3) $lim_{n \to +\infty}\frac{n-\sqrt{n^2+n\sqrt{n}}}{\sqrt{n+1}-\sqrt{n+2}}$$=lim_{n \to + \infty}(\sqrt{n^2+n\sqrt{n}}-n)(\sqrt{n+1}+\sqrt{n+2})$$=lim_{n \to +\infty}\frac{n\sqrt{n}}{\sqrt{n^2+n\sqrt{n}}+n}\left ( \sqrt{n+2}+\sqrt{n+1} \right )$$=lim_{n \to + \infty}(n.\frac{\sqrt{n+2}+\sqrt{n+1}}{\sqrt{n+\sqrt{n}}+\sqrt{n}})$$=lim_{n \to +\infty}(n.\frac{\sqrt{1+\frac{2}{n}}+\sqrt{1+\frac{1}{n}}}{\sqrt{1+\frac{1}{\sqrt{n}}}+1})$$\Rightarrow lim_{n \to +\infty}(...)=+ \infty$
3) $lim_{n \to +\infty}=\frac{n-\sqrt{n^2+n\sqrt{n}}}{\sqrt{n+1}-\sqrt{n+2}}$$=lim_{n \to + \infty}=(\sqrt{n^2+n\sqrt{n}}-n)(\sqrt{n+1}+\sqrt{n+2})$$=lim_{n \to +\infty}=\frac{n\sqrt{n}}{\sqrt{n^2+n\sqrt{n}}+n}\left ( \sqrt{n+2}+\sqrt{n+1} \right )$$=lim_{n \to + \infty}=n.\frac{\sqrt{n+2}+\sqrt{n+1}}{\sqrt{n+\sqrt{n}}+\sqrt{n}}$$=lim_{n \to +\infty}=n.\frac{\sqrt{1+\frac{2}{n}}+\sqrt{1+\frac{1}{n}}}{\sqrt{1+\frac{1}{\sqrt{n}}}+1}$$\Rightarrow lim_{n \to +\infty}=+ \infty$
3) $lim_{n \to +\infty}\frac{n-\sqrt{n^2+n\sqrt{n}}}{\sqrt{n+1}-\sqrt{n+2}}$$=lim_{n \to + \infty}(\sqrt{n^2+n\sqrt{n}}-n)(\sqrt{n+1}+\sqrt{n+2})$$=lim_{n \to +\infty}\frac{n\sqrt{n}}{\sqrt{n^2+n\sqrt{n}}+n}\left ( \sqrt{n+2}+\sqrt{n+1} \right )$$=lim_{n \to + \infty}
(n.\frac{\sqrt{n+2}+\sqrt{n+1}}{\sqrt{n+\sqrt{n}}+\sqrt{n}}
)$$=lim_{n \to +\infty}
(n.\frac{\sqrt{1+\frac{2}{n}}+\sqrt{1+\frac{1}{n}}}{\sqrt{1+\frac{1}{\sqrt{n}}}+1}
)$$\Rightarrow lim_{n \to +\infty}
(...)=+ \infty$