Question

Помогите найти границу​

Answer 1

$4) \ \underset{n\rightarrow \infty}{\lim} \dfrac{(\sqrt{n} + 1)^{2} - n}{\sqrt{n}} = \left(\dfrac{\infty}{\infty} \right) = \underset{n\rightarrow \infty}{\lim} \dfrac{n + 2\sqrt{n} + 1 - n}{\sqrt{n}} = \underset{n\rightarrow \infty}{\lim} \dfrac{2\sqrt{n} + 1}{\sqrt{n}} =\\ = \underset{n\rightarrow \infty}{\lim} \left(\dfrac{2\sqrt{n}}{\sqrt{n}} + \dfrac{1}{\sqrt{n}} \right) = \underset{n\rightarrow \infty}{\lim} \left(2 + \dfrac{1}{\sqrt{n}} \right) = 2 + \dfrac{1}{\infty} = 2 + 0 = 2$