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Haiurre Lim _(xarrow Infty )(x^p)/(e^x) No Npassiny Jonwrana H OObACHHTE NonyqenHoe CpaBHeHKC : GecKOHe9HO 60JIbIIIHX.

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.