференцируем числитель и знаменатель.
.Знаменатель дифференцируем в окрестности нуля. Поищем предел выражения, при стремлении x к 0.
.А значит и искомое выражение стремится к 0.
12.04.2013, 18:49
общий
это ответ
Здравствуйте, Алекс!
5. Неопределенность вида 1[$8734$]. Логарифмированием она сводится к неопределенности вида 0/0, которую можно раскрыть по правилу Лопиталя. Пусть
f(x)=(2x+1)^(th(2x))-1/6
g(x)=ln f(x)=ln(2x+1)/6th(2x)
limg(x)=lim(2/(2x+1))/(12/ch2(2x))=lim ch2(2x)/[6(2x+1)]=1/6
Следовательно,
lim f(x)=e^(lim g(x))=e^(1/6)
5. Неопределенность вида 1[$8734$]. Логарифмированием она сводится к неопределенности вида 0/0, которую можно раскрыть по правилу Лопиталя. Пусть
f(x)=(2x+1)^(th(2x))-1/6
g(x)=ln f(x)=ln(2x+1)/6th(2x)
limg(x)=lim(2/(2x+1))/(12/ch2(2x))=lim ch2(2x)/[6(2x+1)]=1/6
Следовательно,
lim f(x)=e^(lim g(x))=e^(1/6)
5
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