Question

Lim n→∞( (5n–1)/(2n+3)) -1) =

Answer 1

Ответ: приложено

Объяснение:

Answer 2

To find the limit of the expression as n approaches infinity, let's simplify it step by step:

lim n→∞ ((5n - 1)/(2n + 3) - 1)

First, let's simplify the fraction inside the limit:

= lim n→∞ ((5n - 1 - (2n + 3))/(2n + 3))

= lim n→∞ ((5n - 1 - 2n - 3)/(2n + 3))

= lim n→∞ ((3n - 4)/(2n + 3))

Next, let's divide both the numerator and denominator by n:

= lim n→∞ ((3 - (4/n))/(2 + 3/n))

As n approaches infinity, 4/n and 3/n both tend to 0. Therefore, we can simplify the limit further:

= (3 - 0)/(2 + 0)

= 3/2

Therefore, the limit of the expression as n approaches infinity is 3/2.