Задача 30662 ...

vk373959827

2018-10-30 21:29:39

lim_(x → ∞ ) ((1-x)/(2-x))^(3-x)

sova

2018-10-30 23:44:26

★

(1-x)/(2-x)=((2-x)-1)/(2-x)=(2-x)/(2-x) -(1/(2-x))=1+(1/(x-2)).

lim_(x→ ∞ )(1 + (1/(x-2)))^(x-2)=e

lim_(x→ ∞ )((1-x)/(2-x))^(3-x)=

=lim_(x→ ∞ )((1 + (1/(x-2)))^(x-2))^((3-x)/(2-x))=e^(lim_(x→ ∞ )(3-x)/(2-x))=e^(-1)
О т в е т. 1/e