Ответ:
Пошаговое объяснение:
(2х + 1)/(2х - 3) = (2х -3 +4)/(2х - 3) = (1 + 4/(2х - 3))
Сделаем замену 4/(2х - 3) = 1/у
2х -3 = 4у
x = 2y + 3/2
(1 + 1/y)^(2y + 3/2 - 1) = (1 + 1/y)^(2y + 1/2) = (1 + 1/y)^(2y) * (1 + 1/y)^(1/2) =
((1 + 1/y)^y)^2 * (1 + 1/y)^(1/2)
lim((1 + 1/y)^y)^2 * lim(1 + 1/y)^(1/2) = e^2 * 1 = e^2
y->∞ y->∞
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Ответ:
Пошаговое объяснение:
(2х + 1)/(2х - 3) = (2х -3 +4)/(2х - 3) = (1 + 4/(2х - 3))
Сделаем замену 4/(2х - 3) = 1/у
2х -3 = 4у
x = 2y + 3/2
(1 + 1/y)^(2y + 3/2 - 1) = (1 + 1/y)^(2y + 1/2) = (1 + 1/y)^(2y) * (1 + 1/y)^(1/2) =
((1 + 1/y)^y)^2 * (1 + 1/y)^(1/2)
lim((1 + 1/y)^y)^2 * lim(1 + 1/y)^(1/2) = e^2 * 1 = e^2
y->∞ y->∞