Вопрос
Haiurre lim _(xarrow infty )(x^p)/(e^x) no npassiny Jonwrana H OObACHHTE nonyqenHoe cpaBHeHKC : GecKOHe9HO 60JIbIIIHX.
Решения
4.4
(261 Голоса)
Кузьма
Экспертная проверка
мастер · Репетитор 5 лет
Ответ
To evaluate the limit
, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator, we get:
Applying L'Hôpital's Rule again, we get:
Continuing this process, we eventually get:
Since the denominator grows exponentially while the numerator is a constant, the limit is 0.