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emulik1996
@emulik1996
November 2021
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помогите плиииз срочно (( вычислите пределы функции
limx→∞(x/5+x)^x
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avilov41
Решение
lim(x/(5+x))^x=lim((5+x)/x)^(-x)=
=lim[(1+5/x)^(-x)=lim[(1+1/(x/5))^(x/5)^(-5)=e^(-5)
(везде x →∞)
Ответ: e^(-5).
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Answers & Comments
lim(x/(5+x))^x=lim((5+x)/x)^(-x)=
=lim[(1+5/x)^(-x)=lim[(1+1/(x/5))^(x/5)^(-5)=e^(-5)
(везде x →∞)
Ответ: e^(-5).