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benrya
@benrya
July 2022
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Помогите пожалуйста решить предел :с
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srzontmp
Lim(x->∞)((x^-3)/(x^2-4))^(x^2+2) =
= lim(x->∞)(1+1/(x^2-4))^(x^2+2) замена переменной
y = x^2-4 при x -> ∞ y->∞
lim(y->∞)(1+1/y)^(y+6) = lim(y->∞)(1+1/y)^6*lim(y->∞)
(1+1/y)^y = 1^6*lim(y->∞)(1+1/y)^y = 1*e =2,718281828..
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benrya
ОЙ, СПАСИБО ОГРОМНОЕ)
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Answers & Comments
= lim(x->∞)(1+1/(x^2-4))^(x^2+2) замена переменной
y = x^2-4 при x -> ∞ y->∞
lim(y->∞)(1+1/y)^(y+6) = lim(y->∞)(1+1/y)^6*lim(y->∞)
(1+1/y)^y = 1^6*lim(y->∞)(1+1/y)^y = 1*e =2,718281828..